LHC Physics April 20-24, 2009

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SCHOOLOF PARTICLESAND ACCELERATORS INSTITUTEFOR RESEARCHIN FUNDAMENTAL SCIENCES (IPM)

First IPM meeting on LHC Physics April 20-24, 2009

Edited by

A. Moshaii Tarbiat Modares University and Institute for Research in Fundamental Sciences (IPM)

S. Paktinat Mehdiabadi Institute for Research in Fundamental Sciences (IPM)

A. Khorramian Semnan University and Institute for Research in Fundamental Sciences (IPM)

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First IPM meeting on LHC Physics, April 20-24, 2009

was organized by School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM)

and sponsored by Main Sponser: IPM Other Sponsers: CERN(CMS) Center of Excellence in Physics (CEP), Physics Department, Sharif University of Technology

International Advisory Board F. Ardalan (Sharif University of Technology and IPM) M. Baarmand (Florida Institute of Technology) D. Denegri (Saclay, CERN) J. Ellis (CERN) L. Pape (ETH Zurich, CERN) M. Spiropulu (CERN) T. Virdee (Imperial College, CERN)

Organizing Committee H. Arfaei (Sharif University of Technology and IPM) A. Khorramian (Semnan University and IPM) M. Mohammadi Najafabadi (IPM) A. Moshaii (Tarbiat Modares University and IPM) S. Paktinat Mehdiabadi (IPM) S. Rouhani (Sharif University of Technology and IPM)

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Contents

Preface ...... XI

1 Top quark mass measurement from highly boosted jets at LHC I. Ahmed ...... 1

2 Mercury Electric Dipole Moment in the Presence of MSSM Flavored Changing Sources S. Y. Ayazi ...... 17

3 A data driven method to measure electron charge mis-identiﬁcation rate H. Bakhshian, L. Pape, F. Moortgat ...... 25

4 Experimental aspects of neutrino oscillation physics D. Duchesneau ...... 33

5 Search for mSUGRA in µs + Jets + E6 T Final State in CMS A. Fahim, F. Moortgat, L. Pape...... 47

+ − 6 Investigation of the Ds1 structure via Bc to Ds1l l /νν¯ transitions in QCD M. Ghanaatian, R. Khosravi ...... 57

7 Quark-Gluon Plasma Model and Origin of Magic Numbers M. Ghanaatian, N.Ghahramany ...... 63

8 Review of RHIC results R. Granier de Cassagnac ...... 67

9 Measurement of top-quark pair-production with 10 pb-1 of CMS data A. Jafari ...... 79

10 Hadron and Very-Forward Calorimetry in CMS M. Kaya ...... 85

11 Non-singlet QCD analysis of structure function based on associated Jacobi polynomials A. Khorramian, H. Khanpour, S. Atashbar Tehrani ...... 95

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VIII Contents

12 A Phenomenological Analysis of the Longitudinal Heavy Quark Struc- ture Function A. Khorramian, S. Atashbar Tehrani ...... 101

13 Simulation of Resistive Plate Chamber Based on Transport Equa- tions L. Khosravi-Khorashad, M. Eskandari, A. Moshaii ...... 107

14 Silicon Sensors: From basic principles to the largest Silicon detector M. Krammer ...... 117

15 The LHC Grid Challenge F. Malek ...... 127

16 Overview of the Muon System of CMS S. Marcellini ...... 135

17 Target mass correction and its effect in polarized deep inelastic scattering A. Mirjalili, H. Mahdizadeh Saffar ...... 141

18 Single Top Production at the LHC with CMS Detector M. Mohammadi Najafabadi ...... 147

19 Constraints on the Masses of Fourth Generation Quarks M. Mohammadi Najafabadi, S. Hosseini, Y. Radkhorrami ...... 151

20 Study of Top Quark FCNC using Top and Charm Quarks electric dipole moments M. Mohammadi Najafabadi, N. Tazik...... 157

21 Progress in Experimental Activities on RPC Detector in Iran A. Moshaii, K. Kaviani, M. Eskandari, L. Khosravi-Khorashad ...... 163

22 Search for SUSY in CMS S. Paktinat Mehdiabadi ...... 171

23 Two constraints kinematic ﬁt and top quark extraction S. Paktinat Mehdiabadi, A. Mirjalili, S. A. Moosavy ...... 177

24 CMS commissioning with cosmic muon data G. Pugliese...... 183

25 QCD Physics Potential of CMS K. Rabbertz ...... 193

26 Study of the Top Quark Anomalous Wtb couplings using the Top Electric Dipole moments N. Roodi...... 205

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Contents IX

27 Searching for purely hadronic top decays from SUSY B. Safarzadeh, S. Paktinat Mehdiabadi ...... 209

28 Search for Supersymmetry in Top Final States at CMS N. Salimi, S. Paktinat Mehdiabadi ...... 215

NS 29 g1 in the valon model F. Taghavi-Shahri, F. Arash, N. Javadi Mottaghi ...... 221

30 The study of the Diffractive Parton Distribution Functions S.Taheri Monfared, A. Khorramian, S. Atashbar, F. Arbabifar, S. Tizchang ... 225

31 Electron and photon reconstruction in the CMS experiment at the LHC P. Vanlaer ...... 231

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Preface

The first IPM meeting on LHC physics was held in the historic city of Isfahan from April 20th to 24th 2009. It was the first meeting on High Energy Experimen- tal Physics in Iran. It was organized and was basically supported financially by the School of Particles and Accelerators of IPM. It marked an important event in the development of physics in our science community; our active and systematic entrance in High Energy Experimental Physics. It also acted as the inauguration of the School of Particles and Accelerators. The meeting covered a wide spectrum of topics of particle physics, especially the physics in LHC. It included reviews and expository lectures by leading physicists of the field as well as seminars on research results by young scientists. The par- ticipation by Iranian young scientists, in particular the experimentalists and phe- nomenologists was substantial. Lectures on topics outside of Particle Physics was organized, e.g. recent developments in observational Astrophysics by Y. Giraud- Hraud. There were about 60 participants, almost half from Iran and half from the rest of the world. Thirty seven talks were delivered, the morning sessions were devoted to reviews and afternoon sessions to recent research results. IPM has tried to establish this field in the country following the agreement between Iran and CMS and signing the MoU to collaborate. This meeting could not take place without the help of our colleagues at CERN in particular Daniel Denegri. He was with us and maybe ahead of us in all stages of the meeting, from the conception of its idea to even the daily schedules of the talks. As a matter of fact his support in our scientific work at cern has been of great effect and value for all of us. On behalf of IPM and the organizers I find this occasion an opportunity to thank him for his help and support. I also want to use the occasion to thank those whose support and help during the past eight years have been instrumental in making our activities possible, Farhad Ardalan, Marc Baarmand, Reza Mansouri, Tiziano Camporesi, Michel Della Negra, Jim Virdee, Galileo Violini, Nural Akchurin. Special thanks are due to Luciano Maiani and John Ellis whose vision and support were essential in the formation of the IPM activities at CERN. The support by CERN and CMS organization in various ways, is gratefully acknowledged. The secretarial team of the meeting has been behind the smooth running of the event, so I would like to extend our appreciation to Mses. A. Arfaee, N. Barati, Z. Ghasemnezhad, H. Alizadeh, N. Nayyeri, P. Kianfar, K. Aspola and Messrs. Aaslanparviz and I. Bagheri. We hope that this meeting will continue and establish a regular event concerning Experimental Particle Physics not only in Iran but also will grow to be a regional activity. I would also like to thank the colleagues in the advisory committee and the local executive committee without whose effort this gathering would not materialize.

Hessamaddin Arfaei, Chairman of the School of Particles and Accelerators

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School of Particles and Accelerators FIRST IPM MEETING Institute for Research in ON LHCPHYSICS Fundamental Sciences (IPM) VOL. 1, NO. 1 (p. 1) Isfahan, April 20-24, 2009

1 Top quark mass measurement from highly boosted jets at LHC

I. Ahmed

National Centre for Physics, Islamabad, Pakistan

Abstract. In this note an alternative method has been introduced for the top mass estimation in the single lepton plus jets tt¯ → bbq¯ qlν¯ (l = µ) channel using high PT top anti-top pairs where the top and anti-top quark have a transverse momentum above 200 GeV/c. The basic idea is to reconstruct the invariant mass of all calorimeter clusters in a cone around the top quark ﬂight direction and the calorimters clusters invariant mass which is correlated to the real top mass.

1.1 Introduction

The top quark is the only known fundamental particle with a large mass close to the electro-weak symmetry breaking scale. As a result a detailed study of top quark may provide hints of new physics. According to the Standard Model, top quark is a spin 1/2 and charge 2/3 fermion, which transforms as a color triplet under the group SU(3) of the strong interactions and as the weak isospin partner of the bottom quark.

At LHC the top quark will be produced mainly in top anti-top pairs through the strong interactions via gg → tt¯ (90 % of the total cross-section) and qq¯ → tt¯ (remaining 10 percent of the cross-section) through the following tree level Feyn- man diagrams shown in Fig. 1.1. The next-to-leading order cross-section prediction for tt¯ production is σ(tt¯) = 833 pb [1]. Thus the LHC will be a top factory as more than 8 million tt¯ pairs will be produced per year at low luminosity 1033cm−2s−1, which corresponds to an integrated luminosity of 10 fb−1.

The top quark decays almost exclusively into a W boson and a b-quark within the standard model, while the ﬁnal state topology depends on the W bosons decay modes. The W boson decay has a leptonic branching ratio of BR(W → lν = 1/3) and a hadronic branching ratio with BR(W → qq¯ = 2/3). The large top decay −25 rate implies a very short lifetime of τtop = 1/Γtop = 4×10 s which is relatively −24 smaller than the time taken to form hadronic state τhad = 1/λqcd = 2 × 10 s. In other words top quarks decay before they can couple hadronically to light quarks and form hadrons. Since the top quark mass in combination with the W boson mass allows us to test the Standard Model and to set constraints on the mass of higgs boson. The higgs boson, the W boson and the top quark contribute

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g q q g q g

g q q q

g g q q

q q q

g q g

Fig. 1.1. Feynman diagrams for top anti-top pair production at LHC

via radiative corrections.

The best measurement of the top quark mass is achieved in the tt¯ lepton plus jets channel, since it features a relatively high number of signal candidates, moderate background levels and allows for a full reconstruction of top quark momenta with reasonable accuracy. The signatures of the tt¯ lepton plus jets channel comprises a high PT electron or muon, missing transverse energy and four jets. The branching fraction of this channel is about 29 % corresponds to the 2.5 million semi-leptonic events, which is one of the advantages over the dileptonic channel. However, W+multijets background is large and require certain techniques and strategies to improve signal to background ratio. We will focus on the method where the isolated muons are used to tag the event and the value of mtop is extracted as the invariant mass of the three jet systems arising from the hadronic top quark decay.

The study of high PT top events was actually started by ATLAS top quark working group [2], whose aim was to produce the top anti-top pairs with sufﬁ- cient high transverse momentum almost above 200 GeV, due to which tops have decay angles very close to the top ﬂight direction and therefore the mass of the calorimetric objects (clusters, cells, seeds) in a large cone around top direction is correlated with the real top mass. Having higher top boost, the opening angle between W and b from top decay are expected to be much smaller. Therefore the jet cone is reconstructed with a very narrow cone size equal to 0.3. One could calculate the mass of the objects which are in a larger cone around top quark direction.

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1 Top quark mass measurement from highly boosted jets at LHC 3

For this reason top quark needs to have a larger PT (> 200) GeV. Hence one needs to make an event selection in such a way, which is selecting those events with a high S/B ratio.

1.2 Event Generation and Detector Simulation

At the generator level top pair preselection is done by applying hard PT cut on top anti-top pairs in the center of mass of the hard scattering system with PT > 200 GeV and |η| < 3.0. Additionally one of the Ws from the top quark decay is forced µ µ to decay leptonically t → bW → bµν, with PT > 20 GeV and |η | < 2.0, while the second W is allowed to decay hadronically t → bW → bqq¯ (q = u, d), (q¯ = c, s). In addition the partonic level quarks are required to have PT > 20 GeV and |η| < 2.5. This preselection topology gives rise to the cross-section by Pythia that is equivalent to 6.85 pb selected out of 492 pb (LO Pythia) per lepton ﬂavor, which corresponds to more than 1% of the total tt¯ cross-section at leading order.

The tt¯ lepton plus jets events can be selected using signatures such as two high PT central light non b-tagged jets from W → qq¯ , two b-tagged jets, missing Et and a charged lepton (muon) from W → l+ν decay. This study is done using a full GEANT [3] simulation of the CMS calorimeter combined with a parametrized b-tagging algorithm. The expected statistics for 7.23 fb−1 integrated luminosity is roughly 9214 signal events after event selection in leading jets reconstruction scheme, but without including the W mass window cut.

The data samples which are used, are generated by a PYTHIA-130 event generator [4]. While for the reconstruction, a framework for CMS fast detector simulation FAMOS-140 [5] of the particles interactions is used. Furthermore another study has been done at the parton level with jets and lepton momenta smeared to take into account the CMS detector performance. The purpose of this study is to ﬁnd the optimal selection criteria for the tt¯ semi- leptonic high PT top production, which suppresses the backgrounds to a negligible level. For this study a fast detector simulation is used with the speciﬁc trigger requirements and pile-up (minbias events) are taken into account. The pile-up events are included in the signal events. A further study with full CMS detector simulation needs to be done later.

1.3 Particle distributions at partonic level

It is essential to ﬁrst observe the distinct features of a high PT sample at the parton level. The average PT of the top (and W) is observed around 286 GeV (and 170 GeV). The mean values conﬁrm that the jets are produced with a high boost in the hadronic top hemisphere. The main goal is to reconstruct the top quark mass

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Table 1.1. Overview of number of the events simulated with fast detector simulation, their corresponding cross-section and integrated luminosity.

number of events int-luminosity cross-section with pile-up fb−1 pb tt¯ → bWbW → bqqbµν¯ 49535 7.23 6.85

from the invariant mass of calorimeter clusters which includes the combined jets, with their overlap in space, including all energy deposition around top quark direction. To determine the appropriate size of the cone around the top direction it is important to know about the spatial distance of the three quarks resulting from the hadronic top decay; two partonic light jets from W and one associated b-jet. In Fig. 1.2, the top and the corresponding b-quark and W boson distances are shown. The mean values should be lower, which are expecting due to the high PT boost of the top, with an average separation of 0.8 and 0.4 respectively.

Mean 0.8079 Mean 0.3984 1000 RMS 0.6637 RMS 0.2121 700

600 number of events 800 number of events

500

600 400

400 300

200 200 100

0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 MC ∆ R(top,b-par) MC ∆ R(top,W)

Fig. 1.2. ∆R distance between the generated top quark and the b-quark at the parton level (left), and the ∆R distance between the top quark and the W-boson at the partonic level (right)

The ∆R distance between two hadronic quarks is shown in Fig. 1.3, which clearly indicates that most of the events lie below 1.3-1.4, which means that energy sharing between the jets will be taken into account later on during the reconstruction procedure. This is the reason we are reconstructing the jets with a cone size of 0.3 forp low luminosity. The ∆R = ∆η2 + ∆φ2 distance between the closest and furthest quarks from the top axis have been shown in Fig. 1.4, from which it is estimated that the ma- jority of the events lie less than 1.2 parton jet cone sizes apart.

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1 Top quark mass measurement from highly boosted jets at LHC 5

Mean 1.38 Mean 169.6 900 450 RMS 0.7437 RMS 80.12

800 400

number of events 700 350 number of events/3 GeV 600 300

500 250

400 200

300 150

200 100

100 50

0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 0 50 100 150 200 250 300 350 400 MC ∆R(q,qbar) W Pt

Fig. 1.3. ∆R distance between two quarks from hadronic W-boson decay (left),partonic W- boson transverse momentum distribution

1000 Mean 0.4144 Mean 1.194 800 RMS 0.2616 RMS 0.7176

700 800 number of events number of events 600

600 500

400

400 300

200 200

100

0 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.5 1 1.5 2 2.5 3 3.5 4 ∆ MC R(top,minW-quarks) MC ∆ R(top,maxW-quarks)

Fig. 1.4. Left plot shows the ∆R distribution between top quark and the closest quark from the hadronic top quark decay mode. The right-hand plot represents the ∆R distribution between the top quark and the furthest quark from the same hadronic top quark decay

1.3.1 Muons reconstruction and isolation

The muons are reconstructed and identiﬁed in this analysis using GlobalMuonRe- constructor method in FAMOS, which uses the global information from the muon system of CMS. In this note W → eν is not considered. All those global muons should be considered as isolated muons, provided the ratio of the sum of all the transverse momentum of tracks from the tracker (silicon + pixel) except muon itself to the transverse momentum of the reconstructed global muon is less than 5%, within the cone size of ∆R < 0.2 and ∆R > 0.01 around the reconstructed global muon. The minimum PT requirement for the isolated muon to be considered a good muon used in this analysis is above 30 GeV and the absolute pseudorapidity should be less than 2, which is used at pre-selection level. Our study shows that most of the events contain one isolated muon, while efﬁ- ciency of our PT and η cuts to select a good isolated muon is more than 92%. The

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PT and η spectra of isolated muons are shown in Fig. 1.6.

Mean 0.6568 3000 RMS 1.176

2500

number of events 2000

1500

1000

500

0 -3 -2 -1 0 1 2 3 4 combined b-tag (logrithmic scale)

Fig. 1.5. The distribution of the combined b-tag discriminator based on inclusive secondary vertex reconstruction in jets

1.3.2 Jets reconstruction and identiﬁcation

In order to fully reconstruct the single-leptonic tt¯, it is crucial to apply jet algorithms to segregate the b-tagged jets from light jets. The jets are reconstructed by applying the iterative cone algorithm with ∆R = 0.3. Due to the fact that we are not using standard cone size, the clustering in EcalPlusHcalTowers is done without using the default calibration method. The Et scheme is used for recombination due to the uncalibrated jets. For the identiﬁcation of b-jets from other non b- tagged jets, the secondary displaced vertex based CombinedBTagging algorigthm is used [6]. The main signatures in tt¯ → bbµνq¯ q¯ are the presence of high PT b-jets from top decay. The tagging of b-jets is an important tool used to select top quark events to suppress background. The logarithm b-tag discriminant distribution is shown in Fig. 1.5. The b-tag discriminant variable is used above 1.0 (b-tagging efﬁciency gives 60%) for jets to be tagged as b-jets, while less than 1.0 for jets which are tagged as non b-jets. The jet multiplicity and the global muons multiplicity which are used to identify the isolated muons are shown in Fig. 1.6 and Fig. 1.7.

1.3.3 Top mass selection using leading jets

In the leading jets selection method, the selection cuts required on isolated muon is same is mentioned before.and |η| < 2.0. The plane perpendicular to the direction of the isolated muon is used to divide the detector into two hemispheres. The b-jet belonging to the hadronically decaying top is expected to be found in the hemisphere opposite to the lepton. Considering only jets with PT > 20 GeV and

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1 Top quark mass measurement from highly boosted jets at LHC 7

12000 Entries 49535 Entries 49535 35000 Mean 5.771 Mean 1.316

RMS 1.881 RMS 0.5497 10000 30000 number of events number of events 25000 8000

20000 6000 15000

4000 10000

2000 5000

0 0 0 2 4 6 8 10 12 14 16 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Jet Multiplicity Global Muon Multiplicity

Fig. 1.6. Jet multiplicity and the global muons multiplicity distributions are shown

Fig. 1.7. This plot shows the PT spectrum and the η distribution of the reconstructed isolated muon in the leading jets scheme

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|η| < 2.5, the cuts require at least 2 b-tagged jets. The number of events is reduced by a factor of 3 with 2 b-tagged jets, as compared to the 1 b-tagged requirement. Of the two highest pT b-jets, the one with the largest angle to the lepton is considered to be the one from the hadronically decaying top. The two highest pT non b-tagged jets are chosen as the di-jet candidates for the W → jj decay. A Gaussian ﬁt is applied on the reconstructed W mass distribution from uncalibrated di-jet system, for those events in which both of jets are matched within a cone 0.4 with the quarks from the W → jj decay in the Monte Carlo truth information. The ﬁt- ted mean value is 65.24 GeV, which is used as the nominal reference mass value around which the W mass window cut of |mjj − mnominal| < 20 GeV is implemented in all the plots.

For events passing this cut, the di-jet pair is then combined with the b-tagged jet furthest away from the lepton to form the t → jjb candidate. With all these cuts the overall efficiency is 8.5%. Backgrounds other than tt¯ are reduced to a negligible level. The invariant mass distribution of the accepted jjb combinations is shown in Fig. 1.8, while a breakdown of the event’s selection efficiency with different kinematical cuts is shown in Table 1.2. For jet-to-parton matching angle in case of two quarks we use 0.4 whereas for the case of single quark we use 0.2. The fraction of selected events in which the W boson is correctly reconstructed from the light jets is about 42.7% whereas for one quark matching is 18.17%. To optimize the PT selection cut on the jets different values were tried, raising the jet pT cut at 25 and 30 GeV. After all the kinematical cuts this resulting efficiencies are equal to 5.3% and 4% respectively. It is observed that the softer PT cut on the jets give nicer distributions with more events and a sharp peak.

Table 1.2. events selection topology of leading jets selection and measurements of W-boson and top mass

kinematical cuts Selection efﬁciency % no. of events before selection 100 49535 no. of iso. muons 93.6 46370

≥ 1 iso. muon PT > 30 GeV 92.7 45920 ≥ 1 reco. light jets PT > 20 GeV 91.1 45117 ≥ 2 light jets |η| < 2.5 73.6 36484

≥ 1 no. of b-jets PT > 20 GeV 55.6 27543 ≥ 2 b-jets |η| < 2.5 18.6 9214

|mjj − mW | < 20 8.5 4235

1.4 Top mass reconstruction from large calorimeter clusters

Once high PT top quark candidate has been selected, jets associated with it are close to each other in space and it is no longer required that a b-jet is tagged.

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Fig. 1.8. The reconstructed top mjjb invariant mass distribution from the t → jjb uncalibrated jets in the high PT leading jets selection is shown

The invariant mass of t → bjj is reconstructed using two light jets with high PT and one b-jet. Once the invariant mass of top candidate is known one can also determine its direction of flight. Using this direction of flight of top we have ∆R(top, clus) for all the clusters. The variable ∆R is shown in Fig. 1.9. From this figure clearly one can see the large cone mean value from first peak as a big bump at lower values, implies at low distance. While the second peek which lies around 3.14 value, predicts the region where both jets decay back to back. This technique is particularly useful in reducing system errors arising due to jet calibration. It is also useful to avoid the intrinsic complexities of effects due to energy leakage outside a narrow cone. In this analysis we have used several cone sizes for optimizing the value of reconstructed top quark mass around its experimentally 4.1 measured value of mt = 173.54.0GeV [7]. This method is not based on any particular model, but strongly dependent on the detector (calorimeters) bevaviour. The selected jjb combinations are required to have PT > 200 GeV. With this selection criteria, one gets only 2% of the total event. The direction of the top quark is determined from the jet momenta. and azimuthal angle space between the reconstructed top direction and the true direction at the parton level, demonstrating a nice agreement between the measured direction and the true direction.

1.4.1 Identiﬁcation of calorimetric Layers

In order to add the calorimeter clusters from different selected cones, calorimeter is subdivided into three calorimeter layers. The partitions of the calorimeters are performed on the basis of r (radial) and Z (longitudinal) coordinates in CMS. The layer 1 in (r, Z) space corresponds to the values (r < 170 cm, |Z| < 350 cm), while layer 2 corresponds to (r < 300 cm, |Z| < 350 cm). The least energetic clusters be- long to the layer l, which is called Electro-magnetic Calorimeter (ECAL), shows electronic noise contribution among the clusters related to high PT cone. On the

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Fig. 1.9. Angular distance ∆R with respect to the reconstructed top ﬂight direction for all clusters in the calorimeter.

other hand layer 2 is characterized as Hadronic Calorimeter (HCAL). The energy of clusters is summed separately for two layers. The reconstructed clusters transverse energy of each layer as a function of clusters coverage in the detector is shown in Fig. 1.10. A large cone is drawn around the top quark direction. The top mass is deter-

Fig. 1.10. The clusters transverse energy as a function of pseudorapidity of clusters

mined by adding the energies of all calorimeter clusters (cells) in this cone, (a calorimeter cell has a size of (∆η × ∆φ = 0.0175 × 0.0175), while one calorimeter tower has size of ∆η × ∆φ = 0.087 × 0.087). The effective invariant mass of all the

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1 Top quark mass measurement from highly boosted jets at LHC 11

clusters inside a big cone is calculated according to the following formula:

n∆RX n∆RX 2 2 2 2 mjj = (E − P¯ ) = ( Ei) − ( P¯ i) (1.1) i=1 i=1 where the sum runs over all reconstructed clusters with energy above a certain threshold (100 MeV) inside the cone. In our analysis, we assume all clusters to be massless, which implies that

m ≈ 0 (1.2)

E2 = p¯ 2 (1.3)

Px = E(sinθ)(cosφ) (1.4)

Py = E(sinθ)(sinφ) (1.5)

Pz = E(cosθ) (1.6) top After adding energy of all the clusters the invariant mass Mclus spectrum is obtained, shown in Fig. 1.11 for different cone sizes which exhibits a clean peak at the ∆R = 1.3. The reconstructed top mass from clusters after Gaussian fit for each cone size, show a strong dependence on the cone size. The Fig. 1.12 shows the number of clusters corresponding to each cone size for all events. Figure 1.13 top clearly shows, how number of clusters depend on Mclus. This behavior is at- tributed to the effects of the underlying event (UE) from the multiple interaction (MUI) among partons of the colliding pairs of protons. A small contribution may rise from the minbias events (pileup) or the readout electronic noise, which add top clus more energy during the Mclus reconstruction. Figure 1.14 represents the ET values scanned wth fixing cone size at different η regions. Two peaks can be seen clearly in the small η regions, so due to the small number of clusters the peak at clus low ET is referred to the ECAL relevant clusters and the more energetic clusters belongs to the HCAL. Additional effects may come from the initial and final state radiation (ISR/FSR). In the absence of the underlying event and for cone sizes which are sufficiently large to contain all three jets from the hadronic top decay, the fitted mass should be independent of the cone size. Therefore a method has been developed to estimate and subtract this contribution from the underlying event by using the calorimeter clusters, which are not associated with the high PT top products. The more detail about the estimation of underlying event energy is described in the next section.

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12 I. Ahmed

top Fig. 1.11. The strong dependence of mclus on ∆R(top, clus) is shown with gaussian ﬁt. This dependence demonstrates the underlying event contribution in each cone.

1.5 Estimation of Underlying event Contribution

Everything except the higher order process of interest are called Underlying Event (UE), while process with low transverse energy and with low multiplicity are called pileup or minbias events. In this particular case the pileup and electronic noise contribution is usually negligible as compared to the UE contribution, because of the presence of energetic jets in the event due to high PT cut. The UE contribution per calorimeter cluster has been estimated from the same high PT top sample using the reconstructed calorimeter hits. It represents the average transverse energy ET deposited per calorimeter cluster per event, once all the clusters relevant to the high PT products are excluded. The method which we have adopted to estimate UE proportion in each cluster’s transverse energy, is as follows: Calorimeter clusters which are far away from jets are used for UE estimation. We deﬁne jet isolation variable min∆R as the closest distance between a cluster and a jet. This variable is used for scanning jet isolation for all clusters in the calorimeter as shown in Fig. 1.12. For the purpose of summation of clusters transverse energy, we have subdivided calorimeter into 2 main layers whose ET distributions are shown separately in Fig. 1.10. The ﬁrst layer represents Electro-magnetic Calorimeter (ECAL) and 2nd layer represents the Hadronic Calorimeter (HCAL). We have estimated UE contribution on layer by layer. The minimum ∆R(jets, clus), indicates the jet isolation cut for calorimeter clusters. The estimated mean ET for isolated clusters and mean number of clusters obtained in each case are shown in Table 1.3 for layer 1 and similarly for Table 1.4

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1 Top quark mass measurement from highly boosted jets at LHC 13

Fig. 1.12. The jet isolation cone distribution is shown

Table 1.3. Underlying event estimation method for Layer 1 (ECAL)

< ET >/cluster MeV (ﬁrst row) < Nclust > for each ∆R cut at different η values (second row) ∆R(jets, clus) |η| < 0.7 |η| < 1.4 |η| < 2.1 |η| < 3.0 |η| > 2.5 |η| < 5.0 ∆R = 0.7 201.24 173.59 102.26 102.26 53.99 78.73 76 181 708 708 309 1383 ∆R = 0.8 199.50 172.54 100.71 100.71 53.99 77.43 66 66 66 66 66 66 ∆R = 0.9 198.50 171.20 99.28 99.28 54.01 76.23 57 146 630 630 303 1285 ∆R = 1.1 197.46 168.08 96.26 96.26 54.17 73.79 41 112 546 546 295 1175 ∆R = 1.5 192.99 164.27 91.25 69.88 54.77 69.88 16 55 372 922 268 922

for layer 2. The averaging is taken on all possible rapidity regions and jet isolation cuts ranges within the calorimeter acceptance (|η| < 3). Finally the UE energy value 43 MeV from layer 1 and 342 MeV from layer 2 is obtained. These values are subtracted from each cluster separately layer by layer in order to calculate top invariant mass of clusters Mclus, which can ﬁnally be correlated with the real top mass. top Figures 1.13 and 1.14 show that the effect on Mclus before and after UE subtraction respectively, the resultant values are still 45% less than the nominal top quark mass, which needs to be calibrated, and will be a subject of study in future. Three samples of high PT top events, but with different input top quark mass in the generator with 165 GeV/c2, 175 GeV/c2, 185 GeV/c2 were produced and analyzed in exactly the same way as previously explained. For all the samples the UEclus energy estimate per calorimeter cluster was kept the same, no mass

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14 I. Ahmed

top Fig. 1.13. Reconstructed mclus spectrum obtained using a cone size of ∆R = 1.3 around the top direction

top Fig. 1.14. The mclus spectra ﬁtted with gaussian function after the UEclus is subtracted.

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1 Top quark mass measurement from highly boosted jets at LHC 15

Table 1.4. Underlying event estimation method for Layer 2 (HCAL)

< ET >/cluster MeV (ﬁrst row) < Nclust > for each ∆R cut at different η values (second row) ∆R(jets, clus) |η| < 0.7 |η| < 1.4 |η| < 2.1 |η| < 3.0 |η| > 2.5 |η| < 5.0 ∆R = 0.7 626.89 509.19 445.77 363.00 236.77 326.78 38 88 134 229 182 352 ∆R = 0.8 623.07 503.17 439.69 356.43 236.76 321.39 33 80 125 218 181 33 ∆R = 0.9 618.47 496.66 433.11 349.36 236.69 315.67 29 73 116 208 180 330 ∆R = 1.1 614.85 485.24 420.82 335.58 236.35 304.62 22 22 22 22 22 22 ∆R = 1.5 599.83 459.49 394.11 306.64 237.03 283.05 8 28 56 136 169 253

jjb Fig. 1.15. Reconstructed mtop invariant mass, as a function of input top mass in generator taken from three different samples.

scale calibration was used. The purpose of this exercise is to predict whether the reconstruction method is able to determine the input top mass, independently of jjb its value. In Fig. 1.15 the resulting top mass mtop at cone size 1.3, in each sample is plotted versus the input top quark mass in the generator. A correlation with a slop about 0.786 is observed. This means that an error of 0.9 in the mean of the peak translates to an error of 0.9/0.786 = 1.145 GeV/c2 on the measured top mass from jets.

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16 I. Ahmed 1.6 Summary and Conclusion

We describe an alternative method to estimate the top mass using high PT top anti-top events in the lepton plus jets channel. We present an event selection for these events and show that it is possible to observe the energy deposited by the hadronic top decay in a cone around the reconstructed top flight direction. Since the invariant mass of the calorimeter clusters in such a cone depends on the cone size due to the underlying event, a first step towards the estimation and data- based subtraction of underlying event activity is presented. The reconstruction method was verified by generating three samples with three different input top masses 165 GeV/c2, 175 GeV/c2 and 186 GeV/c2. A correlation with a slop about 0.786 is observed between input and reconstructed top masses. This means that an error of 0.9 in the mean of the peak translates to an error of 1.145 GeV/c2 on the measured top quark mass from jets. This means that with 50K events which corresponds to 7.3 fb−1, one can expect a statistical uncertainty of about 1.145 GeV/c2 on top mass. The top quark mass with and without UEclus subtraction was mea- top sured and tried to make mclus independent of the cone around top flight direction. one can expect a statistical uncertainty about δm = 1 − 1.6 GeV/c2 on top top mass mclus. The final calibration and more precise UEclus subtraction method in top the mclus measurement will be the subject of future study.

References

1. R. Bonciani et al., Nucl. Phys. B 529(1998) 424 2. Eur Phys J C 39, s2, s63-s90 (2005) 3. S. Agostinelli et al., ’GEANT4:A Simulation Toolkit’, NIM A 506 (2003), 250-303 4. T. Sjostrand, P. Eden, C. Friberg, L. Lonnblad, G. Miu, S. Mrenna and E. Norrbin, ’High Energy Physics Event Generation with PYTHIA’,Computer Phys. Commun. 5. http://cmsdoc.cern.ch/famos/ (FAMOS home page) 6. CMS NOTE 2006/014 7. CDF and D0 Collaborations. hep-ex/0507106v1

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School of Particles and Accelerators FIRST IPM MEETING Institute for Research in ON LHCPHYSICS Fundamental Sciences (IPM) VOL. 1, NO. 1 (p. 17) Isfahan, April 20-24, 2009

2 Mercury Electric Dipole Moment in the Presence of MSSM Flavored Changing Sources

S. Y. Ayazi

School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran

Abstract. In context of the Minimal Supersymmetric Standard Model(MSSM), there are many new sources for ﬂavor changing and CP-violation. In this paper, we study the effect of phase of trilinear A-term of stop (At) on mercury Electric Dipole Moment (EDM) in presence of ﬂavor changing sources in soft SUSY Lagrangian. We show that in one loop

level this effect for maximum value of φAt can range between zero and two order of magnitude above present bound. For ﬂavor changing sources in soft SUSY Lagrangian, we consider constrains which arise from experimental bounds on Br(B → Xsγ).

2.1 Introduction

The general MSSM introduces new sources for flavor changing as well as CP violation. It is known that new CP phases of MSSM introduce in both flavor- conserving and flavor changing soft SUSY breaking terms. In the literature, the effects of these terms on electric dipole moments (EDM) of fundamental particles have been extensively discussed [1,2]. At one loop level, in flavor-conserving case dominant contribution to the EDMs of electron and quarks come from the chargino and the gluino exchange, respectively. In flavor changing case dominant contribution can arise from neutralino loop [3] . The non-observation of EDM of the thallium, neutron and mercury as well as the absence of large flavor changing neutral current (FCNC) decay put severe constrains on the parameters of MSSM. The effect of the phases of trilinear A-coupling in soft SUSY Lagrangian on EDM of electron and neutron have been studied in literature [4]. Experimental bounds −2 on de and dn constrain Im[Ae], Im[Au,c] and Im[Ad,s] to order O[10 ]MSUSY whereas phases of At and Ab are not restricted in one loop level. However at two loop level, Barr-Zee-type diagram can contribute to EDMs of quarks [5]. In Ref. [5], it have been shown in large tan β scenarios this contribution can exceed the present bounds which can be translated into limit on phases of At and Ab. In the present paper, we assume a general MSSM with non-universal soft supersymmetric breaking mass parameters and trilinear scalar coupling. In the SUSY extension of the SM, for the sfermions of the first and second generation e e e e fL −fR mixing can be neglected. For the third generation sfermion, fL −fR mixing should be taken into account due to the larger Yukawa coupling. Their lighter mass eigenstates may be among the light SUSY particles which could be investigated at the Tevateron and at international linear collider (ILC) [6]. Analysis of

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18 S. Y. Ayazi e the decays of the 3rd generation sfermions et1,2 and b1,2 in the MSSM with complex parameters have been performed in Ref. [7]. Phenomenological studies of production and decays of the 3rd generation sfermions at future e+e− linear colliders, again in the complex MSSM, have been made in Ref. [6]. The lower mass eigenvalue of stau can be rather small and the τe1 could be the lightest charged sparticle. Also in general MSSM the ﬁrst mass eigenvalue of stop can be the lightest colored sparticle. For these reasons, pair production and decays stop and sbot- tom are particularly interesting at international linear collider (ILC). At such a collider, it will be possible to measure masses, cross section and decay branching ratios with high precision [8]. Also it was shown that e+e− linear collider enables us to obtain information on the At and other fundamental soft SUSY breaking parameters of the third generation squark system in the general MSSM with complex phases [6]. As it is mentioned, the studying of FCNC and EDM sources in the SUSY is another approach to learn about parameter space of MSSM. In this paper, we ignore all CP violating (CPV) phases of MSSM except At and study the effect of its on hadronic EDMs. At the one loop level, if off-diagonal elements of mass matrices of squarks are zero, neutron and mercury can not receive a contribution from At. In this paper, we suppose that off-diagonal term of soft breaking mass parameters are nonezero. It is shown that if the only source of FCNC is Yukawa coupling and all CP violating phases of MSSM are zero except CKM phase, MSSM contribution to EDM of electron and neutron are extensively small. As it is mentioned, phases of At and Ab, at two loop level contribute to hadronic EDMs. It is shown that in some part of parameters space, phases of At and Ab are restricted when 40 ≤ tan β ≤ 60. In this paper, we show that if we consider off-diagonal elements of mass matrices of squarks and ignore all CPV phases except At phase, neutron and mercury EDMS can receive contribution through chargino-squark as well as neutralino-squark loops in two order larger than present experimental bound on dHg. We show that in small tan β scenario, At phase can also be restricted. We show that for B → Xs(d)γ close to them present bounds, the bound on dHg can already constrain phase of At. As it is known, the calculation of the EDM of the neutron in the MSSM is subject to very large hadronic uncertainties, which makes the extraction of the limits on CP-violating phases in MSSM tenuous. For this reason we focus on effect of At on EDM of mercury.

2.2 The model and its phenomenological effects

In this section, we introduce the model and sources of ﬂavor violation and CP- violating phases. We consider the Minimal Supersymmetric Standard Model with following superpotential

dc b c dc b c c c WMSSM = (Yu)ijuRi Qj · Hu − (Yd)ijdRi Qj · Hd − µ Hu · Hd (2.1) b c c where Qj, Hu and Hd are doublets of chiral superﬁelds respectively associated with left-handed quarks and the two Higgs doublets of the MSSM. In the above

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2 Mercury Electric Dipole Moment in the Presence of MSSM ... 19

dc dc formula, uRi and dRi are the chiral superfields associated with the right-handed up quarks and down bottom fields. The index ‘‘i" determines the flavor; i = 1, 2, 3. Notice that the Yukawa terms involving the lepton supermultiplets have to be added to (2.1). However, since we are going to concentrate on the quark sector, we have omitted such terms. The soft supersymmetry breaking part of the La- grangian, at the electroweak scale has the form ³ ´ MSSM ff ee Lsoft = − 1/2 M3gege + M2WW + M1BB + H.c. c f gc f − ((AuiYuiδij + Auij)ugi Qj · Hu − (AdiYdiδij + Adij)di Qj · Hd + H.c.) † † † f 2 f gc 2 fc gc 2 fc − Qi mQij˜ Qj − (ui ) muij˜ uj − (di ) mdij˜ dj − m2 H† H − m2 H† H − ( B H · H + H.c.), (2.2) Hu u u Hd d d H u d where the “i” and “j” indices determine the flavor. Notice that, we have taken flavor conserving soft potential except A-terms which in our scenario are proportional with Yukawa matrices. Again, the terms involving the sleptons have to be added to (2.2). As is well-known, the general MSSM Lagrangian possesses 43 new CP violating phases in addition to the CKM phase. After electroweak symmetry breaking, the A-terms in (2.2) as well as the terms in superpotential induce left-right mixing. In above Lagrangian and superpoten- 2 2 tial, if Auij = Adij = 0 and the off-diagonal elements of mQ˜ and mu˜ vanish (for 2 2 i 6= j, (mQ)ij = (mu)ij = Auij = Adij = 0), the only source for flavored violation is Yukawa coupling. In this case, in one loop level, the effect of phases At and Ab on EDMs of neutron and mercury are extremely small. This means no bound on phases of At and Ab from dHg can be derived. As is well-known, dHg and de receive significant contribution from the phases Au, µ and M1 [2]. Thus, the strong bound on dHg and de can be translated into bounds on the phases of these parameters. In the literature, it is shown that for relatively low scale supersymmetry (mSUSY < 500 GeV), the bounds on these phases from dHg and de are very strong [2] unless severe cancelation takes place [1]. At the two-loop level, if there is not any flavored violating sources except Yukawa coupling, the phases of At and Ab can induce a contribution to dHg and dn [9]. For relatively large values of tan β (tan β ≥ 20) and mSUSY ' 100 GeV, the bound on dHg can be translated into a bound of order of few hundred GeV on Im[At]. The limit from the bound on dn even is less stringent. We show that, for small values of tan β and mSUSY ' 100 GeV, in presence of flavored violating sources in soft susy La- grangian which B → Xs(d)γ is close to them present bounds, the phase of At can give significant contribution to dHg even at the one loop-level. For LFV case, the A-term associated with a definite flavor can in principle affect the EDM of a 2 2 quark of another flavor. In particular if (13) elements of mQ and mu or Aij are nonzero, the phase of At can induce an EDM for mercury exceeding the present bound by several orders of magnitudes. As a result, in this case the strong bound on dHg can restrict the phase of At. In order to study this bound, we have to first consider the bounds on the flavored violating sources in mass matrices of squarks and A-terms from the bounds on Br(B → Xs(d)γ) and CP observable ACP. The stronger upper bound on the flavor violating element of squark mass matrices comes from B meson branching ratio Br(B → Xsγ). The measurements of the

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branching ratio at CLEO [10], APLEPH [11] and BELLE [12] give the combined result −4 Br(B → Xsγ) = (3.11 ± 0.42(stat.) ± 0.21(syst.)) × 10 , (2.3) where the ﬁrst error is statistical and the second is systematic. Theoretical calculation in the SM has been performed in several steps [13], The ﬁrst step in the full next-to-leading order (NLO) QCD correction has been calculated in [14] and second has recently been completed in the next-to-next to leading order (NNLO) [14] and have reached to similar experimental precision.

−4 Br(B → Xsγ)SM = (3.29 ± 0.33) × 10 . (2.4)

As is mentioned, SM prediction for these processes approximately correspond with experiment [14]. Nevertheless the SM contributions have very large uncertainty and SUSY contribution can lie inside the experimental allowed region. Supersymmetric contribution to Br(B → Xsγ) have not yet been calculated with similar level of accuracy. The LO analysis of SUSY contribution to this process has been done in [15,16]. In this paper, we consider NLO QCD correction of SM calculation for Br(B → Xsγ) and only LO calculation of MSSM contribution to this process which presented in [17]. The bound on this process can be translated into bounds on the 2 2 (mQ)23 and (mu)23 or (Au)23. Another inclusive decay B → Xdγ has not been detected experimentally. In the SM the branching ratio of this process is very small. However the decay rate asymmetry of the B → Xdγ decay is much larger than for B → Xsγ and is possibly detectable. The CP-asymmetry in the decay rates, deﬁned as

Γ(B → Xs(d)γ) − Γ(B → Xs(d)γ) ACP = . (2.5) Γ(B → Xs(d)γ) + Γ(B → Xs(d)γ)

The CP-asymmetry in the SM is caused by the single phase in CKM matrix and can be strongly affected by new CP-violating sources in MSSM. The direct CP- asymmetry can be detected in the exploration of K and B meson decays. The CP- asymmetries in the decay rates for the B → Xs(d)γ decays in the SM and SUSY extensions was investigated in [18]. The direct CP asymmetry for the B → Xsγ decay found to be in the range (0.4 − 1)% while for B → Xdγ transition it varies in interval (7 − 35)%. In this paper, we consider LO calculation of MSSM which presented in [18]. The measurement of the CP asymmetry has been updated to [19]

ACP(B → Xsγ) = 0.079 ± 0.108stat ± 0.022syst. (2.6)

A direct measurement of the CP asymmetry of B → Xdγ is rather difficult, but perhaps still within the reach of the present high luminosity B factories. For this reason, in this paper, we only consider the bound of ACP(B → Xsγ) on flavor violating sources of MSSM and we also study the effects of CP phases and flavor violating sources of MSSM on ACP(B → Xdγ).

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2 Mercury Electric Dipole Moment in the Presence of MSSM ... 21 2.3 Numerical results

To calculate the EDMs and ChromoElectric Dipole Moments (CEDM) of the elementary particles, we use the formalism developed in [20]. In this paper, we study following formula for the EDM of mercury which according to [21]:

−2 dHg = −(d˜ d − d˜ u − 0.012d˜ s) × 3.2 · 10 e, (2.7)

where d˜ d, d˜ u and d˜ s are respectively the CEDMs of the d, u and s quarks.

100 50 45 40 10 35 ecm] ecm] 30 -27 -27 25

| [10 | [10 20

Hg 1 Hg 15 |d |d 10 5 0.1 0 0 200 400 600 800 1000 0 0.5 1 1.5 2 A ϕ [π] t At (a) (b)

Fig. 2.1. a) dHg versus At. The input parameters are equal to: |µ| = 400 GeV, m0 = 200 GeV, M1/2 = 300 GeV and tan β = 10 and we have set |At|=1000 GeV. All the ﬂavor 2 2 changing elements of the squark mass matrix are set to zero except (mQ)13 = 10000 GeV , 2 2 2 2 2 2 (mu)31 = 100 GeV , (mu)23 = 10000 GeV , (mLR)32(= A32hHui) = 10000 GeV , 2 2 2 2 2 (mLR)23(= A23hHui) = 10000 GeV , (mLR)13(= A13hHui) = 100 GeV , (mLR)31(= 2 A31hHui) = 100 GeV . The dotted blue curve depicts effect of At in one-loop level and the thick red curve depicts effect of At in two-loop level. The horizontal doted line at −28 2.1 × 10 e cm depicts the present experimental limit [22] on dHg. b) dHg versus φAt .

The input parameters are similar to Fig. a. The dotted blue curve depicts effect of φAt in

one-loop level and the thick red curve depicts effect of φAt in two-loop level.

2 2 As is mentioned in previous section for nonzero (mQ)13 and (mu)31, the e phase of At induce a contribution to du. As a result for deﬁnite value of the off-

diagonal mass elements, the bound on dHg can be interpreted as bound on φAt or on Im[At]. The inclusive decays B → Xdγ and ACP(B → Xdγ) have not been 2 2 measured independently, therefore there are no bounds on (mQ)13 and (mu)31 which arise from B → Xdγ and ACP(B → Xdγ). Suppose that both the 32 and 31 elements of squark mass matrices are nonzero. This means neutralino gluino exchanges can contribute to Br(B → Xsγ)). Consider the case that both 32 and 31 elements are nonzero and close the corresponding bounds from Br(B → Xsγ)). For such conﬁguration, we have shown that in SUSY one-loop level contribution

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22 S. Y. Ayazi

of phase At to dHg is approximately thirty times larger than SUSY two-loop level contribution. Figure .2.1 demonstrate this observation.

4 ] -4

)[10 3 γ s X

→ 2 Br(B 1

0 0 0.5 1 1.5 2 ϕ [π] At

Fig. 2.2. Br(B → Xsγ) versus φAt . The input parameters are similar to Fig. (2.1-a). The horizontal doted line at 2 × 10−4 and 4.5 × 10−4 respectively depict the present lower and upper experimental bounds on Br(B → Xsγ) [14].

As seen from Fig. (2.2), we observe that the sensitivity of the B → Xsγ to the 2 2 2 2 phase of At is not signiﬁcant. Notice that (mQ)13, (mQ)23, (mu)32 and (mu)31 have been chosen such that Br(B → Xsγ) lies between lower and upper experimental bounds.

0.02 0.4 0.35 0.015 0.3 ) ) γ γ s d 0.25 X X → 0.01 → 0.2 (B (B CP CP 0.15 A A 0.005 0.1 0.05 0 0 0 0.5 1 1.5 2 0 0.5 1 1.5 2 ϕ [π] ϕ [π] At At (a) (b)

Fig. 2.3. a) ACP(B → Xsγ) versus φAt . b) ACP(B → Xdγ) versus φAt . The input parameters are similar to Fig. (2.1-a).

Fig .(2.3) displays the dependence ACP(B → Xsγ) versus φAt . The measurement of the ACP(B → Xsγ) has very large uncertainty which makes the extraction

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2 Mercury Electric Dipole Moment in the Presence of MSSM ... 23

of the limits on phase of At tenuous. Also a sufﬁciently accurate measurement of the CP asymmetry of ACP(B → Xdγ) will require large statistics and will not be achieved in the near future. Thus if the forthcoming experiments measured the ACP(B → Xsγ) and ACP(B → Xdγ) with high accuracy, there is a hope to solve degeneracy between CP-violation phases by applying ACP(B → Xsγ) and ACP(B → Xdγ) experimental data.

2.4 Conclusions

In this paper, we have discussed the effects of the phase of trilinear A-coupling

of the stop, φAt , on dHg in the presence of nonzero ﬂavor changing elements of the squark mass matrix. We have shown that for a large portion of the parameter space consistent with the present bound on Br(B → Xsγ), the contribution of

φAt to dHg can exceed the present bound by several orders of magnitude. The

effect of φAt on dHg strongly depends on the ratios of the ﬂavor changing elements masses (m2 ) /(m2 ) and (m2 ) /(m2 ) . In other words, for a given Q 13 u 31 At 13 At 31

Br(B → Xsγ) and φAt = ±π/2, |dHg| can take any value between zero and a maximum which depends on the value of Br(B → Xsγ).

Assuming that φAt is the only source of CP-violation contributing to dHg, we

have derived bounds on φAt for various values of the ﬂavor changing elements giving rise to Br(B → Xsγ) close to the present bound.

Acknowledgement

I would like to thank Ali-Naghi Khorramian for careful reading of the manu- script.

References

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24 S. Y. Ayazi

4. A. Bartl, W. Majerotto, W. Porod and D. Wyler, Phys. Rev. D 68 (2003) 053005 [arXiv:hep- ph/0306050]; W. Porod, Prepared for International Workshop on Astroparticle and High- Energy Physics (AHEP-2003), Valencia, Spain, 14-18 Oct 2003 5. D. Chang, W. Y. Keung and A. Pilaftsis, Phys. Rev. Lett. 82 (1999) 900 [Erratum-ibid. 83 (1999) 3972] [arXiv:hep-ph/9811202]. 6. A. Bartl and S. Hesselbach, Pramana 63 (2004) 1101 [arXiv:hep-ph/0407178]; S. Hes- selbach, O. Kittel, G. A. Moortgat-Pick and W. Oller, Eur. Phys. J. C 33 (2004) S746 [arXiv:hep-ph/0310367]; E. Boos, H. U. Martyn, G. A. Moortgat-Pick, M. Sachwitz, A. Sherstnev and P. M. Zerwas, Eur. Phys. J. C 30 (2003) 395 [arXiv:hep-ph/0303110]; A. Freitas et al., arXiv:hep-ph/0211108. 7. T. Gajdosik, R. M. Godbole and S. Kraml, JHEP 0409 (2004) 051 [arXiv:hep-ph/0405167]; A. Bartl, K. Hidaka, T. Kernreiter and W. Porod, Phys. Rev. D 66 (2002) 115009 [arXiv:hep-ph/0207186]; O. Kittel, arXiv:hep-ph/0504183. A. Bartl, H. Fraas, S. Hes- selbach, K. Hidaka, T. Kernreiter, O. Kittel and W. Porod, arXiv:hep-ph/0312306; 8. M. M. Nojiri, Phys. Rev. D 51 (1995) 6281 [arXiv:hep-ph/9412374]; M. M. Nojiri, K. Fu- jii and T. Tsukamoto, Phys. Rev. D 54 (1996) 6756 [arXiv:hep-ph/9606370]; A. Bartl, H. Eberl, S. Kraml, W. Majerotto, W. Porod and A. Sopczak, Z. Phys. C 76 (1997) 549 [arXiv:hep-ph/9701336]; A. Bartl, H. Eberl, S. Kraml, W. Majerotto and W. Porod, Eur. Phys. J. direct C 2 (2000) 6 [arXiv:hep-ph/0002115]. 9. D. Chang, W. Y. Keung and A. Pilaftsis, Phys. Rev. Lett. 82 (1999) 900 [Erratum-ibid. 83 (1999) 3972] [arXiv:hep-ph/9811202]. 10. S. Ahmed et al. [CLEO Collaboration], hep-ex/9908022. 11. R. Barate et al. [ALEPH Collaboration], Phys. Lett. B 429, 169 (1998). 12. K. Abe et al. [Belle Collaboration], hep-ex/0103042. 13. C. Greub, T. Hurth and D. Wyler, Phys. Rev. D 54, 3350 (1996) [hep-ph/9603404]; K. Adel and Y. Yao, Phys. Rev. D 49, 4945 (1994) [hep-ph/9308349]; A. Ali and C. Greub, Phys. Lett. B 361, 146 (1995) [hep-ph/9506374]. 14. K. Chetyrkin, M. Misiak and M. Munz, Phys. Lett. B 400, 206 (1997) [Erratum-ibid. B 425, 414 (1997)] [hep-ph/9612313]; T. Hurth, hep-ph/0106050; 15. M. Ciuchini, G. Degrassi, P. Gambino and G. F. Giudice, Nucl. Phys. B534, 3 (1998) [hep-ph/9806308]. 16. F. Borzumati, C. Greub, T. Hurth and D. Wyler, Phys. Rev. D 62, 075005 (2000) [hep- ph/9911245]. 17. A. L. Kagan and M. Neubert, Eur. Phys. J. C 7 (1999) 5 [arXiv:hep-ph/9805303]. 18. A. L. Kagan and M. Neubert, Phys. Rev. D 58 (1998) 094012 [arXiv:hep-ph/9803368]. 19. T. E. Coan et al. [CLEO Collaboration], Phys. Rev. Lett. 86 (2001) 5661 [arXiv:hep- ex/0010075]. 20. T. Ibrahim and P. Nath, Phys. Rev. D 57 (1998) 478 [Erratum-ibid. D 58 (1998 ER- RAT,D60,079903.1999 ERRAT,D60,119901.1999) 019901] [arXiv:hep-ph/9708456]. 21. T. Falk, K. A. Olive, M. Pospelov and R. Roiban, Nucl. Phys. B 560 (1999) 3 [arXiv:hep- ph/9904393]. 22. C. Amsler et al. [Particle Data Group], Phys. Lett. B 667 (2008) 1.

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School of Particles and Accelerators FIRST IPM MEETING Institute for Research in ON LHCPHYSICS Fundamental Sciences (IPM) VOL. 1, NO. 1 (p. 25) Isfahan, April 20-24, 2009

3 A data driven method to measure electron charge mis-identiﬁcation rate

H. Bakhshiana,b, L. Papec, F. Moortgatc

a Sharif University of Technology, Tehran, Iran b School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran c ETH Zurich, Zurich, Switzerland.

Abstract. Electron charge mis-measurement is an important challenge in analyses which depend on the charge of electron. To estimate the probability of electron charge mis-measurement a data driven method is introduced and a good agreement with MC based methods is achieved. The third moment of φ distribution of hits in electron SuperCluster is studied. The correlation between this variable and the electron charge is also investigated. Using this ‘new’ variable and some other variables the electron charge measurement is improved by two different approaches.

3.1 Introduction

In Table 3.1 the inclusive cross section of SUSY LM1 and some of the potential backgrounds to the Same Sign DiElectron channel are listed. The backgrounds can be categorized in three groups :

1. Real Backgrounds : The only member of this group is W±W± when both of W’s decay to an electron and a ν. 2. Fake Backgrounds : Events like W + Jets can be a background if one jet fakes an electron. These are the dominant backgrounds. 3. Charge mismeasured Backgrounds : Events with two opposite sign electrons in the ﬁnal state are background when one of the electrons charge is mis- identiﬁed.

In section 3.3, a data driven method to measure the probability of charge mis-measurement is introduced. Knowing this probability based on real data, one can estimate the systematic uncertainty more realistically. The third moment of φ distribution of hits in electron SuperCluster, Skewness, is studied in section 3.4. The correlation between skewness and electron charge is also studied. Using this variable and some other variables, two methods are explained to improve the charge identiﬁcation. These methods are presented in section 3.5. Im- proving charge measurement is useful in reducing the opposite sign background contamination and increase the efﬁciency of signal selection.

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26 H. Bakhshian, L. Pape, F. Moortgat

Process XSection (pb)

SUSY (LM1) inclusive 41.9 3 W + Jets inclusive 190 × 10 3 Z + Jets inclusive 56 × 10

tt¯ inclusive 830 + − W W dilepton-decays 117 ± ± W W inclusive ∼ 0.3(no CSA07 data available)

Table 3.1. All of the cross sections are for 14 TeV center of mass energy

3.2 Data sets and Data selection

The data driven method is based on events from Z0 production without jet. An electron candidate is a track segment in the tracker which is matched with a collection of energy deposits in the electromagnetic calorimeter [1,2]. Electrons are selected with transverse momentum (PT ) greater than 7GeV and |η| < 2.4. The η range corresponds to the acceptance of silicon tracker. Tracker isolation requirement is placed on the electron candidates to distinguish leptons from Z decay from leptons in jets. A tracker isolation variable is deﬁned by forming the sum of the transverse momenta of all tracks found within a cone of size R = 0.2 around the lepton direction, excluding the lepton track. Dividing this value by the PT of the electron, relative tracker isolation variable is calculated. Electron candidates are asked to have relative tracker isolation value less than 0.2. Furthermore, these electrons should be ’tight’ identiﬁed [3,4]. A jet candidate is reconstructed by the IterativeCone jet algorithm with radius of R = 0.5 using calorimeter towers as input. An event is accepted if it does not have any jet within |η| < 3 and corrected energy greater than 30 GeV. Moreover, exactly two electrons are required in each event. To select Z events, these two electrons should meet the criteria below:

• ∆φe1,e2 > 0.5 • Their SuperClusters Invariant Mass, must be between 60 and 120

Using energy deposits in calorimeter to ﬁnd the invariant mass, guaranties less tracker effect in the event selection. Needless to say that the error in measuring the track momentum is very correlated with the uncertainty of charge identiﬁca- tion. The results of these selection cuts applied on W+Jets, Z+Jets and inclusive tt samples are listed in Table 3.2. All samples have been simulated and reconstructed within the scope of the 2007 CMS Computing, Software and Analysis Challenge CSA07.

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Table 3.2. Number of events after applying cuts Total Same-Sign Opposite-Sign Z → ee 89190 2560 86630 other Z decays 95 5 90 W + jets 241 81 160 tt 10 2 8

3.3 Electron charge mis-measurement

In this method which is based on reconstructed data, events are separated into Same Sign and Opposite Sign categories. This separation is not biased as there is no criteria on the electron charge at the event selection level. The charge mis- measurement rate is deﬁned as the number of SS Events divided by twice of number of all events:

Nss Pmm ≡ 2 × (Nss + Nos)

(Pmm ≡ Probability of charge Mis-Measurement per electron) To verify the results, in a similar analysis, the charge of each electron is compared with the charge of its best-matched generated electron, and the mis-identiﬁcation rate is calculated. To ﬁnd the best-matched, within a cone of size 0.2 around a GsfElectron, the MC electron which minimizes ∆PT is chosen. In Fig. 3.1 the probability of charge mis- PT measurement vs. different variables is shown.

3.4 A ’new’ variable : Skewness of hits in φ direction

3.4.1 Definition To understand the charge of electron, many variables have been studied. But all of them use track information. The SuperCluster position is also used in variables like (φinnermost − φseed) to improve the charge measurement [5]. Another possibility to extract electron charge information is using SuperCluster shape variables. To find such a variable, the distribution of supercluster hits in φ direction is studied in detail. Bremsstrahlung photons are emitted tangential to the electron path. In the presence of magnetic field, the path curvature is different for positive and negative electrons. Therefore the position of hits of emitted photons with respect to the position of electron itself, is different for positive and negative electrons in the φ direction.The third moment of φ distribution of hits can show this difference. The third moment of each distribution is called Skewness of that distribution and describes the asymmetry of that dataset from the normal distribution. Here is the exact formula for skewness of φ distribution of hits :

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28 H. Bakhshian, L. Pape, F. Moortgat

Gen data Gen data Reco data Reco data 0.3 0.06

0.25 0.05 mis-measurement 0.2 0.04 charge mis-measurement prob. e

0.03

charge 0.15 e

0.1 0.02

0.05 0.01

0 0 20 40 60 80 100 120 140 0 0.5 1 1.5 2 2.5 Transverse Momentum of electron η

Gen data Gen data 0.06 0.9 Reco data Reco data

0.8 0.05 0.7

0.04 0.6

mis-measurement pro 0.5 mis-measurement prob. 0.03 charge e charge 0.4 e

0.02 0.3

0.2 0.01 0.1

0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 BremFraction TIPPV

Fig. 3.1. Pmm vs. Pt, η , fbrem and Transverse Impact Prameter(TIP). Almost in all of the plots, the results of data driven method agree with the generator based results. The charge mis-measurement rate is of the order of 1.5%, except in the high η and fbrem regions. The charge mis-measurement rate is very sensitive to (TIP)

i ∈Xhits 1 3 n wi(φi − φseed) Skewness = X 1 2 3/2 ( n wi(φi − φseed) ) i ∈ hits

Where wi is proportional to the logarithm of the energy of the hit and is ofﬁcially used in calculating one of the electron identiﬁcation variables (σηη) at CMS [6]. In Fig. 3.2(a) the distribution of this new variable for positive and negative electrons is plotted.

3.4.2 fbrem and its relation to Skewness As is expected from the deﬁnition of Skewness, it must be very dependent on the Brem-Fraction which is denoted by fbrem afterwards. fbrem is the fraction of energy of an electron which is emitted by Bremsstrahlung photons. Its value can be calculated using the transverse momentum of the track in its initial and ﬁnal points:

Innertrack Outertrack Pt − Pt fbrem = Innertrack Pt

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The dependency of Skewness to fbrem is shown in Figs. 3.2(b) , 3.2(c) and 3.2(d). To make the rest of the study easier, these two variables are combined in Sharpened

NegElectron_Electron_Skewness_ECALHits NegElectron_BM03_Electron_Skewness_ECALHits

NegElectron Entries 67605 NegElectron_BM03 Entries 37129 103 PosElectron Mean 0.05386 PosElectron_BM03 Mean 0.2506 3 10 RMS 1.519 RMS 1.605

PosElectron_Electron_Skewness_ECALHits PosElectron_BM03_Electron_Skewness_ECALHits

Entries 67775 Entries 37221 Mean -0.06324 Mean -0.2619 RMS 1.526 RMS 1.613 102 102

10 10

1 1

-10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 <(φ -φ )3> Skewness hit seed

(a) For all electrons (b) fbrem > 0.3

PosElectron_BM07_Electron_Skewness_ECALHits NegElectron_BM09_Electron_Skewness_ECALHits PosElectron_BM07 NegElectron_BM09 Entries 16332 Entries 5801 NegElectron_BM07 Mean -0.6894 PosElectron_BM09 Mean 0.8817 2 RMS 1.65 10 RMS 1.857

NegElectron_BM07_Electron_Skewness_ECALHits PosElectron_BM09_Electron_Skewness_ECALHits

Entries 16045 Entries 5938 Mean 0.683 Mean -0.8423 102 RMS 1.654 RMS 1.863

1 1

-10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 <(φ -φ )3> <(φ -φ )3> hit seed hit seed

Fig. 3.2. Skewness of positive and negative electrons for different regions of fbrem

up Skewness which is deﬁned as: exp( −1 ) × Skewnwss (Fig. 3.3) fbrem

3.5 Improving the measurement of charge

Here improvement means ﬁnding the badly measured electron in a same sign Z event. From here after, these badly measured electrons are denoted by ’bad’ while ’good’ is referring to the well-measured ones. One possibility to reach the goal is to study the behavior of good electrons and compare it with bad ones. Knowing the differences, it is not so difﬁcult to recog- nize the bad electron in a same sign Z event. The problem is that the method is not completely independent from MC information, because considering an electron as bad or good, needs a comparison with generator level.

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30 H. Bakhshian, L. Pape, F. Moortgat

PosElectron_Electron_BremFraction_Exp1_Multiply_Skewness_ECALHits

PosElectron Entries 67775 NegElectron Mean -0.05143 104 RMS 0.3035

NegElectron_Electron_BremFraction_Exp1_Multiply_Skewness_ECALHits

Entries 67605 Mean 0.05031 RMS 0.3027 103

102

-3 -2 -1 0 1 2 3 e-1 ⁄ brem × <(φ -φ )3> hit seed

Fig. 3.3. Sharpened up Skewness is a combination of Skewness and fbrem to make further studies easier

Variable name Correlation with goodness of charge TrackMomentumError →− 60% | P track| charge × TIPpv 58% charge × (φinnermost − φseed) 49% Calo. Energy Error 33% charge × Sharpened up Skewness 19% Table 3.3. Most correlated variables with goodness of charge

Variable name Correlation with charge

φinnermost − φseed 85% TIP Significance 36% Sharpened up Skewness 18% Table 3.4. Most correlated variables with charge

Good Electrons Bad Electrons Efficiency Purity Efficiency Purity Likelihood 89.4% 94.6% 94.8% 89.9% CFM NN 95.5% 93.3% 93.1% 95.3% Table 3.5. Efficiencies of finding the bad and good electrons in same sign Z events using the first method are listed here. Efficiency means the ratio of electrons that are recognized NMVA correctly by the method (² = g(b) ). g(b) NMC g(b)

The other possibility which is independent from MC information is based on the assumption that the electron charge is measured correctly in an opposite sign Z event. By this assumption the behavior of negative and positive electrons can be studied. Then this knowledge can be applied to a same sign Z event to ’re- measure’ the charge and separate the positive electron from the negative one. For both methods, many variables have been studied and the most relevant ones are selected. These variables and their correlations to charge identiﬁcation are

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Positive electrons Negative electrons Efficiency Purity Efficiency Purity Likelihood 71.2% 70.0% 70.0% 70.7% CFM NN 85.6% 84.6% 84.5% 85.6% Table 3.6. Efficiencies of finding the positive and negative electrons in same sign Z events using the second method are listed here. Efficiency means the ratio of electrons that are NMVA recognized correctly by the method (² = p(n) ). p(n) NMC p(n)

listed in Tables 3.3 and 3.4. All these variables are given as an input to two different multivariate methods, Likelihood and The Clermont-Ferrand (ROOT) neural network [7]. To see how efﬁcient these methods are, their outcomes are compared with MC electron charge. The results are shown in Tables 3.5 and 3.6.

3.6 Conclusions

A method, fully based on real data, to find the charge mis-measurement probability was introduced. The data driven method agrees with the generator based results. Skewness of φ distribution of SuperCluster hits, seemed to be a powerful variable in charge identification, as it is not so correlated to other variables. Two ways to find the mis-measured electrons were tested separately and the results were studied. Although the second method is slightly less efficient, being independent of generator-level info makes it more interesting.

***

I would like to thank the organizers of the First IPM meeting on LHC for the opportunity to present this talk.

References

1. S. Bafﬁoni, C. Charlot, F. Ferri, D. Futyan, P.Meridiani, I. Puljak, C. Rovelli, R. Salerno, and Y. Sirois, Technical Report CMS-NOTE-2006-040. CERN-CMS-NOTE-2006-040, CERN, Geneva, Feb 2006. 2. The CMS Collaboration, Journal of Instrumentation, 3(08):S08004,2008. 3. F. Beaudette, C. Charlot, E. Delmeire, C. Rovelli, and Y. Sirois, Technical Report CMS- NOTE-2006-114. CERN-CMS-NOTE-2006-114, CERN, 2006. 4. CMS Collaboration, volume 1 of Technical Design Report CMS, chapter 10.4.7, pages 401–403. CERN, Geneva, 2006. 5. D. Wardrope, Presented in EGamma POG meeting at CERN, Oct 2007. 6. Cmssw source code for calculating σηη. RecoEcal/EgammaCoreTools/src/ClusterShapeA- lgo.cc

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32 H. Bakhshian, L. Pape, F. Moortgat

7. A. Hocker,¨ J. Stelzer, F. Tegenfeldt, H. Voss, K. Voss, A. Christov, S. Henrot- Versill, M. Jachowski, A. Krasznahorkay, Y. Mahalalel, X. Prudent, and P. Speck- mayer, TMVA - Toolkit for Multivariate Data Analysis with ROOT:Users guide. oai:cds.cern.ch:1019880. Technical Report CERN-OPEN-2007-007, CERN, Geneva, Mar 2007.

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School of Particles and Accelerators FIRST IPM MEETING Institute for Research in ON LHCPHYSICS Fundamental Sciences (IPM) VOL. 1, NO. 1 (p. 33) Isfahan, April 20-24, 2009

4 Experimental aspects of neutrino oscillation physics

D. Duchesneau

LAPP, Universite´ de Savoie, CNRS/IN2P3, Annecy-le-Vieux, France

Abstract. The experimental review of this paper is mainly focussed on a particular aspect of the neutrino physics which is the observation and understanding of the neutrino oscillation process. This quantum mechanical mechanism involves several parameters linked to the neutrino properties which are described through a lepton mixing matrix. The detailed knowledge of those parameters may provide a key tool to answer several fundamental questions including the existence or not of ﬂavour violation in the leptonic sector. The discovery of neutrino ﬂavour oscillation 10 years ago was followed by an intense experimental activity with several key experiments which provided many clues to start to unravel the neutrino oscillation puzzle. The program is still active and impressive experimental challenges are underway to pursue this goal. The aim of the talk is to recall the main neutrino historical path and to give an overview of the many experimental aspects of the neutrino oscillation studies performed since 10 years and the main results obtained.

4.1 Introduction: some history and neutrino basis

The proof of existence of the particle called neutrino has not been a trivial exer- cice. Before detailing the experimental measurements it is worth to quote some anecdotes about their birth and existence to understand better the scientiﬁc approach and appreciate the evolution of ideas through time. W. Pauli [1] introduced for the ﬁrst time in 1930 the concept of a new spin half light neutral particle as a remedy to explain the observed violation of the principle of energy- momentum conservation in radioactive β decays. The electron energy spectrum was found to be continuous and not discrete and the new hypothetic neutral particle which could be emitted at the same time as the electron was a good solution to solve this anomaly. However this new idea was even not thought as a seri- ous one by its author. Pauli, in a discussion with one of his friends the german astronomer W. Baade, apparently confessed [2]: ’Today I have done something which no theoretical physicist should ever do in his life: I have predicted something which shall never be detected experimentally’. In 1933, exploiting the concept of this additional neutral particle, E. Fermi built a coherent theory of beta decays [3] which later became the basis of the weak interaction theory. However this theory was not accepted by everybody as one can see from one referee’s comment when he submitted the article to Nature: ’Abstract speculations too far from physical reality to be of any interest to the readers’. To complete this quite strange picture, Bethe and Peierls computed in 1934 [4]

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34 D. Duchesneau

the interaction cross section of the neutrinos based on the available theory. Un- fortunately, using too simplistic hypothesis they found that few MeV neutrinos resulted to have an interaction length of about one light year of lead and formu- late the conclusion: ’...this meant that one obviously would never be able to see a neutrino’. However despite those claims some physicists succeeded in building speciﬁc experiments to track and catch those quite ’elusive’ particles called neutrinos.

4.1.1 Neutrino detection and discovery

The discovery path started 30 years after the introduction of the neutrino concept when F. Reines and R. Cowan observed in 1956 for the first time [5] an interaction coming from anti-neutrino produced in the core of the Savannah River nuclear plant. Three large tanks filled with liquid scintillator were used to detect the anti- + neutrino using the inverse beta decay reaction (ν ¯ ep → e n). They saw a number of events corresponding to the process in which a delayed coincidence signature between two flashes of light, one from an electron-positron annihilation and the other one from a neutron capture, separated by a few microseconds is measured. It was the νe discovery. Six years later the second neutrino (νµ) was discovered by Lederman et al. [6] at the Brookhaven National Laboratory using for the first time an intense beam of neutrino produced in a pion beam. They found that the neutrino produced in the pion decays interact in the detector differently than would have done a electron neutrino. They saw in their spark chambers several tens of interactions where a muon was produced instead of an electron. The idea of using a neutrino beam was proposed by M. Schwartz in 1960 [7] to provide a tool to investigate the weak interactions. The basis is to use a high intensity proton beam to hit a target and produce an intense source of pions which produce neutrinos when decaying. This principle is the one used in what is called conventional neutrino beams. Finally the third neutrino type (ντ) was only discovered in 2000 by the Donut Collaboration at Fermilab [8]. The collaboration uses an intense beam dump in which charmed mesons decaying into taus and ντ are produced. Its existence was expected since the beginnning of the eighties and it was suggested after the discovery of the charged tau lepton in 1974 for which a new flavour neutrino has been theoretically associated. The proof of the existence of the ντ is based on the detection of the tau particle produced in charged current interaction in the detector. To detect this short lived particle it has been necessary to use a tracking detector with micrometer position resolution. The technology used for this goal was based on nuclear emulsion cloud chamber principle. This technology is also the one used in the current OPERA experiment [9].

4.1.2 Neutrino as laboratory tools

In the early time, the neutrino has been extensively used as a probe to study the weak interaction. The ﬁrst important result came with the discovery of the neutral current in 1973 [10] at CERN with the Garagamelle heavy liquid bubble chamber

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4 Experimental aspects of neutrino oscillation physics 35

well suited for the study of neutrino interactions. Figure 4.1 shows one of those events. Neutrino beams were also intensively used to probe the nucleon structure and to derive the structure functions of the neutrons and protons.

Fig. 4.1. Picture of an event seen in Fig. 4.2. Compilation of neutrino and anti- the Gargamelle bubble chamber. It corre- neutrino interaction cross section from sponds to an elastic νµ-e scattering. The a few hundred MeV to a few hundred observation of such events were essential GeV [11]. to conﬁrm the existence of neutral current processes.

Starting from this period it was possible to measure ν interaction cross sections on various target elements and over a large energy range extending from a few hundred MeV to a few hundred GeV. Figure 4.2 shows a compilation of the measured cross sections for neutrino and anti-neutrinos [11]. The corresponding −38 2 values are for neutrinos σνN/Eν ≈ 0.67x10 cm /GeV and for anti-neutrinos −38 2 σνN¯ /Eν¯ ≈ 0.34x10 cm /GeV. It is interesting to note that those values are 1 million times larger than the cross section computed in 1934 by Bethe and Peierls. The major activities around the neutrinos in the 80’s and 90’s were essentially the measurement of the weak interaction parameters (up to a few % precision) and the study of the quark structure of the nucleon. To succeed in measuring those interactions in a large energy range it was essential to build high energy intense pure neutrino beams together with massive detectors. The detector technology has evolved in mainly three categories coming with the electronic development and the computer assisted technology development. The ﬁrst category of detectors included heavy liquid bubble chambers like the Gargamelle chamber shown in Fig. 4.3 able to offer a large target mass, a long interaction length and a precise tracking reconstruction. The second generation of detectors used from the late 80’s were essentially calorimetric detectors similar to the CHARM detector shown in Fig. 4.4 with a few 100 tons of target with gaseous or plastic sintillator planes sometimes in al- ternance with layers of absorber material.

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36 D. Duchesneau

Fig. 4.3. Gargamelle bubble chamber at Fig. 4.4. CHARM experiment at CERN. CERN.

In more recent times another type of detectors looking at neutrinos appeared. They are of spherical or cylindrical shapes and correspond to large containers of liquid surrounded by large numbers of photodetectors. The principle is to track the light coming from Cherenkov emission of fast particles in the liquid medium or light coming from annihilation or scintillation processes. Three types of such detectors are shown in Fig. 4.5. The left picture shows the internal tank of the Super-Kamiokande detector in Japan ﬁlled with 22 ktons of water. The picture in the middle shows the SNO detector in Canada which contained about 1 kton of heavy water. The picture on the right shows the inner vessel of the Borexino detector in Italy which contains 300 tons of pseudocumen liquid scintillator. All those detectors offer large volumes for interaction and necessitate a large number of photodetectors going from 1000 to 10000.

Fig. 4.5. a) Super-Kamiokande water Cherenkov detector; b) SNO heavy water detector; c) BOREXINO liquid scintillator detector.

4.1.3 The neutrinos and the Standard Model In the minimal Standard Model (SM) of particle physics the neutrinos are deﬁned as neutral spin 1/2 fermions subject to Weak interactions only. LEP exeperiments have determined from the width of the Z resonance lineshape that the number of

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active light neutrino flavours is Nν= 2.9840±0.0082 [12]. There is clearly no room for an additional light ν species. In the Standard Model the ν are always Left Handed (LH) and their mass equals 0. Since 1998 there is evidence for flavour changing process in the neutrino sector. This oscillation mechanism implies that ν are massive which can be translated in the first hints for physics beyond the Standard Model. Obviously the SM should be extended to be reconciled with massive ν and the Higgs mechanism. In order to find a solution, two main approaches exist. One is to add a new particle called Dirac ν. It is minimal extension with a new Dirac mass term. However it is not very satisfactory since the Right Handed (RH) ν interacts with the Higgs too weakly (1012 times weaker than that of the top) to acquire mass. The second idea is to introduce a different type of particle which could be the Majorana ν. In this case heavy RH neutrinos are created for a brief moment (via the See-Saw mechanism) from LH ν interaction with Higgs. The consequence is that there is no fundamental distinction between matter and anti-matter. The question is not yet solved and more studies are needed to find the key for this issue. It is clear that many fundamental questions concerning the neutrino sector remain open. Here is a brief list of them with the possible experimental steps needed to answer them. • What is the absolute neutrino mass scale? This question is fundamental for cosmology and unification scheme of interactions. Possible experimental methods to answer is to measure ν time of flight (ex: Supernova 1987A gave the limit m< 20 eV) or to measure precisely the end point of electron beta decay spectrum. The actual limit obtained is m< 2.5 eV. Another method consists of inferring it from fluctuations of Cosmological Microwave Background (ex: WMAP gives m<0.23 eV). • Are neutrinos their own antiparticle (Majorana neutrinos) or not (Dirac neutrinos)? The answer can be obtained through the search for neutrinoless double beta decay which can also provide an additional clue to the absolute mass scale. • What are the relations between neutrino flavor eigenstates and mass eigenstates? Is there CP violation in the neutrino sector (leptogenesis)? The study to answer those questions are described in the next section. The idea is to exploit all possible neutrino sources which are the Sun, nuclear reactors, atmospheric showers, beam accelerators of various energies.

4.2 Mixing matrix and 3 massive ν oscillation

4.2.1 Formalism

There are three known neutrino flavor eigenstates να = (νe, νµ, ντ). Since 1998 there is clear evidence of the existence of transitions between the flavor eigenstates suggesting that neutrinos have non-zero masses. This oscillation mechanism can be formulated in a way that the mass eigenstates νi = (ν1, ν2, ν3) with masses mi = (m1, m2, m3) are related to the flavor eigenstates by a 3×3 unitary

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mixing matrix Uν called Maki-Nakagawa-Sakata-Pontecorvo (MNSP) matrix, X ν ∗ |ναi = (Uαi) |νii (4.1) i From this formulation, four numbers are needed to specify all of the matrix elements, namely three mixing angles (θ12, θ23, θ13) and one complex phase (δ). The parametrisation of the mixing matrix is usually represented following the form proposed by Chau and Keung [13] deﬁned by:

 −iδ  c13c12 c13s12 s13e ν iδ iδ U =  −c23s12 − s13s23c12e c23c12 − s13s23s12e c13s23  (4.2) iδ iδ s23s12 − s13c23c12e −s23c12 − s13c23s12e c13c23

where cjk ≡ cos θjk and sjk ≡ sin θjk. Neutrino oscillations are driven by the splittings between the neutrino mass eigenstates. It is useful to define the differ- 2 2 2 ences between the squares of the masses of the mass eigenstates ∆mij ≡ mi −mj . With this parametrization the probability that a neutrino of energy E and initial flavor α will “oscillate” into a neutrino of flavor β is given by Pαβ ≡ P(να → 2 νβ) = |hνβ| exp(−iHt)|ναi| , which in vacuum gives ¯ ¯ ¯ ¯2 Ã ! ¯X3 ¯ X3 X3 ∆m2 P = ¯ U∗ U exp(−iE t)¯ = U U∗ U∗ U exp −i kj t αβ ¯ αj βj j ¯ αj αk βj βk 2E ¯j=1 ¯ j=1 k=1 (4.3) If neutrinos of energy E travel a distance L then a measure of the propagation 2 time t is given by L/E. Non-zero ∆mij will result in neutrino flavor oscillations that have maxima at given values of L/E, and oscillation amplitudes that are de- ν termined by the matrix elements Uαi, and hence by θ12, θ23, θ13, and the CP violation phase δ. The oscillation frequency is governed by the ratio L/E and any experiment dedicated to oscillation studies will be designed to control this ratio as much as possible to infer the neutrino oscillation parameters.

4.2.2 Matter effects- the MSW effect It is important to understand that the propagation in vacuum is the simplest case. However neutrino sources, like the sun, can be far from the detection point and the neutrinos have to travel also matter densities before reaching the detectors.The induced effect is understood as the Mikheyev, Smirnov, Wolfenstein (MSW) effect [14] which was first confirmed by the solar neutrino observation. The effect is to add an additional term in the hamiltonian for describing the neutrino propagation in matter. The extra term arises because νe have an extra interaction via W boson exchange with electrons in the Sun or Earth. This is not the case for the two other neutrino flavours. The MSW effect can produce an energy spectrum distortion and flavor regeneration in Earth giving a day-night effect. If observed, an important consequence is that the matter interactions depend on the 2 mass hierarchy defined by the sign of ∆m31. If one includes the matter effects in the 3ν transition probability described above,

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4 Experimental aspects of neutrino oscillation physics 39

Eq. 4.3 becomes much more complicated. As an example here is the probability of transition betweem νµ and νe including dominant, sub-dominant oscillations, matter and CP violation terms:

√ where the matter densities is embedded in a = ±2 2GfNeEν.

4.2.3 Experimental status Several experiments exploiting all the possible sources of neutrino gave important and coherent results to determine the various oscillation parameters. The 2 determination of ∆m31 and θ23 came initially from the observation of a clear disappearance of the νµ produced in the atmospheric particle showers. This observation was made by the Kamiokande, Soudan II and MACRO experiments in the 90’s. However the first compelling evidence for neutrino oscillation in the atmospheric shower came in 1998 with the measurement by Super-Kamiokande [15] of a dependance of this deficit as a function of the zenith angle which is directly related to the distance the neutrinos are traveling through the Earth. While the νe were not showing such distortions the preferred hypothesis fitting well all the data is the νµ → ντ oscillation origin. Applying this hypothesis the best fit result 2 −3 2 gives ∆m31 = 2.1x10 eV and a maximal mixing with θ23 = 1. This result was confirmed by the K2K experiment [16] which used a home made neutrino source with the first long baseline neutrino beam in Japan. The beam was sent from KEK laboratory to Super-Kamiokande detector 250 km away. The mean neutrino energy was 1.3 GeV and they observed a slight deficit of neutrino interaction compared to what was expected from the extrapolation of the interactions seen in a 2 near detector without oscillation. The resulting values of ∆m31 and θ23 were fully compatible with the parameter space measured with the atmospheric neutrinos. 2 The determination of ∆m21 and θ12 is coming essentially from the solar and reactor neutrinos. Since more than 30 years experiments (37Cl, Gallex/GNO, SAGE, SuperK etc...) got a puzzling fact with the observation of a deficit of more than 30-50% of the solar neutrino arriving on the earth compared to the prediction given by the standard model of the sun. The real breakthrough arrived with the SNO detector which observed not only the same deficit but unlike the others was sensitive to all neutrino flavours and not only to νe interactions. Thanks to the use of heavy water, it was possible to measure the neutral current process via the

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breaking of the tritium nucleus liberating a neutron which gives a neutron capture signal in the detector. From their measurements shown in Fig. 4.6 they found that the ’all ﬂavour’ rate is compatible with the model of the sun and that the ﬂux of νe is compatible with an oscillation hypothesis favouring also a large mixing angle [17].

Fig. 4.6. Flux of 8B solar neutrinos that are Fig. 4.7. Ratio of the background sub- µ or τ flavor vs flux of electron neutrinos tracted anti-neutrino spectrum to the ex- deduced from the three neutrino reactions pectation for no-oscillation as a function of in SNO [18]. L/E. L is the effective baseline taken as a flux-weighted average (L=180 km) [19].

The solar neutrino solution was tested and confirmed by the Kamland experiment [19] which performed the first observation of neutrino oscillations from reactor sources by measuring the energy spectrum of neutrinos produced in about 55 nuclear reactors in Japan. The mean distance for the neutrino to reach the Kamioka mine were the detector is located is about 180 km. The result of the KamLAND measurement, shown in Fig. 4.7, exhibits the expected oscillatory behavior and constitutes compelling evidence for neutrino oscillations. By combining all solar and Kamland results the oscillation hypothesis fit gives the fol- 2 lowing values for the second mass difference and the second angle: ∆m21 = −5 2 2 +0.06 (7.59 ± 0.21)x10 eV and a large mixing with tan θ12 = 0.47−0.05. The third mixing angle θ13 is still not measured. There exist only an experimental 2 constraint from the CHOOZ reactor experiment [20] giving sin (2θ13) < 0.20 at 90% CL. Table 4.1 summarises the present knowledge of the oscillation parameters exploiting all the possible data available. The numbers shown are obtained from a global 3-ν analysis performed in summer 2008 [21].

4.3 Running accelerator oscillation projects

The goals of the presently running and future experiments are to go deeper in the understanding of the MNSP mixing matrix and oscillation mechanism. The main

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Table 4.1. Global 3ν oscillation analysis (2008) extracted from [21]: best-ﬁt values and allowed nσ ranges for the mass-mixing parameters.

2 −5 2 2 2 2 2 −3 2 Parameter δm /10 eV sin θ12 sin θ13 sin θ23 ∆m /10 eV Best ﬁt 7.67 0.312 0.016 0.466 2.39 1σ range 7.48 – 7.83 0.294 – 0.331 0.006 – 0.026 0.408 – 0.539 2.31 – 2.50 2σ range 7.31 – 8.01 0.278 – 0.352 < 0.036 0.366 – 0.602 2.19 – 2.66 3σ range 7.14 – 8.19 0.263 – 0.375 < 0.046 0.331 – 0.644 2.06 – 2.81

2 items are: more precise measurements of ∆m31 and θ23, the quest of θ13, studies 2 of the mass hierarchy with the sign of ∆m31 through matter effects and study possible CP violation in leptonic sector by comparing the transition probabilities of neutrino with the ones of anti-neutrinos. All this list represents a lenghty experimental and theoretical program with several challenging steps. The current phase corresponds to the ﬁrst long baseline generation using conventional muon neutrino beam. Two projects are running. The Minos/NUMI project in the USA and the OPERA/CNGS european project. They have both a baseline of about 730 km. Minos is performing detailed studies [22] of νµ disappearance to improve the parameter precisions while OPERA is designed to provide a direct proof of the existence of νµ → ντ transition looking at direct ντ appearance [9,23]. Both projects aim to measure also θ13 looking at the appeance channel νµ → νe. First results on this subject from Minos have been presented during 2009 winter con- ferences [24]. Figure 4.8 shows the ratio of the MINOS Far Detector data energy spectrum to the energy spectrum expected in the absence of neutrino disappearance where a clear distortion and deﬁcit is visible at low energies compatible with the oscillation hypothesis. Figure 4.9 shows the reconstruction in emulsions of a neutrino interaction vertex recorded in OPERA during the 2008 run. The vertex tracks show a kink on one of them similar to what is expected from a short lived particle like a charm meson or a tau particle decaying in the target emulsions.

4.4 Future experiments

The second experimental phase corresponds to the quest of θ13 which remains the missing mixing angle. For this search two approaches are confronted. As it was shown previously the transition νµ → νe combines effects from θ13 and the CP violation phase δ. The two parameters are correlated in the νe appearance channel. In addtion, matter effects could modify the transition probabilities depending on the mass hierarchy. Each experiment should carefully take into account all those effects. A positive result with accelerator experiment will give a bi-parameter contour solution while a disappearance experiment like in reactor experiment will give access to the θ13 value.

4.4.1 Long Baseline Experiments There are two projects going on. The T2K experiment [25] which is well advanced using a νµ beam from Tokai to Super-Kamiokande with a baseline of 295 km. The

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Fig. 4.8. Ratio of the MINOS Far Detector Fig. 4.9. Reconstruction of a neutrino inter- data energy spectrum to the energy spec- action vertex in a emulsion target element trum expected in the absence of neutrino of OPERA. One track shows a clear kink disappearance (black points) [22]. similar to the ones expected from tau or charm particle decays.

mean neutrino energy is 0.7 GeV with an νe contamination of about 0.4%. The second project called NOνA[26] is under study and is using a baseline of 810 km with mean νµ energy of about 2.2 GeV. The very long distance will give possibility to study matter effects on the neutrino oscillation rate. The neutrino beams are conventional beams but with an increased power going from 0.4-0.8 MW exploiting also the ’off-axis’ technique which allows a much narrower neutrino energy spectrum with reduced background contamination as well as a better control of the L/E ratio to maximise the νe appearance. Details about the T2K project and the advancement can be found in Ref. [25]. The beam has been already commis- sioned in May 2009 and a gradual beam power increase is expected from 0.2 MW to 1.0 MW in 4 years. There are two near detectors at 280m from the neutrino source, one at 0 degree angle and one at 2.0o. The Super-Kamiokande detector will be used as the far detector and is ready for data taking. A full running period should start at the end of this year. The NOνA experiment will search for νµ → νe oscillations in the existing NuMI neutrino beam using a 15 kiloton liquid scintillator detector. Funding has been recently approved and construction is about to start on the far detector site.

4.4.2 Reactor experiments

The alternative method is to measure the survival rate ofν ¯ e close to nuclear reactor like it was done with the CHOOZ experiment. Up to second order in sin 2θ13 2 ∆m21 and α = 2 the survival probability can be expressed as: ∆m31

2 2 2 2 2 2 4 2 Pν¯ e→ν¯ e ' 1 − sin 2θ13 sin (∆m31L/4E) + α (∆m31L/4E) cos θ13 sin 2θ12 , (4.4) The last term of this expression can be easily neglected if the ratio L/E is chosen close to the atmospheric maximum. Reactor experiments thus provide a clean

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4 Experimental aspects of neutrino oscillation physics 43

measurement of the mixing angle θ13, free from contamination coming from matter effects and other parameter correlations or degeneracies. They are essentially dominated by statistical and systematic errors. In order to reduce the systematic uncertainties the principle of the new generation of reactor experiment is to use two detectors. One near at about 100 to 200 m from the reactor core and one far at about 1 to 2km. This garantees that the L/E ratio is close to the atmospheric maximum value. The comparison of the measuredν ¯ e between the two sites will cancel part of the systematical uncertainties from the reactor ﬂux and cross sections. The target mass of the two detectors vary from 8 tons to about 100 tons. The real challenge is to be able to reduce the relative normalisation uncertainty below 1%. There are several projects under way. The Double-Chooz experiment is the most advanced one [27]. The far (1km) detector site is constructed and the 11.2 tons detector should start taking data beginning of 2010. The near site (400m) is under construction and will be completed to host a second identical detector in 2011. The full setup should take data in 2011. Figure 4.10 shows the θ13 sensitivity limit as a function of the year which can be obtained by Double-Chooz running in two phases. CL)

% Chooz Excluded (90 13 θ 2

2 -1 OPERA 10 MINOS Sin World limit Double Chooz

T2K

NOνA Daya Bay -2 10 90% CL sensitivity Computed with: δ CP=0 sign(∆m2)=+1

2009 2010 2011 2012 2013 2014 2015 2016 Year

Fig. 4.10. Double CHOOZ prospects for Fig. 4.11. World perspectives for θ13 sensi- θ13 sensitivity limit. tivity limit [29].

The second main project is called Daya Bay [28] and it can be considered as a second generation experiment which is more amibitious since it aims to reduce 2 the systematic uncertainty by a factor 2 and be able to give a limit on sin 2θ13 < 0.01 at 90% CL. The principle will be to use 6 to 10 mobile detectors which can be interchanged to compare their efﬁciencies. The project may start after 2011. Figure 4.11 shows the world limit which can be achieved as a function of time by combining all the experiments which aim to contribute to θ13 measurements. The Double-Chooz, T2K and Daya Bay projects will allow to reduce the limit on 2 sin 2θ13 by more than one order of magnitude in a decade if the angle stays too small to be detected.

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44 D. Duchesneau 4.5 Conclusions and perspectives

The reactor and accelerator experiments are complementary; At the 2016 horizon there should be confirmation of the transition νµ → ντ, more precise measure- 2 ments of θ23 and ∆m31 and more constraints on θ13 if not a discovery. And why not maybe the first indication for mass hierarchy choice. It is the first step to pinpoint the true nature of the leptonic flavour transformation. It will not allow to see CP violation but it will help in defining what should be the path to follow beyond 2015. This next step will be the quest for δCP and precision measurements of the neutrino parameters. The technology and experiments foreseen are various. They include more powerful superbeams of second generation together with BetaBeam coupled to large volume detectors like Megatonne Water cherenkov, liquid argon, liquid scintillator detectors and a facility called Neutrino Factory. Neutrino physics is a very active field. Since 10 years several new results changed our view of the field and comforted us to revise our current knowledge within the Standard Model. A lot of experimental and theoretical challenges are in front of us and worth being pursued.

References

1. W. Pauli’s letter to L. Meitner, Scientiﬁc correspondence with Bohr, Einstein, Heisen- berg, a.o., v.2: 1930-1939, Pauli Archive at CERN. 2. H. Pietschmann, George Marx Memorial Lecture(2005),Inst. Theor. Physics, Univ. Vi- enna, UWThPh2005-8. 3. E. Fermi, La Ricerca Scientiﬁca 4 (II), (1933), 491-495; and Z.Physik, 88 (1934) 161. 4. H. Bethe and R. Peierls, Nature 133 (1934) 532. 5. F. Reines and C. Cowan, Science 124 (1956) 103. 6. G. Danby et al., Phys. Rev. Lett. 9 (1962) 36. 7. M. Schwartz, Physical Review Letters 4 (1960) 306. 8. DONUT Collaboration, K. Kodama et al., Phys. Lett. B504 (2001) 218-224. 9. OPERA Collaboration, R Acquafredda et al JINST 4: P04018 2009. 10. F.J. Hasert et al., Phys. Lett. 46B (1973) 121 and Phys. Lett. 46B (1973) 138. 11. PDG 2008, C. Amsler et al., Phys. Lett. B667, (2008) 1. 12. Precision Electroweak Measurements on the Z Resonance, Phys. Rept. 427 (2006) 257. 13. L.-L. Chau and W.-Y. Keung, Phys. Rev. Lett. 53, 1802 (1984). 14. L. Wolfenstein, Phys. Rev. D 17, 2369 (1978); S. Mikheyev and S. Yu. Smirnov, Nuovo Cimento Soc. Ital. Fis. C 9, 17 (1986). 15. Super-Kamiokande Collaboration, Y. Ashie et al., Phys.Rev. D71 (2005) 112005, hep- ex/0501064. 16. K2K Collaboration, E. Aliu et al., Phys. Rev. Lett. 94 (2005) 081802. 17. SNO Collaboration, Phys. Rev. C 72, 055502 (2005); Phys. Rev. Lett. 101, 111301 (2008). 18. SNO Collaboration, B. Aharmim et al., Phys. Rev. C 75 045502 (2007). 19. Kamland Collaboration, S. Abe et al., Phys.Rev.Lett. 100, 221803 (2008). 20. CHOOZ Collaboration, M. Apollonio et al., Phys. Lett. B466 (1999) 415. 21. G.L. Fogli et al. arXiv:0805.2517v3. 22. Minos Collaboration, P. Adamson et al., Phys.Rev.Lett.101:131802,2008. 23. OPERA Collaboration, R Acquafredda, New Journal of Physics 8 (2006) 303.

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24. M. Sanchez, Initial results on νe appearance in MINOS, Talk given at the Rencontres de Moriond 2009. 25. R. Terri and the T2K Collaboration, Nuclear Physics B - Proc. Suppl. Vol.189 (2009) 277-281. 26. The NOνA Experiment at Fermilab (E929), http://www-nova.fnal.gov/. 27. Double Chooz, A Search for the Neutrino Mixing Angle θ13, arXiv:hep-ex/0606025v4. 28. Daya Bay proposal, http://arxiv.org/abs/hep-ex/0701029. 29. M. Mezzetto, arXiv:0905.2842v1, Workshop on ”Neutrino Telescopes”,Venice, Italy, March 2009.

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School of Particles and Accelerators FIRST IPM MEETING Institute for Research in ON LHCPHYSICS Fundamental Sciences (IPM) VOL. 1, NO. 1 (p. 47) Isfahan, April 20-24, 2009

5 Search for mSUGRA in µs + Jets + E6 T Final State in CMS

A. Fahima,b, F. Moortgatc, L. Papec

a School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran b Sharif University of Technology, Tehran, Iran c ETH Zurich, Zurich, Switzerland

Abstract. A theory of supersymmetry from minimal supergravity (mSUGRA) with R- parity conservation, is considered. The possibility of observing evidence for this theory is reviewed, with the early CMS detector data in ﬁnal states containing one or more muons, multiple jets, and missing transverse energy E6 T . The results are reported for an integrated luminosity of 100 pb−1 and a centre-of-mass energy of 10 TeV. The strategy is based on a cut-based search after optimization of the selection criteria. The study focuses on the LM0 benchmark point of SUSY but results are applied to the other low mass points. The events containing fake E6 T are suppressed in the early stage to reduce the effect of the such E6 T on the optimization procedure.

5.1 Introduction

One of the most promising candidates for new physics beyond the Standard Model is Low energy supersymmetry (SUSY). SUSY predicts the existence of a new particle for each Standard Model (SM) particle. The quantum numbers for each SM particle and its superpartner are the same only differing by half a unit in spin. The mechanism which breaks supersymmetry and yields the superpartners their masses, in the most general form introduces 105 parameters, in addition to the 19 of the SM. Some of them are omitted, as they would induce flavour changing neutral currents (FCNC) or CP violation at an unacceptable level[1]. In the most popular model, inspired from supergravity (mSUSGRA) with radiative E.W. symmetry breaking, it requires only four input parameters and a sign, to determine the low energy Phenomenology from the scale of Grand Unifi- cation: the universal soft breaking mass parameter for all scalars at the unification scale, m0; the common gaugino mass, m1/2; a universal trilinear coupling, A0; the ratio of the vacuum expectation values of the two neutral Higgs fields, tan(β); and the sign of the higgsino mixing mass parameter, sgn(µ). This study concerns a scenario of mSUGRA with conserved R-parity, which guarantees that the lightest supersymmetric particle (LSP) is stable. It also implies that superpartners are produced in pair at colliders. Decay cascades of superpar- ticles always end up with the LSP which has to be neutral and colourless due to

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cosmological constraints. So the generic signature comprises large missing transverse energy 6ET together with other prompt observable objects such as jets and leptons. Many combinations of these input parameters are possible and CMS has chosen several ones to explore phenomenological signatures and scan phase space. Some points and their parameter values are included in Table 5.1. In CMS there are several analyses which have studied mSUGRA in these points and used µs, Jets and E6 T as the signature[2,3].

m0 m1/2 tanβ sgn(µ) A0 σ[pb] LM0 200 160 10 + -400 110 LM1 60 250 10 + 0 16.06 LM2 185 350 35 + 0 2.42 LM3 330 240 20 + 0 11.79 LM4 210 285 10 + 0 6.70 LM5 230 360 10 + 0 1.94 LM6 85 400 10 + 0 1.28 LM7 3000 230 10 + 0 2.90 LM8 500 300 10 + -300 2.86 LM9 1450 175 50 + 0 11.58 LM10 3000 500 10 + 0 6.55

Table 5.1. The CMS benchmark points LMx(low mass)

5.2 Signal Selection and Backgrounds Considered

All Standard Model processes which include at least one µ, several jets and missing transverse energy (E6 T ) in their final state, must be taken into account as background. QCD, top (tt¯) and Electroweak Vector Bosons (W and Z) are more important than others, due to their high cross-section. In Table 5.2, there is a list of processes and their cross-section with the number of events used. QCD is generated in 4 bins from HT 100 GeV to Infinity where HT is the scalar sum of all partons (i.e. Jets from the hard process) and used to show the energy level of objects in the events. In fact, QCD does not intrinsically have the mentioned final state, but owing to its large cross-section, can produce configurations similar to the signal. QCD can produce multiple jets. Energy mis-measurement of these jets, can easily fake a large amount of E6 T missing transverse energy. And also, muons can be faked in several ways such as a hadron misidentified as a muon (punch- through hadrons) or real muons from pion or kaon decays-in-flight (DIF). In the signal study, all the LM (Low Mass) points are considered. Their cross- section and number of events, used in analysis, are listed in Table 5.3. The cross- section of the LM0 point is larger than the others. Therefore this sample is selected for the main study. All calculations and counting are weighted and reported for an integrated luminosity of 100 pb−1 and a centre-of-mass energy of 10 TeV. For a real analysis

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at this luminosity, the number of QCD events are insufﬁcient and therefore this analysis should be repeated later with an adequate number of QCD events.

Dataset σ[pb] Events Dataset σ[pb] Events TT-Jets 317 933644 LM0 110 192686 LM1 16.06 89800, Dataset σ[pb] Events LM2 2.42 129600 Z-Jets 3700 1194819 LM3 11.79 148000 W-Jets 40000 1022758 LM4 6.70 106400 LM5 1.94 165600 Dataset σ[pb] Events LM6 1.28 132400

QCD HT 100to250 15000000 1079000 LM7 2.90 82200 QCD HT 250to500 400000 210000 LM8 2.86 211302 QCD HT 500to1000 14000 1319566 LM9 11.58 195250 QCD HT 1000toInf 370 50000 LM10 6.55 201860 LM11 3.24 208314

Table 5.2. The Standard Model background datasetsTable 5.3. The signal datasets used used for analyses. for analyses.

The physics objects, used in this analysis, are listed in the following. The applied selection criteria are also reported in each object description.

Muons Selection: Identiﬁed Muons [4] are considered and the cuts of pt > 10 GeV and |η| < 2.5 are applied on them. These cuts ensure that the muon candidates are reconstructed with good efﬁciency above the trigger thresholds. Furthermore, a combined relative isolation, RelIso < 0.1 cut, shown in Fig. 5.1, is applied to reduce the fake muons. The isolation value is given by the ratio of the sum of allpET or pt objects ( subtracting the muon ) within a cone 2 2 in η-φ-space of ∆R = ∆η + ∆φ < 0.3 around the muon and the muon pt.

PECal PHCal PTracker ∆R<0.3 ET + ∆R<0.3 ET + ∆R<0.3 pt RelIso = µ < 0.1 pt where the ﬁrst sum runs over transverse energy in the electromagnetic calorimeter, the second sum runs over the transverse energy in the hadronic calorimeter and the third sum runs over the transverse momentum in the tracker within the cone subtracting the muon. Jets Selection: Jets are reconstructed by using an iterative cone algorithm with R = 0.5 [5]. The algorithm is applied on the energy deposited in the calorimeter. The energy of jets is corrected for detector effects [6]. The corrected jets are taken into account with pt > 30 GeV and |η| < 3 which again ensure that the jet candidate is reconstructed with good efﬁciency. E6 T Selection: The Missing Transverse Energy 6ET is calculated by the transverse vector sum over uncorrected energy deposits in the calorimeter [7]. X −→ b b b b E6 T = − (En sin θn cos φni + En sin θn sin φnj) =E6 xi+ E6 yj n i i i i i i

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Fig. 5.1. isolation for µs whose pt > 10 and |η| < 2.5

Fig. 5.2. Number of Jets with pt > 30 and |η| < 3

where the index n runs over all calorimeter input objects. The E6 T is corrected for muon energy deposition and jet energy scale. After imposing these corrections, in the QCD or other processes without highly energetic invisible particles, 6 ET is still expected to be faked by mis-reconstruction of the jets leading to 6 ET parallel to the hardest jets. Therefore the angle between the 6 ET and the hardest jets can be used to discriminate between the real and fake 6 ET . A two dimensional plot of the angle between 6 ET and the second

hardest jet ∆φ2 = ∆φ(jet2E,6 T ) versus the same angle for the ﬁrst hardest jet

∆φ1 = ∆φ(jet1E,6 T ), can show how the 6ET is parallel to the two hardest jets. This plot is prepared for two samples, SUSY (LM0 point) in Fig. 5.3 and QCD in Fig. 5.4. Figure 5.4 shows that the QCD events are gathered more around two points (0, π) and (π, 0) as opposed to SUSY events (Fig. 5.3) which are nearly scattered uniformly. Using this property, we can deﬁne a function Rsum to select the events for which the E6 T is more parallel to the two hardest jets. q q 2 2 2 2 Rsum = ∆φ1 + (∆φ2 − π) + ∆φ2 + (∆φ1 − π)

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5 Search for mSUGRA in µs + Jets + E6 T Final State in CMS 51

Fig. 5.3. ∆φ2 vs. ∆φ1 for SUSY:LM0

Fig. 5.4. ∆φ2 vs. ∆φ1 for QCD. Events gathered mostly in circles centered (0, π) and (π, 0)

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52 A. Fahim, F. Moortgat, L. Pape

Figure 5.5 shows that a crude lower limit on this variable, Rsum > 4.45 suppresses the backgrounds from the fake 6ET . So this cut is applied on the 6ET object.

Fig. 5.5. Rsum for SUSY(LM0), QCD, TTJets and VJets

Event Offline Selection: The Strategy in this analysis is to optimize the selection cuts for the LM0 point. It makes sense to use a simple estimate of the significance S = Ns/σb, for the optimization, where Ns is the number of events from the signal,√ after passing all cuts and σb is the background Poisson uncertainty σb = Nb, neglecting the systematic uncertainties. In the first step, the events including one or more muons and more than three jets are selected. Next, the cuts on pt of the first and second hardest jets are tuned to maximize the significance. The left plot in Fig. 5.6 shows the pt cut of the first jet for signal (LM0) and backgrounds. The right plot in this figure also shows the same for the second jet. The results for this optimization are pt >150 GeV for the first jet and pt > 60 GeV for the second jet. In the last step, a cut on the missing transverse energy 6ET is tuned with the mentioned procedure. The highest significance value is reached by the event selection with E6 T > 130 GeV as is shown in Fig. 31.5.

5.3 Results and Conclusions

The main results of these studies are shown in Table 5.4 and Fig. 5.8 (only for LM0) for an integrated luminosity of 100 pb−1 of data. Figure 5.8 shows that the most of QCD events have no µ in their ﬁnal state (the second bin) and also that they have no more than 3 jets (the third bin). Due to the fake E6 T , the QCD events

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5 Search for mSUGRA in µs + Jets + E6 T Final State in CMS 53

Fig. 5.6. pt of the ﬁrst Jet (left plot) and pt of the second jet (right plot) for the signal (LM0) and the backgrounds

Fig. 5.7. E6 T for the SUSY(LM0) and the backgrounds

are suppressed actually by applying the cut on the Rsum (the fourth bin ). The plot also shows that the effect of the cut on the pt of the second jet, is not very efﬁcient and it can be neglected after more investigation. A summary of the remaining events after each cut for all the signal samples and backgrounds are listed in Table 5.4. After all cuts about 90 events of all considered backgrounds remain. The largest number of remaining events from signal is related to the LM0 point with 260 events and the smallest number is related to LM5 with 7 events. So the selected cuts and their optimization achieve a separation of signal from background with signal to background ratio Ns/Nb from 0.08 for LM5 to 2.89 for LM0 in the inclusive single muon analysis (not included systematic uncertainties).

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54 A. Fahim, F. Moortgat, L. Pape

Fig. 5.8. Results for LM0

Cut / Sample LM11 LM10 LM9 LM8 LM7 LM6 LM5 LM4 All Data 417 606 1,172 211 329 132 166 638 Number of µs 66 106 140 41 49 30 19 74 Number of Jets 32 22 59 30 16 10 9 37 Rsum 29 19 47 26 13 9 8 32 pt of Jet1st 27 13 37 24 12 9 8 30 pt of Jet2nd 27 13 37 24 12 9 8 30 miss ET 24 10 24 20 8 8 7 25

Cut / Sample LM3 LM2 LM1 LM0 TTJets VJets QCD All Data 1,184 259 1,616 10,983 31,744 4,370,381 1,541,436,950 Number of µs 158 30 232 1,580 5,541 944,144 144,347 Number of Jets 96 12 75 752 1,001 339 1,616 Rsum 82 11 66 590 575 156 12 pt of Jet1st 72 11 59 399 194 73 8 pt of Jet2nd 72 11 58 391 188 71 8 miss ET 58 10 52 260 61 24 5

Table 5.4. Results

This study demonstrates that SUSY (mSUGRA) in the LM0 point with de- ﬁned parameters in Table 5.1, can be potentially discovered for 100 pb−1 of data and other low mass points need more integrated luminosity. However it ﬁnal conclussions can only be reached after supplementary work such as:

• taking into account systematic uncertainties. • using sufﬁcient simulated data statistics for the backgrounds. • using data-driven techniques.

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• using more samples of background such as di-vector bosons.

Finally, it implies that some cuts can be neglected, like the pt of the second jet and also it illustrates the effect of the kinematic variable Rsum on the fake E6 T suppression which must be investigated further.

∗ ∗ ∗ I gratefully acknowledge the special efforts of the conference organizers to manage these very nice and stimulating meetings. I would like to thank them for their hospitality during the conference time in Isfahan.

References

1. Rep. Prog. Phys. 69 2843 (2006), L. Pape and D. Treille, Supersymmetry facing experiment: much ado (already) about nothing (yet) 2. CMS NOTE 2006/134, Y. Pakhotin et al., Potential to Discover Supersymmetry in Events √ with Muons, Jets and Missing Energy in pp Collisions at s = 14 TeV with the CMS Detector. 3. CMS NOTE 2008/034, Ph. Biallass et al., Search Strategies for mSUGRA in the Muons + Jets + met Final State 4. CMS Note 2006/010 (2006), E. James et al., Muon Identiﬁcation in CMS 5. CMS PAS JME-07-003 (2008), CMS Collaboration, Performance of Jet Algorithms in CMS 6. CMS PAS JME-07-002 (2007), CMS Collaboration, Plans for Jet Energy Corrections at CMS 7. CMS PAS JME-07-001 (2007), CMS Collaboration, E6 T performance in CMS

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School of Particles and Accelerators FIRST IPM MEETING Institute for Research in ON LHCPHYSICS Fundamental Sciences (IPM) VOL. 1, NO. 1 (p. 57) Isfahan, April 20-24, 2009

6 Investigation of the Ds1 structure via Bc to + − Ds1l l /νν¯ transitions in QCD

M. Ghanaatiana, R. Khosravib

aPhysics Department , Payame Noor University, Iran bPhysics Department , Shiraz University, Shiraz 71454, Iran

P + Abstract. We investigate the structure of the Ds1(2460, 2536)(J = 1 ) mesons via ana- + − lyzing the semileptonic Bc → Ds1l l , l = τ, µ, e and Bc → Ds1νν¯ transitions in the frame work of the three–point QCD sum rules. We consider the Ds1 meson as a conventional cs¯ meson in two ways, the pure |cs¯i state. The obtained results for the form factors are used to evaluate the decay rates and branching ratios. Any future experimental measurement on these form factors as well as decay rates and branching fractions and their comparison with the obtained results in the present work can give considerable information about the structure of this meson.

6.1 Introduction

In this work, taking into account the gluon condensate corrections, we analyze + − the rare semileptonic Bc → Ds1 l l , l = τ, µ, e and Bc → Ds1νν¯ transitions in ∗ ∗ three–point QCD sum rules (3PSR) approach. Note that, the Bc → (D ,Ds,Ds1(24 60))νν¯ transitions have been studied in Ref. [1], but assuming the Ds1 only as cs¯. + − ∗ + − The Bc → Dq l l /νν¯ [2], Bc → Dq l l , (q = d, s) [3] transitions have also been analyzed in the same framework. The heavy Bc meson contains two heavy quarks b and c with different charges. This meson is similar to the charmonium and bottomonium in the spectroscopy, but in contrast to the charmonium and bottomonium, the Bc decays only via weak interaction and has a long lifetime. The study of the Bc transitions are useful for more precise determination of the Cabibbo, Kabayashi, Maskawa (CKM) matrix elements in the weak decays. + − The rare semileptonic Bc → Ds1l l /νν¯ decays occur at loop level by electroweak penguin and weak box diagrams in the standard model (SM) via the ﬂa- vor changing neutral current (FCNC) transition of b → sl+l−. The FCNC decays of Bc meson are sensitive to new physics (NP) contributions to penguin operators. Therefore, the study of such FCNC transitions can improve the information about: • The CP violation, T violation and polarization asymmetries in b → s penguin channels, that occur in weak interactions . • New operators or operators that are subdominant in the SM , • Establishing NP and ﬂavor physics beyond the SM.

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58 M. Ghanaatian, R. Khosravi

To obtain the form factors of the semileptonic Bc → Ds1(2460[2536]) transitions, ﬁrst, we will suppose the Ds1(2460) and Ds1(2536) axial vector mesons as the pure |cs¯i state and calculate the related form factors. Second, we will consider the Ds1 meson as a mixture of two components |Ds11i and |Ds12i states and calculate the form factors of the Bc → Ds11 and Bc → Ds12 transitions. With the help of Eq. (6.1) and the deﬁnition of the form factors which will be presented in the next section, we will derive the transition form factors of Bc → Ds1(2460[2536]) decays as a function of the mixing angle θs. The future experimental study of such rare decays and comparison of the results with the predictions of theoretical calculations can improve the information about the structure of Ds1 meson and the mixing angle θs.

6.2 The form factors of Bc → Ds1 transition in 3PSR

To calculate the form factors within three-point QCD sum rules method, the following three-point correlation functions are used [1,2,3,4]: Z 0 † V−A 2 02 2 2 4 4 −ipx ip y Ds1 V−A Bc Πµν (p , p , q ) = i d xd ye e h0 | T[Jν (y)Jµ (0)J (x)] | 0i, Z 0 † T−PT 2 02 2 2 4 4 −ipx ip y Ds1 T−PT Bc Πµν (p , p , q ) = i d xd ye e h0 | T[Jν (y)Jµ (0)J (x)] | 0i, (6.1)

Ds1 Bc where Jν (y) = cγνγ5s and J (x) = cγ5b are the interpolating currents of the V−A T−PT initial and ﬁnal meson states, respectively. Jµ = sγµ(1 − γ5)b and Jµ = s ν σµνq (1 + γ5)b are the vector-axial vector and tensor-pseudo tensor parts of the transition currents. In QCD sum rules approach, we can obtain the correlation function of Eq. (6.1) in two sides. The phenomenological or physical part is calculated saturating the correlator by a tower of hadrons with the same quantum numbers as interpolating currents. The QCD or theoretical part, on the other side is obtained in terms of the quarks and gluons interacting in the QCD vacuum. To drive the phenomenological part of the correlators given in Eq. (6.1), two complete sets of intermediate states with the same quantum numbers as the currents

JDs1 and JBc are inserted. This procedure leads to the following representations of the above-mentioned correlators:

† D 0 0 V−A Bc h0 | J s1 | Ds1(p , ε)ihDs1(p , ε) | J | Bc(p)ihBc(p) | J | 0i ΠV−A(p2, p 02, q2) = ν µ µν (p 02 − m2 )(p2 − m2 ) Ds1 Bc + higher resonances and continuum states ,

† D 0 0 T−PT Bc h0 | J s1 | Ds1(p , ε)ihDs1(p , ε) | J | Bc(p)ihBc(p) | J | 0i ΠT−PT (p2, p 02, q2) = ν µ µν (p 02 − m2 )(p2 − m2 ) Ds1 Bc + higher resonances and continuum states . (6.2)

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+ − 6 Investigation of the Ds1 structure via Bc to Ds1l l /νν¯ transitions in QCD 59

The following matrix elements are deﬁned in the standard way in terms of the leptonic decay constants of the Ds1 and Bc mesons as:

2 fB m h0 | Jν | D (p 0, ε)i = f m εν , h0 | J | B (p)i = i c Bc . (6.3) Ds1 s1 Ds1 Ds1 Bc c mb + mc To parameterized the matrix elements in terms of the transition form factors considering the Lorentz invariance and parity considerations.

Bc→Ds1 2 0 2AV (q ) ∗ν α 0β hDs1(p , ε) | sγµγ5b | Bc(p)i = εµναβε p p , mBc + mDs1 0 Bc→Ds1 2 ∗ hDs1(p , ε) | sγµb | Bc(p)i = − iA0 (q )(mBc + mDs1 )εµ

Bc→Ds1 2 A1 (q ) ∗ + i (ε p)Pµ mBc + mDs1 Bc→Ds1 2 A2 (q ) ∗ + i (ε p)qµ , mBc + mDs1

0 ν Bc→Ds1 2 ∗ν α 0β hDs1(p , ε) | sσµνq γ5b | Bc(p)i = 2 TV (q ) iεµναβε p p ,

hD (p0, ε) | sσ qνb | B (p)i = T Bc→Ds1 (q2)[ε∗ (m2 − m2 ) − (ε∗p)P ] s1 µν c 0 µ Bc Ds1 µ q2 + T Bc→Ds1 (q2)(ε∗p)[q − P ], 1 µ m2 − m2 µ Bc Ds1 (6.4)

Bc→Ds1 2 Bc→Ds1 2 where Ai (q ), i = V, 0, 1, 2 and Tj (q ), j = V, 0, 1 are the transition 0 0 2 form factors, Pµ = (p + p )µ and qµ = (p − p )µ. Here, q is the momentum transfer squared of the Z boson (photon). In order to our calculations be simple, the following redeﬁnitions of the transition form factors are considered :

Bc→Ds1 2 0 Bc→Ds1 2 2AV (q ) AV (q ) = , mBc + mDs1 0 Bc→Ds1 2 Bc→Ds1 2 A0 (q ) = A0 (q )(mBc + mDs1 ) , Bc→Ds1 2 0 Bc→Ds1 2 A1 (q ) A1 (q ) = − , mBc + mDs1 Bc→Ds1 2 0 Bc→Ds1 2 A2 (q ) A2 (q ) = − , mBc + mDs1 0 Bc→Ds1 2 Bc→Ds1 2 TV (q ) = −2TV (q ) , 0 T Bc→Ds1 (q2) = − T Bc→Ds1 (q2)(m2 − m2 ) , 0 0 Bc Ds1 0 Bc→Ds1 2 Bc→Ds1 2 T1 (q ) = − T1 (q ) . (6.5)

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60 M. Ghanaatian, R. Khosravi

Using Eq. (6.4), Eq. (6.5) and Eq. (6.3) in Eq. (6.2) and performing summation over the polarization of Ds1 meson we obtain:

2 h fB m f m 0 ΠV−A(p2, p 02, q2) = − c Bc Ds1 Ds1 × iA Bc→Ds1 (q2)ε pαp 0β µν 02 2 2 2 V µναβ (mb + mc) (p − m )(p − m ) Ds1 Bc i 0 0 0 Bc→Ds1 2 Bc→Ds1 2 Bc→Ds1 2 + A0 (q )gµν + A1 (q )Pµpν + A2 (q )qµpν + excited states, 2 h fB m f m 0 ΠT−PT (p2, p 02, q2) = − c Bc Ds1 Ds1 × T Bc→Ds1 (q2)ε pαp 0β µν 02 2 2 2 V µναβ (mb + mc) (p − m )(p − m ) Ds1 Bc i 0 0 Bc→Ds1 2 Bc→Ds1 2 − i T0 (q )gµν − i T1 (q )qµpν + excited states. (6.6)

0 0 0 0 0 0 0 To calculate the form factors, AV , A0, A1, A2, TV , T0 and T1, we will choose α 0β V−A α 0β the structures, iεµναβp p , gµν, Pµpν, qµpν, from Πµν and εµναβp p , igµν T−PT and iqµpν from Πµν , respectively. On the QCD side, using the operator product expansion (OPE), we can obtain the correlation function in quark-gluon language in the deep Euclidean re- 2 2 0 2 2 2 gion where p ¿ (mb + mc) , p ¿ (mc + ms). For this aim, the correlators are written as:

V−A 2 02 2 V−A α 0β V−A V−A V−A Πµν (p , p , q ) = i ΠV εµναβp p + Π0 gµν + Π1 Pµpν + Π2 qµpν, T−PT 2 02 2 T−PT α 0β T−PT T−PT Πµν (p , p , q ) = ΠV εµναβp p − i Π0 gµν − i Π1 qµpν, (6.7)

where, each Πi function is deﬁned in terms of the perturbative and non-perturbative parts as:

2 02 2 per 2 02 2 nonper 2 02 2 Πi(p , p , q ) = Πi (p , p , q ) + Πi (p , p , q ) . (6.8)

0 Performing the double Borel transformations over the variables p2 and p 2 on the physical as well as perturbative parts of the correlation functions and equating the coefﬁcients of the selected structures from both sides, the sum rules 0 Bc→Ds1 for the form factors Ai are obtained:

2 ± m2 m Z 0 Z B D s s0 0 c s1 0 B →D (mb + mc) M2 M2 1 0 V−A 0 2 c s1 1 2 Ai = − 2 e e − 2 ds ρi (s, s , q ) f m f m 4π 2 Bc Bc Ds1 Ds1 mc sL 0 ² −s −s D E V−A M2 M2 2 2 αs 2 Ci e 1 e 2 − iM M G , (6.9) 1 2 π 6

0 Bc→Ds1 where i = V, 0, 1, 2 and for form factors Tj , we get

2 ± m2 m Z 0 Z B D s s0 0 c s1 0 B →D (mb + mc) M2 M2 1 0 T−PT 0 2 c s1 1 2 Tj = − 2 e e − 2 ds ρj (s, s , q ) f m f m 4π 2 Bc Bc Ds1 Ds1 mc sL 0 ² −s −s D E CT−PT M2 M2 2 2 αs 2 j e 1 e 2 − iM M G . (6.10) 1 2 π 6

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+ − 6 Investigation of the Ds1 structure via Bc to Ds1l l /νν¯ transitions in QCD 61

0 where j = V, 0, 1. The s0 and s0 are the continuum thresholds in Bc and Ds1 channels, respectively and lower bound sL in the integrals. We calculated the explicit V−A(T−PT) expressions of the coefﬁcients Ci(j) correspond to gluon condensates.

6.3 Numerical analysis

In this section, we present our numerical analysis of the form factors Ai , (i = V, 0, 1, 2) and Tj , (j = V, 0, 1). From the sum rules expressions of the form factors, it is clear that the main input parameters entering the expressions are gluon condensates, elements of the CKM matrix Vtb and Vts, leptonic decay constants 2 2 fBc , fDs1 , fDs11 and fDs12, Borel parameters M1 and M2 as well as the contin- 0 uum thresholds s0 and s0. We choose the values of the condensates (at a ﬁxed renormalization scale of about 1 GeV), leptonic decay constants , CKM matrix elements, quark and meson masses [5,6,7,8,9,10,11,12,13]. First, we would like to consider the Ds1 meson as the pure |cs¯i state. To + − calculate the branching ratios of the Bc → Ds1(2460[2536])l l /νν¯ decays, we

use the total mean life time τBc = (0.46 ± 0.07) ps [13]. Our numerical analysis shows that the contribution of the non-perturbative part (the gluon condensate diagrams ) is about 12% of the total and the main contribution comes from the perturbative part of the form factors. The values for the branching ratio of these decays are obtained as presented in Table 6.1, when only the short distance (SD) effects are considered.

MODS BR MODS BR

−7 −7 Bc → Ds1(2460)νν¯ (3.26 ± 1.10) × 10 Bc → Ds1(2536)νν¯ (2.76 ± 0.88) × 10

+ − −6 + − −6 Bc → Ds1(2460)e e (5.40 ± 1.70) × 10 Bc → Ds1(2536)e e (2.91 ± 0.93) × 10

+ − −6 + − −6 Bc → Ds1(2460)µ µ (2.27 ± 0.95) × 10 Bc → Ds1(2536)µ µ (1.96 ± 0.63) × 10

+ − −8 + − −8 Bc → Ds1(2460)τ τ (1.42 ± 0.45) × 10 Bc → Ds1(2536)τ τ (0.68 ± 0.21) × 10

+ − Table 6.1. The branching ratios of the semileptonic Bc → Ds1(2460)l l /νν¯ and Bc → + − Ds1(2536)l l /νν¯ decays with SD effects.

References

1. K. Azizi, R. Khosravi, V. Bashiry, Eur. Phys. J. C 56, 357, (2008). 2. K. Azizi, R. Khosravi, Phys. Rev. D 78, 036005 (2008). 3. K. Azizi, F. Falahati, V. Bashiry, S. M. Zebarjad, Phys. Rev. D 77, 114024 (2008). 4. N. Ghahramany, R. Khosravi, K. Azizi, Phys. Rev. D 78, 116009 (2008). 5. M. A. Shifman, A. I. Vainshtein, V. I. Zakharov, Nucl. Phys. B 147, 385 (1979).

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62 M. Ghanaatian, R. Khosravi

6. A. Ceccucci, Z. Ligeti,Y. Sakai, PDG, J. Phys. G 33, 139 (2006). 7. A. J. Buras, M. Muenz, Phys. Rev. D 52, 186 (1995). 8. V. Bashiry, K. Azizi, JHEP 0707, 064 (2007). 9. S. Veseli, I. Dunietz, Phys. Rev. D 54, 6803 (1996). 10. P. Colangelo, G. Nardulli, N. Paver, Z. Phys. C 57, 43 (1993). 11. V. V. Kiselev, A. V. Tkabladze, Phys. Rev. D 48, 5208 (1993). 12. T. M. Aliev, O. Yilmaz, Nuovo Cimento. A 105, 827 (1992). 13. C. Amsler et al., Particle Data Group, Phys. Lett. B 667, 1 (2008).

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School of Particles and Accelerators FIRST IPM MEETING Institute for Research in ON LHCPHYSICS Fundamental Sciences (IPM) VOL. 1, NO. 1 (p. 63) Isfahan, April 20-24, 2009

7 Quark-Gluon Plasma Model and Origin of Magic Numbers

M. Ghanaatiana, N.Ghahramanyb

aPhysics Department, Payame Noor University, Iran bPhysics Department, Shiraz University, Shiraz 71454, Iran

Abstract. Using Boltzman distribution in a quark-gluon plasma sample it is possible to obtain all existing magic numbers and their extensions without applying the spin and spin-orbit couplings. In this model it is assumed that in a quark-gluon thermodynamic plasma, quarks have no interactions and they are trying to form nucleons. Considering a lattice for a central quark and the surrounding quarks, using a statistical approach to ﬁnd the maximum number of microstates, the origin of magic numbers is explained and a new magic number is obtained.

7.1 Introduction

There are certain elements in the universe with relative high stability and abun- dance whose neutron or proton numbers are called magic numbers. Historically, their stability and excited energies were first found [1] but the origin of magic numbers remained as a mystery. Of course there are some explanations about these numbers from shell model of nuclei, mainly from observation of apparent similarities between these magic numbers and nucleon numbers that fill the nuclear shells. In nuclear shell model it is assumed that the nucleon is orbiting in a nuclear spherical potential well and the energy gaps between the spectral lines obtained from such potential well correspond to the stability of nuclei. Such correspondence was not accurate enough, therefore several researchers, mainly Maria Goepert Mayer [2] included the effect of spin and spin-orbit coupling in the nuclear Hamiltonian as a perturbation from which new energy gaps were observed in more agreement with the observed magic numbers. Eventually the shell model was built explaining the nuclear structure and position of constituent particles with no satisfactory explanation about the origin of the magic numbers. In this research it is intended to investigate the origin of these magic numbers via quark-gluon plasma media. In this model it is assumed that in a quark-gluon thermodynamic plasma in which the quark have no interaction, quark are trying to form nucleons. If we accept that the stability of a thermodynamical system is obtained when the system is in maximum disorder or maximum number of complexions, then by considering different isolated system containing one central quark and 2, 3, 4, 5, 6, 7 and at most 8 surrounding quarks embracing the central quark, these can find maximum number of microstates that correspond exactly

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64 M. Ghanaatian, N.Ghahramany

to magic numbers. From statistical point of view it will be clear that why it is unlikely to have a central quark with 8 surrounding quarks and therefore very likely to have a central one with 2 or 3 quarks around it.

7.2 Colored quark-gluon plasma and magic numbers

The hot quark-gluon plasma (QGP) exists right after big-bang and by relativistic expansion cool down and change to proton and neutron. In the continued process of expansion, different nuclei are formed (nucleation) via Boltzman equilibrium process [3,4,5,6,7]. These formed nuclei are most stable at magic numbers. We in- tend to investigate how and under what conditions the quarks with color and flavor form proton and neutron and what the origin of magic numbers is in such QGP. It is not intended to describe the quark distribution after the formation of proton which is given in terms of structure functions. If the QGP is considered as a thermodynamical media then it should proceed toward maximum disorder. It should be investigated that how such system approach equilibrium. The thermodynamical state is a stable system with maximum probability state, i.e., the most probable state with maximum number of complexion. Now consider a thermodynamical state of quarks in motion. In such QGP soup the quarks are not absolutely free. This is known from lattice QCD theory [8]. In fact in such QGP soup, the gluons connect to the nearby quarks with a force much weaker than the binding force. The QGP media is assumed as an ideal gas model. In such model consider a quark to be trying to form a nucleon capturing two quarks of different flavor. In such competing space between quarks different nucleon formation cases happen. If there is only two d-quark with no color neighboring the central u-quark, then there is no competition and state ud1d2 is formed. But from standard model each quark have 3 color and d1 and d2 must be of different color say green and blue, therefore two competing cases exist namely, a red u with blue d1 and green d2 or with green d1 and blue d2. So we get number 2 as the first magic number. Now consider that there are three d-quarks neighboring the central u-quark, then there are three cases namely, ud1d2, ud1d3 and ud2d3. If their color is also taken into account, then there are six cases in addition to the previous two cases and we get eight cases to form a proton, i.e., the second magic number. Lets consider four neighboring d-quarks. If only two of them compete, we have 2 cases and if three of them participate in this competition then we have six cases and if all four compete then we get 12 cases. The total number of cases is therefore 2+6+12=20. This is the third magic number. It is interesting to note that in both the spin and spin-orbit coupling interpre- tations to explain magic numbers [9] and numerical explanation of Bagge [10], two separate series were introduced namely,(2,8,20,40,70,112) and (2,6,14,28,50,82 ,126). After the magic number 20, there was a jump from the first series to the second series to obtain number 28. If we consider 5 quarks neighboring the central one, the competition between these 5 quarks in addition to previous ones given us 40 cases which is exactly the fourth number from the first series and for 6 and 7 neighboring quarks 70 and

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7 Quark-Gluon Plasma Model and Origin of Magic Numbers 65

112 cases are obtained and the same historical problem do exist. To resolve this problem in our model, the QGP condition is utilized and ”imposed quarks” are introduced. From lattice QCD theory it is clear that quarks are not free and there exist some weak attractive forces between quarks in QGP soup and that is why it is called a soup. Now suppose there are four d quarks neighboring the central u-quark one as obtained before there are 20 cases competing to form a proton. If each d-quark is considered to be close to its own neighbors. then if for example d is absorbed by it then the closest quark to d which has the strongest attraction force to d will accompany it and participate. Lets call it d0 and this is named as imposed quark. This quark come from the second level, therefore with one imposed quark for 0 0 0 0 each initial 4 d-quarks we have ud1d1 ,ud2d2, ud3d3 and ud4d4 and considering their colors there are 8 cases in addition to the pervious 20 cases, adding to 28 competing states to form a proton. Lets consider ﬁve d-quarks surrounding the central u-quark, then we have twenty new cases in addition to ten imposed cases adding to 50 cases 20+20+10=50, which consist of ud1d2, ud1d3, ud1d4, ud1d5, 0 0 0 0 ud2d3, ud2d4, ud2d5, ud3d4, ud3d5, ud4d5 and ud1d1, ud2d2, ud3d3, ud4d4 0 and ud5d5. Now lets consider six d-quarks around the central u-quark, then we have: 40+30+12=82. For seven d-quarks participating: 70+42+14=126. Eventually for eight d-quarks we get 184 cases. This is a new magic number that is obtained in this model. For more than 8 quarks one has to consider the imposed quarks from the third level and no additional magic number is obtained.

7.3 Conlusion

A quark-gluon plasma soup model is presented based upon Boltzman distribution and an alternative approach is suggested to obtain not only the existing magic numbers exactly but new magic number is introduced. A quark shell structure in the form of cubic lattice is considered to ﬁnd the most probable cases and maximum number of ways that a stable element is formed corresponding to the magic numbers. While work is in progress to understand how exactly the same magic numbers appear in nuclear formation, this paper is intended to provide insight and extended the concept of magic numbers from nuclei to nucleon formation independently.

References

1. W. Elsasser, J. Phys. Radium, 4, 549 (1933). 2. M. G. Mayer, Phys. Rev., Vol. 74, 235 (1948); M. G. Mayer, Phys. Rev., Vol. 75, 1969 (1949); M. G. Mayer, and J. H. D. Jensen, Elementary Theory of Nuclear Shell Structure, John Wiley & Sons, New York, 1955. 3. A. Lefebvre et al, Nuclear Physics, A621, 199 (1997). 4. R. Kippenhahn, and A. Weigert, Stellar Structure and Evolution, Springer, Heidelberg, 1990. 5. F. Osman, N. Ghahramany, and H. Hora, Laser and Particle Beams, 23, 461-466, (2005). 6. H. Hora, Plasma Model for Surface Tension of Nuclei and the Phase Transition to the Quark Plasma, Report CERN-PS/DL-Note-91/05, 1991.

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66 M. Ghanaatian, N.Ghahramany

7. T. Ranscher, J. H. Applegate, J. J. Cowan, F. K. Thielmann, and M. Weiseher, Astrophys. J., 429, 499 (1994). 8. K.G. Wilson, Phys. Rev. D 10, 2445 (1974); K. G. Wilson, rev. Mod. Phys. 55, 583 (1983); K. G. Wilson et al, Phys. Rev. D49, 6720 (1994). 9. O. Haxel, J. H. D. Jensen and H. E. Suess, Zeitscher. f. Physik 128, 295 (1950). 10. E. Bagge, Naturwissenschaften 35, 376 (1948).

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School of Particles and Accelerators FIRST IPM MEETING Institute for Research in ON LHCPHYSICS Fundamental Sciences (IPM) VOL. 1, NO. 1 (p. 67) Isfahan, April 20-24, 2009

8 Review of RHIC results

R. Granier de Cassagnac

Laboratoire Leprince-Ringuet, Ecole´ polytechnique, CNRS-IN2P3, Palaiseau, France

Abstract. The question of mass generation is central to the field and was discussed several time in this conference, from different perspectives. Only 5% of the Universe is made of known objects: essentially baryons, of which masses are themselves not well understood. The Higgs boson should provide mass to the quarks, accounting for only 2% of the total mass of a baryon, while the main 98% arise from quantum chromodynamics (QCD) energy, which binds quarks together. This article is about the reverse process: unbinding the quarks and releasing this energy. QCD indeed predict that if one raises the temperature and/or pressure of baryonic matter, a phase transition should occur leading to the so called quark gluon plasma (QGP). Though such a deconfined state of nuclear matter must have formed the entire Universe during its first microseconds, and may nowadays lie in the core of very dense stars, the only experimental tool we have to study it are heavy ion collisions. Nowadays, the most violent heavy ion collisions available to experimental study occur at the Relativistic Heavy Ion Collider (RHIC) of the Brookhaven National Labo- √ ratory. There, gold ions collide at sNN = 200 GeV. The early and most striking RHIC results were summarised in 2005 by its four experiments, BRAHMS, PHENIX, PHOBOS and STAR, in their so-called white papers [1,2,3,4] that will be largely referenced thereafter. Beyond and after this, a wealth of data has been collected and analysed, providing additional information about the properties of the matter created at RHIC. It is categorically impossible to give a comprehensive review of these results in a 40 minutes talk or a 8 pages report. I have made a selection of the most striking and understandable signatures: jet quenching in section 8.2, partonic collective phenomena in section 8.3, thermal photons in section 8.4, open heavy flavours and quarkonia suppressions in section 8.5. A slightly longer and older version of this review can be found in [5]. Some updates are given here, as well as emphasis on new probes recently made available.

8.1 Energy densities

One of the obvious manifestation of the collision violence is the transverse (i.e. unboosted by the initial parton longitudinal momenta) energy liberated. Measur- ing it allows one to estimate the energy density ε of the medium after a given time τ0, through the Bjorken formula [6]: ε = dET /dy|y=0/τ0AT , where AT is the transverse area of the collision. The four RHIC experiments measure consistent 3 values of dET /dy|y=0 that correspond to an energy density of at least 5 GeV/fm at τ0 = 1 fm/c, and for the most central collisions. The question of the time to be considered is not trivial, but 1 fm/c is a maximum if one cares about the earliest as possible thermalised medium. Indeed, hydrodynamical analyses of collective

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phenomena provide thermalisation times ranging from 0.6 to 1 fm/c, while the formation time is estimated to be 0.35 fm/c and the nucleus-nucleus crossing time is 0.13 fm/c. For a detailed discussion of energy density and time scale estimates, see section 2 of Ref. [2]. What matters here is that the lower energy density estimate is much higher than the threshold for the transition to a quark gluon 3 plasma, as predicted by QCD on the lattice [7]: εc ∼ 1 GeV/fm . This tells us that the matter should be deconﬁned, i.e. made of free quarks and gluons. The following sections review some of the measurements that indicate that it is indeed the case.

8.2 Jet quenching

8.2.1 High transverse momentum suppression

Figure 8.1 is an illustration of the first and most striking QGP signature seen at RHIC, namely the quenching of jets [8,9]. Displayed is, for various particules, the nuclear modification factor RAA defined as the yield of particles seen in A+A collisions, normalised by the same yield from p+p collisions scaled by the average number of binary collisions hNcolli corresponding to the considered centrality: RAA = dNAA/hNcolli×dNpp. Hard processes (high pT particles in particular) are expected to respect such a scaling (RAA = 1). This is indeed the case of the direct photon1 [12] (gray squares), while the corresponding π0 (blue circles) and η (red triangles) are suppressed by a factor of five at large pT , as well as other mesons. This is understood as an energy loss of the scattered partons going through a very dense matter, and producing softened jets and leading (high pT ) particles. This medium is so dense that it cannot be made of individual hadrons, but rather of quarks and gluons. In [13], PHENIX has released π0 modification factors up to 20 GeV/c, and performed a quantitative estimate of the constraints they put +270 on theoretical models. As an example, gluon densities of dNg/dy = 1400−150 are needed to produce such a strong quenching in the model depicted in [14]. High pT suppressions are seen for various particles with various pT reaches and by the four experiments [1,2,3,4]. It gets stronger for more central collisions. Checking that normal nuclear matter cannot induce what is seen in heavy ion collisions is a crucial test for any QGP signature and property. It is usually done through p+A like collisions. Indeed, high pT suppression is not observed in d+Au collisions (in particular for neutral pions [15] to be compared to the ones on Fig. 8.1) where a moderate enhancement is even seen as a function of pT , probably due to multiple scattering of the incoming partons providing additional transverse momentum (the so-called Cronin effect). In any case, the quenching of high pT particles shows that the matter they traverse is dense. 1 PHENIX has released preliminary photons up to 18 GeV/c [10], which start to deviate below unity. As discussed for instance in [11], this can be explained by several phenomena (nucleus to proton isospin difference, EMC effect, or quark energy loss prior to photon emission) which have nothing to do with a QGP.

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2 Au+Au, sNN = 200 GeV γ η AA direct 0-10% 0-10% 0 R 1.8 PHENIX Preliminary π 0-10% (PRL, 101, 232301) 1.6 (p+p)/2 0-5% (PRC, 74, 024904) φ 0-10% ω 0-20% - 1.4 (K++K )/2 0-5% (PRC, 74, 024904) 1.2 0-20% 0-10% 0-5% 1 0.8 0.6 0.4 0.2 0 0 1 2 3 4 5 6 7 8 9 10 p (GeV/c) T Fig. 8.1. Nuclear modiﬁcation factors for photon, π0, η, protons, φ, ω and kaons for central collisions, from the PHENIX experiment.

8.2.2 Azimuthal correlations

Another way to look at jets is to consider back to back high transverse momentum hadron correlations. Figure 8.2 shows the measurements of such correlations for various collision types performed by the STAR experiment and reported in section 4.2 of reference [4]. Displayed are the azimuthal distributions of hadrons around a “trigger” particle of high enough pT to reﬂect the main direction of jets (4 GeV/c for the trigger particle and 2 GeV/c for the others in this example). In p+p collisions (black histogram), one clearly sees particles belonging to both the narrower same (∆φ = 0) and broader opposite (∆φ = π) jets, while in central Au+Au collisions (blue stars) the away-side jet disappears [16]. This is also at- tributed to jet quenching, the away-side jet being absorbed by the dense matter produced at RHIC. As for the high pT suppression we saw in the previous section, this effect is not observed in d+Au collisions (red circles) in which away-side hadrons are clearly distinguishable [17]. Jet-induced hadron production has been further and extensively investigated at RHIC and various effects corroborate the jet quenching hypothesis, among which:

• In Au+Au collisions, the away-side disappearance grows with centrality. In fact, the most peripheral collisions exhibit a very similar away-side pattern as in p+p and d+Au collisions. • The jets emitted in the reaction plane are less suppressed than in the perpendicular direction, where they have more matter to traverse [18,19]. In fact, the high pT (near-side) particles we see in central Au+Au collisions are likely to come from the periphery, the “corona”, of the collision.

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70 R. Granier de Cassagnac ) φ d+Au FTPC-Au 0-20% ∆

) 0.2 φ p+p min. bias ∆

dN/d( Au+Au Central dN/d( 0.1 TRIGGER Trigger 1/N 1/N 0

-1 0 1 2 3 4 ∆ φ (radians) Fig. 8.2. Dihadron azimuthal correlations in p+p, d+Au and Au+Au central collisions, from the STAR experiment.

• By lowering the pT requirements (down to ∼1 GeV/c), one can ﬁnd back the away-side jets [20]. • These weakened away-side jets are depleted at ∆φ = π and exhibit two displaced maxima around ∆φ = π ± 1.1 radians [21,22]. This camel-back or conical-like shape provides insight in the quenched parton interactions with the medium. Various scenarios are proposed, such as radiative loss [23], Cerenkov-likeˇ or Mach-cone emissions [24]. The later allows one to compute an average speed of sound in the medium of cS ∼ 0.45. • Analyses of three particles correlations also exhibit the conical pattern [25]. • The near-side jet exhibits a “ridge” along pseudorapidity (thus perpendicular to the azimuthal structure) that suggests the jets are indeed ﬂowing with the expanding matter [20,22,26].

In brief, these high pT dihadron correlation studies show that the matter is opaque to jets to a ﬁrst approximation, and clearly modifying their remaining structure.

8.2.3 New tools

In addition to all the above, new tools were recently made available, thanks to the statistics accumulation at RHIC:

• The correlation of a jet (or leading hadron) with a high energy photon helps calibrating the jet, since the photon, essentially unmodiﬁed by the medium, should balance its initial transverse momentum. Both PHENIX [27] and STAR [28]

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8 Review of RHIC results 71

have seen away side jets and released preliminary analyses of the so called IAA (or ICP), which is the jet particle yield per photon seen in central A+A collisions with respect to p+p (or peripheral A+A). Though limited by statistics, IAA exhibit a similar suppressions as RAA. • Another long awaited tool was the full reconstruction of jets in a heavy ion collision environment. Reconstructed jets have been shown recently by the STAR [29] and PHENIX [30] experiments, in Au+Au and Cu+Cu collisions respectively. The STAR preliminary result exhibits jet broadening with RAA going from close to unity to much lower values (RAA < 0.1) when varying the radius of the jet reconstruction cone (from R = 0.4 to 0.2).

Both these novel methods should allow, in the near future to derive modiﬁed fragmentation functions.

8.3 Partonic collective behaviour

8.3.1 Elliptic ﬂow and hydrodynamics

Coming back to azimuthal correlation, it is noticeable that for moderate centralities, overlapping colliding nuclei form a transverse almond-shape area. It is then relevant to look at the “elliptic flow” of particles, namely the second Fourier harmonic v2 of the azimuthal distribution: dN/dφ = N0(1 + 2v1 cos(φ) + 2v2 cos(2φ) + ...). Experimentally, v2 happens to be positive, meaning that the particle emission is enhanced in the plane of the reaction (along the smaller axis of the almond) with respect to the out-of-plane emission (along the larger axis). This reflects pressure gradients, i.e. strong interactions, that must exist at the very early stage of the collision to provide more transverse momentum to the emitted hadrons along the shortest axis. Moreover, the rather large values (up to v2 ∼ 20 % for pT = 2 GeV/c) of the elliptic flow measured at RHIC contradict hadronic transport models (for instance accounting for only ∼ 60 % of the observed value [31]). On the opposite, ideal hydrodynamical models (for a list see section 3.5 of reference [2]) that assume a QGP equation of state, a high energy density (² ∼ 20 GeV/fm3) and fast equilibration time (τ from 0.6 to 1 fm/c) fit reasonably well a broad selection of data:

• The transverse momentum dependence of elliptic flow is reproduced up to 2 GeV/c, and properly ordered for various species [32,33], from pions to cas- cades2. 2 2 2 2 • These v2(pT ) scales with the eccentricity (hy i − hx i/hy i + hx i) of the reaction for various collision systems, centralities and energies, underlining the facts that elliptic flow does reflect the very early stage of the reaction and that thermalisation must arise rapidly [34].

2 Being faster, higher pT particles share less the collective behaviour of the bulk, which does not mean they do not see it, since we saw in the previous sections that they are very suppressed by this dense matter they traverse.

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• Hydrodynamics pressure gradients also imply a scaling by the transverse kinetic energy. While this property is veriﬁed for low pT (less than ∼ 1 GeV/c) hadrons, it extends its validity to much higher pT when one divides both v2 and pT by the number n of constituent quarks [34]. This result holds for pions, kaons, protons, Λ, Ξ, but also for the φ mesons [35,36] (of baryonic-level mass) and deuterons [36] (with n = 6), as shown on Fig. 8.3.

π+ + π- (PHENIX) p + p (PHENIX) π0 (PHENIX) Λ + Λ (STAR) 0.15 + K+ + K- (PHENIX) Ξ- + Ξ (STAR) 0 KS (STAR) d (PHENIX Preliminary) φ (STAR)

q 0.1 /n 2 v

0.05

0 0 1 2 3 [m T - m] /nq (GeV)

Fig. 8.3. Scaling of the elliptic ﬂow parameter v2 versus transverse kinetic energy for various particles. Both quantities are divided by the number of consistent quarks.

• The adjunction of even a low viscosity in hydrodynamical models deterio- rates their fits to the data, in particular by moderating v2 as pT grows [37] (departing from ideal hydrodynamics around pT ∼ 1 GeV/c). The matter created at RHIC must then have a very low viscosity and was thus qualified as a “perfect liquid”. • The transverse mass spectra, i.e. the radial flow, are also reproduced by hydrodynamical models (with kinematic freeze-out temperature of ∼ 100 MeV and transverse speed of hβT i ∼ 0.6 for the most central Au+Au collisions [4]). This high degree of collective ideal hydrodynamical behaviours, setting up at very early times and exhibiting a low viscosity, tells us that the matter is strongly interacting, in a liquid-like manner.

8.3.2 Partonic scalings

By mentally unfolding Fig. 8.3, we see that dividing by the number of constituent quarks is crucial to make the elliptic ﬂow parameter v2 to scale with transverse

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8 Review of RHIC results 73

kinetic energy at moderate pT (1 to 2 GeV/c per constituant quark). This is not the first observable to exhibit a strong difference based on the baryonic/mesonic nature of the probe. Indeed, as one can see on Fig. 8.1 the nuclear modification factor RAA also shows a dramatically different pattern between baryons (protons) and mesons (including the φ which is of baryonic-level mass), in the same intermediate pT range. This was also seen by the STAR experiment, for strange particles: the kaons and φ, compared to the Λ, Ω and Ξ baryons (see for instance the central to peripheral ratio of Fig. 15 in [4]). Thus, one relevant property to determine the fate of these intermediate pT particles is their baryonic/mesonic nature. In particular, the baryon peak production is higher and lays at ∼ 3/2 times larger pT than the mesonic one, suggesting that a quark coalescence or recombination mechanism is at play. To test this hypothesis, the p/π+ and p/π− ratios can be studied in detail. Baseline p+p and peripheral Au+Au collisions exhibit very similar patterns, while the p/π ratio is clearly enhanced in the moderate pT range. These particle ratios are equally reproduced by coalescence or recombination approaches [38]. Added to the elliptic flow versus transverse kinetic energy scaling (figure 8.3), and to the partonic strength of jet quenching (Fig. 8.1), this result suggests that the matter is of partonic nature.

8.4 Thermal Radiation

A thermalised matter should emit its own thermal radiation. We saw on Fig. 8.1 that photons are unmodiﬁed by the medium and the nuclear modiﬁcation factor is compatible with unity. This holds for large pT (typically larger than 4 GeV/c), but lower pT photons exhibit an enhancement. On the left part of Fig. 8.4, the bottom curves and points show the p+p photon spectrum (as stars but from PHENIX) compared to NLO pQCD calculation. The upper spectra are from various centrality selection of Au+Au collisions. The dashed lines are derived from the p+p collisions and scaled up by the number of collisions. The lowest pT photons (obtained through an internal conversion method [39]) clearly exhibit an enhancement. Various hydrodynamical models (for a review, see [40]) fairly reproduce the data assuming early (typically at a time of the order of 0.15 to 0.6 fm/c) temperature of 300 to 600 MeV, well above the critical temperature of Tc = 190 MeV provided by lattice QCD [7] as the phase transition boundary to a quark-gluon plasma. We thus see thermal photons that demonstrate that the matter is hot.

8.5 Heavier ﬂavours

8.5.1 Open charm and/or beauty

Being heavier, charm or bottom quarks are produced earlier than the light ﬂavours, and their production yields can be in principle calculated by perturbative QCD. They are thus considered as good probes of the plasma earliest times. As we saw

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4 )

3 10

c 4

-2 AuAu MB x10 1.8 3 10 AA (a) 0-10% central

R Armesto et al. (I) AuAu 0-20% x102 1.6 2 10 1.4 van Hees et al. (II) AuAu 20-40% x10

(mb GeV 3/(2πT) Moore &

3 1.2 10 12/(2πT) Teaney (III) p+p

/dp 1 σ 3 1 0.8

10-1 0.6 ) or Ed

3 0.4 c -2 -2 10 0.2 Au+Au @ sNN = 200 GeV -3 0.2

(GeV 10 3 HF 2 (b) π0

v R , p > 4 GeV/c AA T -4 0.15 minimum bias π0 v , p > 2 GeV/c 10 2 T N/dp 3 e± R , e± vHF -5 AA 2 Ed 10 0.1

-6 10 0.05 PH ENIX 10-7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 8 9 p (GeV/c) p [GeV/c] T T Fig. 8.4. Left: Thermal + perturbative QCD fits to the photon yield in Au+Au collisions, as seen by the PHENIX experiment. The lower points are from p+p collisions and are matched to perturbative QCD only. Right: Heavy flavour decay electrons in-medium behaviour as measured by the PHENIX experiment, compared to π0 and models, quenching in the most central Au+Au collisions on the top, minimum bias elliptic flow on the bottom, both as a function of transverse momentum.

for light quarks, the nuclear modification factors and elliptic flow are good observables of the medium effects on produced particles. The right part of Fig. 8.4 shows both quantities for electrons from heavy flavour decays (blue circles) and π0 (shaded band or red squares), as measured by the PHENIX experiment [41]. It is to be noted that even if the STAR [42] and PHENIX experiments disagree on the charm cross-section, they do agree on v2 and RAA. They both see that high pT heavy quarks3 are quenched by a factor of 5 and that they do exhibit a significant flow (up to 10 %, while pions reach 20 %). As for light flavours, both observables reveal a strong coupling to the medium. These were surprises. Energy loss in a gluon medium was expected to be reduced for heavy quarks. Indeed, in order to reproduce the data, one would need a much higher gluon density than the one required for light flavours (dNg/dy ∼ 3500 versus 1100, neglecting less quenched beauty decays [43]). Various hypotheses are made to reinforce the heavy quark quenching (adjunction of elastic energy loss, change in the charm/beauty ratio, modification of the strong coupling constant. . . ). Another approach is to quantify the medium effects by transport or diffusion coefficients. The models displayed on Fig. 8.4 follow such approaches. With rather high values of these coefficients (qˆ = 14 GeV2/fm in model I) they roughly manage to reproduce the amount of suppression and flow [44,45,46].

3 Note that the low pT (up to 1.5 GeV/c) dominant yield scale with the number of collisions (RAA ∼ 1) as expected.

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It is fair to say that the way the RHIC matter impacts heavy quarks is not perfectly understood yet, but it is also clear that it is strong. To that extend, I will dare to say that the matter is “tough”, tough to understand as well as tough enough to shake the heavy ﬂavours.

8.5.2 Quarkonia suppression

We saw on the right part of Fig. 8.4 that the bulk (low pT ) charm production scales to ﬁrst order with the number of binary collisions (RAA ∼ 1). This forms a good baseline for the study of bound states made of charm-anticharm quarks, the more stable of which being the J/ψ particle. In fact, charmonia were predicted to melt in the QGP, due to Debye screening of the colour charge [47]. Furthermore, J/ψ √ suppression was indeed observed at lower energy ( sNN = 17.3 GeV) by the NA50 experiment [48] and is the main signature that led CERN to claim for the discovery of QGP. It was thus very awaited at RHIC energies. Figure 8.5 shows J/ψ nuclear modiﬁcation factors as measured by the PHENIX experiment [49], for both mid (red circles, |y| < 0.35) and forward rapidity (blue squares, 1.2 < |y| < 2.2), as a function of centrality (given by the number of participants Npart). These results brought two surprises:

• First, the midrapidity result is surprisingly similar to the one observed by the NA50 experiment which also lies close to midrapidity (black crosses, 0 < y < 1). There is no fundamental reason for this to happen since the energy density for a given Npart is higher at RHIC and should further melt quarkonia. • Even more surprising is the fact that, at forward rapidity, J/ψ are further suppressed (by ∼ 40%), while any density induced suppression scenario, such as the Debye screening mentioned above would predict the opposite trend. S AA ±

R NA50, Pb+Pb, 0

1 0.8 0.8 0.6 0.6

0.4 0.4

0.2 NA50, Pb+Pb, 0

Fig. 8.5. J/ψ suppression measured by the PHENIX and NA50 experiments, as a function of centrality, given by the number of participants. Left: nuclear modiﬁcation factor. Right: J/ψ survival probabilities after normal nuclear effects subtraction.

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But one needs to be careful in interpreting these results since J/ψ are known to be suppressed by regular nuclear matter as it is seen in p+A or d+A collisions [48,50]. In order to compare two regimes, one thus first needs to subtract these normal nuclear matter effects. At RHIC, they are poorly constrained by a relatively low statistics d+Au data set. Several methods, summarised in [50], can nevertheless be used to estimate them. The most data-driven one, inspired by [51] is used to obtain the right part of Fig. 8.5. The very large error bar displayed as a box is essentially reflecting the large normal suppression uncertainties. It illustrates that the two surprises mentioned above may be caused by normal effects: anomalous suppression could be different at SPS and RHIC, and similar at forward and rapidity at RHIC. More RHIC d+Au data were very recently released [52] that will help to reduce the normal suppression uncertainty. However, we clearly see that J/ψ are suppressed beyond normal nuclear effects, both at SPS and RHIC (especially at forward rapidity). An alternate scenario was (prematurely) proposed to explain the RHIC rapidity difference. J/ψ could indeed be recreated in the plasma by recombination of independent charm and anticharm quarks (a large variety of recombination or coalescence models exists, see references in [53]). This beautiful idea of reconfine- ment, and thus of deconfinement, unfortunately do not provide very quantitative predictions of the nuclear modification factors (recombination models suffering from the lack of input charm quark distributions). Other observables (pT dependence, elliptic flow, feed-down contributions...) start to be available4 but so far, they do not allow to conclude. However, even if the details of the mechanisms responsible for the exact J/ψ yield at RHIC are not known, we do not need them to reckon that J/ψ do melt beyond normal nuclear effects, at least in the most central collisions. This is a sign that the matter is deconfining. It is to be noted that the era of Υ studies (bb bound states) was recently opened [54,55] and should provide new insights in quarkonia suppression. At present, preliminary result gives RAA < 0.64 with a confidence level of 90% for minimum-bias upsilon-mass dielectrons, while RdA = 0.98 ± 0.32 ± 0.28, and do not allow strong conclusions.

8.6 Conclusions

Even if we have not (yet) observed any sharp change in the behaviour of the Au+Au observables related to the predicted phase transition, nor numbered degrees of freedom, it is clear that the matter produced at RHIC behaves very differently than ordinary hadronic matter. Indeed, we saw that the matter is dense, opaque, strongly interacting, liquid-like, deconﬁning, hot, as well as of partonic nature. It is thus very likely to be formed by deconﬁned quarks and gluons.

References

1. I. Arsene et al. Nucl. Phys. A757 (2005) 1, nucl-ex/0410020.

4 For a comprehensive review on the subject, see [53].

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2. K. Adcox et al. Nucl. Phys. A757 (2005) 184, nucl-ex/0410003. 3. B. B. Back et al. Nucl. Phys. A757 (2005) 28, nucl-ex/0410022. 4. J. Adams et al. Nucl. Phys. A757 (2005) 102, nucl-ex/0501009. 5. R. Granier de Cassagnac. Int. J. Mod. Phys. A22 (2008) 6043, arXiv:0707.0328. 6. J.D. Bjorken. Phys. Rev. D27 (1983) 140. 7. F. Karsch. Lect. Notes Phys. 583 (2002) 209. 8. A. Adare et al. Phys. Rev. Lett. 101 (2008) 232301, arXiv:0801.4020. 9. S. S. Adler et al. Phys. Rev. C75 (2007) 024909, nucl-ex/0611006. 10. T. Isobe. J. Phys. G34 (2007) S1015, nucl-ex/0701040. 11. F. Arleo. JHEP 09 (2006) 015, hep-ph/0601075. 12. S. S. Adler et al. Phys. Rev. Lett. 94 (2005) 232301, nucl-ex/0503003. 13. A. Adare et al. Phys. Rev. C77 (2008) 064907, 0801.1665. 14. I. Vitev and M. Gyulassy. Phys. Rev. Lett. 89 (2002) 252301, hep-ph/0209161. 15. S. S. Adler et al. Phys. Rev. Lett. 91 (2003) 072303, nucl-ex/0306021. 16. C. Adler et al. Phys. Rev. Lett. 90 (2003) 082302, nucl-ex/0210033. 17. J. Adams et al. Phys. Rev. Lett. 91 (2003) 072304, nucl-ex/0306024. 18. J. Adams et al. Phys. Rev. Lett. 93 (2004) 252301, nucl-ex/0407007. 19. S. Afanasiev et al. submitted to Phys. Rev. C. 20. J. Adams et al. Phys. Rev. Lett. 95 (2005) 152301, nucl-ex/0501016. 21. S. S. Adler et al. Phys. Rev. Lett. 97 (2006) 052301, nucl-ex/0507004. 22. A. Adare et al. Phys. Rev. C78 (2008) 014901, arXiv:0801.4545. 23. A. D. Polosa and C. A. Salgado. Phys. Rev. C75 (2007) 041901, hep-ph/0607295. 24. J. Ruppert and B. Muller. Phys. Lett. B618 (2005) 123, hep-ph/0503158. 25. B. I. Abelev et al. Phys. Rev. Lett. 102 (2009) 052302, arXiv:0805.0622. 26. J. Adams et al. Phys. Rev. C73 (2006) 064907, nucl-ex/0411003. 27. A. Adare et al. submitted to Phys. Rev. C., arXiv:0903.3399. 28. A. M. Hamed (for the STAR collaboration). arXiv:0907.4523. 29. M. Ploskon (for the STAR collaboration). arXiv:0908.1799. 30. Y.-S. Lai (for the PHENIX collaboration). arXiv:0907.4725. 31. X.-L. Zhu et al. Phys. Rev. C72 (2005) 064911, nucl-th/0509081. 32. S. S. Adler et al. Phys. Rev. Lett. 91 (2003) 182301, nucl-ex/0305013. 33. P. Huovinen et al. Phys. Lett. B503 (2001) 58-64, hep-ph/0101136. 34. A. Adare et al. Phys. Rev. Lett. 98 (2007) 162301, nucl-ex/0608033. 35. B. I. Abelev et al. Phys. Rev. Lett. 99 (2007) 112301, nucl-ex/0703033. 36. S. Afanasiev et al. Phys. Rev. Lett. 99 (2007) 052301, nucl-ex/0703024. 37. D. Teaney. Phys. Rev. C68 (2003) 034913, nucl-th/0301099. 38. B. I. Abelev et al. Phys. Rev. Lett. 97 (2006) 152301, nucl-ex/0606003. 39. A. Adare et al. submitted to Phys. Rev. Lett., arXiv:0804.4168. 40. D. d’Enterria and D. Peressounko. Eur. Phys. J. C46 (2006) 451, nucl-th/0503054. 41. A. Adare et al. Phys. Rev. Lett. 98 (2007) 172301, nucl-ex/0611018. 42. B. I. Abelev et al. Phys. Rev. Lett. 98 (2007) 192301, nucl-ex/0607012. 43. M. Djordjevic et al. Phys. Lett. B632 (2006) 81, nucl-th/0507019. 44. N. Armesto et al. Phys. Lett. B637 (2006) 362-366, hep-ph/0511257. 45. H. van Hees, V. Greco, and R. Rapp. Phys. Rev. C73 (2006) 034913, nucl-th/0508055. 46. G. D. Moore and D. Teaney. Phys. Rev. C71 (2005) 064904, hep-ph/0412346. 47. T. Matsui and H. Satz. Phys. Lett. B178 (1986) 416. 48. B. Alessandro et al. Eur. Phys. J. C39 (2005) 335, hep-ex/0412036. 49. A. Adare et al. Phys. Rev. Lett. 98 (2007) 232201, nucl-ex/0611020. 50. A. Adare et al. Phys. Rev. C77 (2008) 024912, Erratum-ibid. C79 (2009) 059901, arXiv:0711.3917. 51. R. Granier de Cassagnac. J. Phys. G34 (2007) S955, hep-ph/0701222.

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52. C.-L. da Silva (for the PHENIX collaboration). arXiv:0907.4696. 53. R. Granier de Cassagnac. J. Phys. G35 (2008) 104023, arXiv:0806.0046. 54. E.-T. Atomssa (for the PHENIX collaboration). arXiv:0907.4787. 55. H. Liu (for the STAR collaboration). arXiv:0907.4538.

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School of Particles and Accelerators FIRST IPM MEETING Institute for Research in ON LHCPHYSICS Fundamental Sciences (IPM) VOL. 1, NO. 1 (p. 79) Isfahan, April 20-24, 2009

9 Measurement of top-quark pair-production with 10 pb-1 of CMS data

A. Jafari

School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran

Abstract. The plan for the observation of top-quark signal in the µ+jet channel with the ﬁrst LHC data is reported. Accounting jets, missing transverse energy and a high transverse momentum muon, a robust event selection is developed. The non-ideal detector condition in the phase of early data taking is considered. It is shown that a clear top-quark signal can be observed in this channel already with 10 pb-1 of integrated luminosity at √ s = 14 TeV.

9.1 Introduction

Thanks to the large top-quark pair production at the LHC, top-quark signal can be established with the CMS experiment [1] at fairly low integrated luminosities. Top-quark events contain most of the experimental signatures which need to be well-understood for a successful commissioning in CMS. Moreover, top-quark pairs are very useful for calibration. The identification efficiency of the jets originating from a b-quark, ( b-jets ), together with the jet energy scale can be extracted from the t¯t events [2,3]. The CMS collaboration is well prepared with a rich top- quark physics program to measure the top-quark mass and cross section more accurately, as well as to use the t¯t events as a powerful calibration tool. This report is based on CMS PAS TOP-08-005 [4], in which the potential of the CMS detector to establish a top-quark signal with first 10 pb-1 of LHC data, is addressed. For the channel of study - the semi-leptonic muon channel - the experimental signatures are missing transverse energy ( MET ), at least four jets and an isolated, high PT muon. The goal is to identify top-quark pairs with the lowest possible integrated luminosity using a simple robust selection. Advanced methods like the neural network and likelihood ratio are not used. Neither is the b-jet identification applied. The conditions of the early phase of data taking, such as the non-optimal alignment of the silicon tracker and the muon detector, in addition to the non-optimal calibration of the calorimeters, are taken in to account in the simulation.

9.2 Main Physics Backgrounds

The production of the W boson associated with extra jets is the main source of background when the W decays leptonically. Another source of background is

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the Z boson production, plus extra jets. If the Z boson decays in to two leptons, and one of them is not reconstructed or is out of the acceptance range ( |η| < 2.4 ), the event signature will be very similar to t¯t. Finally, with several jets and a lepton passing the selection cuts, QCD multi-jet events are a significant source of background. The lepton can be either a real lepton, e.g. coming from the semi-leptonic decays of hadrons containing b and c quarks, or an isolated fake lepton. Comparing with the other sources of backgrounds, QCD is more challenging as it is difficult to be modelled by Monte Carlo simulation and it needs to be determined by data. As most of the QCD events are rejected after the selection, events in the tail of distributions will play an important role. Needless to say that the tail of the distribution is very sensitive to the details of the simulation. In the absence of data, simulation can give only an estimation of the size of this background. The QCD sample is pre-filtered by requiring a muon with PT > 15 GeV using the generator level information.

9.3 Event Reconstruction and Selection

A muon candidate is defined as a muon track segment in the muon chamber, matched with a track reconstructed in the silicon tracker. A jet candidate is reconstructed using the IterativeCone jet algorithm, with the radius of R = 0.5, using calorimeter towers as input [5]. • Offline pre-selection Having been accepted by the non-isolated single muon trigger, each event is requested to have a reconstructed muon with PT > 20 GeV and at least one jet with un-calibrated ET > 30 GeV in offline pre-selection level. • Loose selection At loose selection level, exactly one muon candidate, isolated in the tracker tracker with PT > 30 GeV, is required. The tracker isolation variable, PT,iso , is the sum of the PT of all tracks within R < 0.3 around the lepton direction, excluding the lepton track itself. Similarly, the isolation variable in the calorimeter, calo E iso, is defined as the sum of the energy of all calorimetric towers inside a cone of size R = 0.3 around the lepton direction, excluding the energy deposit of the lepton in the calorimeter. The cut on PT will reduce the backgrounds with fake muons ( e.g. QCD ). On the other hand, asking for exactly one muon will reject di-leptonic backgrounds. Furthermore, this muon should have |η| < 2.1 to be in the tracker acceptance region of the muon trigger. The other criterion for the event to be selected is to have at least four jets within |η| < 2.4. It guaranties the jet to be in the tracker acceptance region for the possible b-jet identification. An extra requirement for the jet with the highest transverse energy, is ET > 65 GeV while the other jets should have ET > 40 GeV. The cut on the hardest jet is applied to be safe, with respect to the pre-selection requirement Figure 9.1 shows the distributions for 10 pb-1 after the loose selection. The results of this selection are listed in Table9.1.

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Table 9.1. Number of events after per-selection and loose selection t¯t (signal) t¯t (others) W+Jets Z+Jets QCD S/B(QCD) S/B Pre-selection 749 527 7474 1430 − − − 4 Jets PT > 65/40/40/40 GeV 236 135 83 16 − − − 1 Muon PT > 30 GeV 163 32 57 8 110 1.48 0.79

Fig. 9.1. Jet multiplicity (top left), missing transverse energy (top right), transverse energy sum of all jets and the muon, HT , (bottom left), and muon transverse momentum ( bottom right ), presented for the loose selection. Here and in the following ﬁgures, the event numbers are normalized to 10 pb-1 of integrated luminosity. The pseudo data corresponds to a Poissonian smeared distribution which is obtained from the summed MC distribution.

Table 9.2. Different scenarios to improve signal over QCD background ratio t¯t (signal) t¯t (others) W+Jets Z+Jets QCD S/B(QCD) S/B MET > 20 GeV 151 31 53 7 91 1.66 0.83 MET > 30 GeV 138 29 47 6 76 1.82 0.87 MET > 60 GeV 87 23 28 2 29 3.04 1.07 HT > 300 GeV 153 30 54 8 50 3.09 1.08 HT > 400 GeV 104 22 39 6 14 7.27 1.27 µ PT > 40 GeV 131 24 46 9 32 4.11 1.18 PT , 4jet > 50 GeV 94 19 27 4 20 4.76 1.35 tracker PT,iso < 0.5 GeV 134 26 47 7 61 2.22 0.95 calo E iso < 3 GeV 157 30 55 8 56 2.79 1.04 calo E iso < 1 GeV 131 25 47 7 17 7.91 1.37 dRmin > 0.5 152 30 52 8 44 3.44 1.14 dRmin > 0.3 159 31 54 8 48 3.28 1.12 calo dRmin > 0.3, E iso < 1 GeV 128 25 45 7 11 11.62 1.47

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• Further QCD Rejection To reject more QCD background, many variables and scenarios such as tighter cuts on the lepton, cuts on the missing transverse energy, etc., were studied and each could give an improvement in the signal to QCD background ratio ( Table 9.2 ). It seems that asking for lepton isolation in the calorimeter ( Ecaloiso < 1 GeV ) together with a good separation between muon and the nearest jet in rφ plane, is very effective as it improves the signal to background ratio, to 11.6 and rejects only 20% of signal events. It should be mentioned that as it is currently not known how large the uncertainties on the shapes and normalizations of the various backgrounds are, no uncertainty of such backgrounds is quoted.

9.4 Data Driven Methods to Reject QCD

While for W/Z +jets backgrounds, shapes can be taken from the simulation, and their normalization can be ﬁxed with a control data sample at low jet bins, the QCD background will have to be mostly determined from data. So, data driven background estimation is indispensable. In CMS, several methods and approaches are under study to estimate the QCD background. As an example, the ABCD matrix method is explained here. A brief review of other methods, like the template ﬁt method and the fake rate method, can be found in [4].

• ABCD Matrix method Two variables,V1 and V2, that characterize signal and QCD background, are selected. They are assumed to be uncorrelated in QCD. In a bi-dimensional plot, there should be one signal dominated region. The other regions are QCD dominated (Fig. 9.2). Deﬁning E1(2) as the event of passing the cut on V1(2), one can deduce

P(E1 | E2) = P(E1) by considering no correlation between two variables in QCD. It means that for the QCD background,

QCD QCD QCD NC NC +NB QCD QCD = QCD QCD QCD QCD NC +ND NA +NC +NB +ND As regions A, B and D are QCD background dominated, one can approximate the total number of events there as the number of QCD events, i.e. QCD all ND(A,B) = ND(A,B). Therefore, after a simple manipulation, the equation above will reduce to

all QCD NB all NC = all ND NA

QCD where NC is the estimated number of QCD events in the signal region. The method is usually used in more complicated ways while the main concept is the same. There are also tricks to check the method stability and the weak correlation between variables.

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Fig. 9.2. A typical bi-dimensional plot for ABCD matrix method. Background ( left ) and Signal ( right )

9.5 Results

To present the results of the final selection, described in the previous sections, M3 distribution can be used to verify that indeed t¯t events are selected, ( Fig.9.3 ). To find the so-called M3 variable, which carries the top-quark mass information, the vectorially summed transverse momentum of any combination of three jets, is calculated. The combination with the highest summed transverse energy is deemed to come from the hadronic decay of top-quark. M3 is the invariant mass of these three jets. In Fig. 9.3, a clear peak can be observed around the nominal top-quark mass value. The shift of the peak from the expected value of 175 GeV, comes from firstly the non-optimal calibration introduced in the hadronic calorimeter and secondly, the jet energy scale correction applied on the ( quark induced ) jets. This correction is obtained from QCD di-jet events that also contain gluon jets for which the response is different. The width of the observed peak is due to the jet energy resolution. Furthermore, one or more of the selected jets, may not come from the hadronic decay of top-quark.

Fig. 9.3. M3: Invariant Mass of 3 jets with highest summed ET

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84 A. Jafari 9.6 Conclusions

CMS is well prepared for examining at the first top-quark events. Methods to estimate QCD background from data are under study, to be ready for the LHC collisions. t¯t signal can be established in first 10 pb-1 of CMS data. In the presented study, after the final selection cuts, 128 t¯t signal events are expected, corresponding to the selection efficiency of 10.3%. Signal events are accompanied by 25 other t¯t final state events and 45(7) W(Z)+jet events. The number of QCD events is estimated 11 with a large uncertainty.

***

The author would like to thank all CMS collaboration involved in the development of this analysis.

References

1. CMS Collaboration, ”The CMS experiment at the CERN LHC”, JINST 3:S08004, 2008. 2. S. Lowette, J. D’Hondt, J. Heyninck, and P. Vanlaer, ”Offline Calibration of b-Jet Identifica- tion Efficiencies”, CMS Note 2006/013 (2006). 3. CMS collaboration, ”Measurement of jet energy scale corrections using top quark events”,CMS PAS TOP-07-004 (2008). 4. CMS collaboration, ”Observability of Top Quark Pair Production in the Semi-leptonic Muon Channel with the first 10 pb-1of CMS Data”, CMS PAS TOP-08-005 (2008). 5. CMS collaboration, ”Performance of Jet Algorithms in CMS”, CMS PAS JME-07-003 (2008).

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School of Particles and Accelerators FIRST IPM MEETING Institute for Research in ON LHCPHYSICS Fundamental Sciences (IPM) VOL. 1, NO. 1 (p. 85) Isfahan, April 20-24, 2009

10 Hadron and Very-Forward Calorimetry in CMS

M. Kaya

Kafkas University, Kars, Turkey

Abstract. The CMS Hadron Calorimeter (HCAL) and the very forward calorimeters are essential part of the CMS detector system. HCAL is crucial for many new physics discoveries. In this report we describe these calorimeters and to give some test beam results.

10.1 Introduction

CMS detector system designed to search wide range of physics such as Higgs Boson, Supersymetric particles, new massive vector bosons, extra dimensions, Heavy-ion physics and many more. The detector requirements for CMS to meet this physics programme are well planned and designed. The overall dimensions of the CMS detector are a length of 21.6 m, a diameter of 14.6 m and a total weight of 12500 tons. The thickness of the detector in radiation lengths is greater than 25 X0 for the ECAL, and the thickness in interaction lengths varies from 7-11λI for HCAL depending on η[1]. More than 90 percent of the CMS detector system is completed and lowered the underground in 2008. In 2009 rest of the detector is ﬁnished and lowered. The whole system will be ready for the October 2009 beam collision. From 2008 till now the CMS is getting data from the cosmic particles mostly muons. Cosmic data are used mostly for the background study and detector calibration. The CMS detector is organized into specialized subdetectors that are Magnet, Muon system, Electromagnetic Calorimeter, Hadron Calorimeter and Inner Tracking Sys- tem. In this proceeding we will mainly concentrate on the hadron calorimeter and very forward calorimeter. The hadron calorimeter (HCAL) plays an important role in discovering new particles and physics at the LHC. The HCAL measures the timing and energy of hadronic showers, as well as their angle and position, needed for the generation of level-1 trigger primitives, the high level trigger, and ofﬂine reconstruction of jets and missing transverse energy [2,3,4]. Hadron calorimeters will be used to study mainly jet physics, since without jets there won’t be any new physics at all. Especially to measure the Higgs particle HCAL is the dominant calorimeter.

10.2 Hadron Calorimetry

Hadron calorimeters (HCAL) consist of several parts. The HCAL is organized into barrel (HB and HO), endcap (HE) and forward (HF) sections. It consists of 11

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separate physical pieces. The positive and negative barrels : HB+ and HB-. The positive and negative endcaps: HE+ and HE-. The positive and negative forward calorimeters: HF+ and HF-. The five rings of the outer HCAL: HO2-, HO1-, HO0, HO1+, and HO2+. The HB, HO and HE calorimeters have a similar structures. They all made of C26000 cartrige brass (70% Cu and 30% Zn ) as a passive material and plastic scintillator(3.7 mm SCSN81 from Kuraray and 1.0 cm BC408 from Bicron) tiles as active regions. Light emission from the tiles is in the blue violet, with wavelength in the range λ = 410-425 nm. This light is absorbed by the wave length shifting fibers which fluoresce in the green at λ= 490 nm. The green, waveshifted light is conveyed via clear fiber waveguides to photodetectors. The individual tiles of scintillator are machined to a size of ∆ηx∆φ=0.087x0.087 and instrumented with a single wave length shifting fibers [5]. The HF calorimeters are made of quartz fibers embeded into steel plates.

10.2.1 Hadronic barel (HB)

Fig. 10.1. Pictures of 200 HB wedges (left). Each wedges segmented into four azimuthal angle (∆φ=50 ) (right) .

The HB is divided into two half-barrel sections, each half-section being inserted from either end of the barrel cryostat of the super-conducting solenoid magnet that carries 4T magnetic ﬁeld. Each half-barrel sections consists of 18 identical azimuthal wedges (∆φ = 200) (see Fig. 10.1 (left) ) and each wedge which weighs 26 tones is segmented into four azimuthal angle (∆φ = 50 ) sectors (see Fig. 10.1 (right) ). The wedges composed of ﬂat brass alloy absorber plates parallel to the beam axis. The innermost and outermost absorbers are made of stainless steel for struc- tural strength. 17 active plastic scintillator tiles inserted between the steel and brass absorber plates[5].

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µ response The calorimeter is an excellent device to identify muons. Figure 10.2 shows the response of 150 GeV/c muons in the HB using η × φ = 3 × 3 HB tower structure. Since the noise in a single tower of the HB is equivalent to 0.2 GeV, this calorimeter system is a perfect device for identifying single isolated muons. The HB front-end electronics is also designed to generate an isolated muon trigger based on this capability. Using the 50 GeV/c electron calibration, the mean energy deposited by a 150 GeV/c muon is 2.4± 0.1 GeV (see Fig. 10.2)[6].

Fig. 10.2. The HB signal distribution for 150 GeV/c µ- from tower 4 (η = 0.3). The solid curve represents a ﬁt using combined Gaussian and Landau distributions [6]

10.2.2 Hadronic Outer (HO)

Since the barrel HCAL inside the coil is not sufficiently thick to contain all the energy of high energy showers, additional scintillation layers (HO) are placed just outside the magnet cryostat. The HO scintillator tiles are divided into quad- rants, each with light collection a wave-length shifting (WLS) optical fiber. The full depth of the combined HB and HO is app. 11 λI. 1 cm thick Bicron BC408 scintillator tiles are used. Each tile is read out with 4 WLS fibers of 0.94 mm diameter, one in each quadrant of the tile. As can be seen from the Fig. 10.3 the WLS fibers are placed in groves which follow the boundary of each quadrant. The HO system is divided into six sections that follow the division of the barrel muon system. Ring 0 (+ and -) are in the central muon system and are composed of two layers of scintillators one immediately outside of the magnet cryostat and the other layer after a 28 cm thick iron layer. Ring 0 in the muon barrel system YB0 (the central part of CMS) covers the |η| range of 0 to 0.35. Rings -2, -1, +1 and +2 are single layer scintillators inserted in the muon barrel systems YB1 and YB2 on both positive and negative sides of CMS immediately inside the first muon iron layer covering the |η| range of 0.35 to 1.2. Scintillation light from the tiles is collected using multi-clad Y11 Kuraray wave-length shifting fibres, of diameter 0.94 mm, and transported to the photo

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Fig. 10.3. Bicron sintillator tiles with WLS Fig. 10.4. HO sectors from H2 test Beam ﬁbers

detectors located on the structure of the return yoke by splicing a multi-clad Ku- raray clear ﬁbre (also of 0.94 mm diameter) with the WLS ﬁbre. HO detector system took data from the H2 test beam area and the setup is shown in Fig. 10.4 and the results can be summarized as follows. The HO trays were calibrated using the radioactive wire source test as well as by exposing them to a beam of muons. The operating voltage of the HPD for the HO readout was 8 kV and 10 kV. For the muon runs, the high voltage for the HPD was 10 kV. Separate data sets were collected for the two settings. the calibration constants obtained with these two sets of data for source and 150 GeV/c muon signal is shown in Fig. 10.5 [7]. Figure 10.6 shows two different energy distribution from the 300 GeV pion beam. One is the EB+HB in the beam and the other is the EB + HB + HO in the beam. The measured energy distribution which HO included is more symmetric and smaller width above the 100 GeV beam energy [7].

Fig. 10.5. Calibration constant from muon Fig. 10.6. Energy distribution for a 300 signal plotted against the corresponding GeV pion beam measured with EB + value from the wire source analysis HB(long tail) and with EB + HB + HO(symmetric one).

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10.2.3 Hadronic Endcap (HE)

The hadron calorimeter endcaps cover the rapidity range, 1.3 < |η| <3 a region containing about 34% of the particles produced in the ﬁnal state. The endcaps that weighs 300 tons are inserted into the ends of a 4T solenoidal magnet and attached to the muon end cap yoke as shown in Fig. 10.7.

Fig. 10.7. HE calorimeter at the CMS

The total number of tiles and trays for both HE calorimeter is 20916 and 1368 respectively. The Megatiles are large sheets of plastic scintillator which are subdivided into component scintillator tiles to provide for reconstruction of hadronic showers. Scintillation signals from the megatiles are detected using waveshifting ﬁbers [4].

10.2.4 Forward Hadron Calorimeter (HF)

HF covers a large pseudorapidity range, 3 < |η| <5, and thus significantly improve jet detection and the missing transverse energy resolution which are essential in top quark production studies, Standard Model Higgs, and all SUSY particle searches. Higgs boson production through weak boson fusion as a potential Higgs discovery channel requires identification of high energy quark jets by the forward calorimeters. HF is also an optical device, but a Cherenkov light device, sitting in a very high radiation environment. The Cherenkov light is produced and transmitted via quartz fibers to photomultipliers. The entire electronics and calibration chain for HF is similar/identical to that of HB. The HF calorimeter is based on steel absorber with embedded fused-silica-core and polymer hard- clad optical fibers. The fiber diameter is roughly 0.6 mm and the wire spacing is 5 mm. Half a million of fiber are read out by 1728 Phototubes (PMT). The Front face is located at 11.2 m from the interaction point. HF consists of two different fiber length, Electromagnetic (EM) 165 cm long and Hadronic (HAD) 143cm

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long. Light is generated by Cherenkov effect in quartz ﬁbers sensitive to relativistic charged particles (Compton electrons...). Amount of collected light depends on the angle between the particle path and the ﬁber axis. Figure 10.8 shows the internal structure of the HF wedges and Fig. 10.9 shows the completed form of the HF calorimeters[8].

Fig. 10.8. Fiber view Fig. 10.9. Completed HF

Magnetic Field Effect on HF 3 different measurements have been done in various magnetic field on the HF. First Fringe Field at HF ROBoxes is measured. The results is as expected which increases to 100 Gauss at 4 tesla. Second LED signal is measured at the magnetic field and the stability of LED(B)/LED(0) is app 1 which tells us PTMs are well shielded. Special fibers are inserted inside the HF to measure radiation damage called Raddam. Last test was made with Raddam which Stability of RADDAM(B)/RADDAM(0) is ∼1. RADDAM Fibers are not damaged through B field ramp-up/down, see Fig. 10.10.

Fig. 10.10. Magnetic Field effect on HF

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10 Hadron and Very-Forward Calorimetry in CMS 91

HF Light Leak Study For the normal pedestal runs we expect a signal just sitting on the pedestal region but sometimes we are getting an unwanted signal besides pedestal. This signal can be one or more single photoelectron (spe) peak. This is called light leak. For instance at the Fig. 10.11 (top, left) there are two different signals, the highest one is the pedestal the lower one is the spe which is light leak. After doing several test regarding light leak study we discovered couple of bad source connectors which allows the light to penetrate through inside. The another possible source of light leak was on the open surface of HF (see Fig. 10.9 bottom, left). After painting black at the open surfaces and closing the HF removed the light leaks from the detector.

Fig. 10.11. HF light Leak Study

Signal Timing on HF One of the unique features of the HF response is its speed. The deeper shower signals do reach the PMTs earlier because of the fact that the generated light travels shorter (ﬁber) distance. The difference between the electromagnetic (tEM max is 15 cm) and the hadronic (tHAD max is 32 cm) shower maxima is about 17 cm, which corresponds to ∼ 1 ns time difference between the arrivals of electron and pion signals to the PMTs[8]. 2004 test beam result is shown on Fig. 10.12.

10.3 Very Forward Calorimetry

10.3.1 CASTOR (Centauro And STrange Object Research)

The detector will contribute mainly to forward QCD studies (diffractive, low-x) and cosmic rays-related physics in both proton-proton and heavy-ion collisions at the LHC energies. In a heavy ion collisions it will search for the exotic particles. The calorimeter is located behind the HF calorimeter. CASTOR has 14 azimuthal

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Fig. 10.12. The peak position of pulses from 100 GeV electrons is app 1 ns later compared to that of pions at the same energy. The average distance between electromagnetic and hadronic shower maxima is ∼ 17 cm (2004 test beam results)[8].

sectors (semi-octants) which are mechanically organized in two half calorimeters which are made of tungsten plate and quartz plates of 4 mm thickness. CASTOR is 1.5 m long (10 λI ) and it’s radius changing from 3.7cm to 14cm around beam pipe. Full view of the detector can be seen from the Fig. 10.13 and Fig. 10.14. Sampling calorimeter with tungsten and quartz is covered of pseudo-rapidity of 5.2<η<6.6. CASTOR extends the rapidity coverage in the forward region by one and a half unity. Cherenkov light read out by PMTs electronic chain handles pulses for every bunch crossing. Magnetic ﬁeld in the CASTOR measured to be 0.1T - 0.16T. Mesh type of PMTs are used at the CASTOR [9].

Fig. 10.13. Place of CASTOR at the CMS Fig. 10.14. View of two half wadges

A full length prototype of castor has been tested during the 2007 summer test beam. To get the energy resolution full energy scan has been performed using 10, 30, 50, 80, 100, 120, 150, 180 and 200 GeV/c electron beam and 50, 80, 100, 120, 150, 180, 250, and 300 GeV/c pion beam momenta. The result of this test beam for the energy resolution is shown in Fig. 10.15. As can be seen from the ﬁgure that the energy resolution for the 100 GeV electron and pion beam is around 6% and 20% respectively [9].

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10 Hadron and Very-Forward Calorimetry in CMS 93

Fig. 10.15. Energy resolution for (a)electrons and (b) pions.

10.3.2 Zero Degree Calorimetry (ZDC) The ZDCs are designed to measure neutrons and very forward photons in the heavy-ion and early pp collisions and also it will measure real-time luminosity, beam tuning and accelarator monitoring during AA (where A stands for heavy ion), pA and pp running. It is located inside the neutral particle absorber (TAN) ∼ 140 m from the interaction point of CMS detector and it covers the eta range of 7<η<10. The ZDC consists of two independent calorimeter sections which are Electromagnetic (EM) and Hadronic (HAD) sections respectively. They both use a Quartz fiber ribon stack and tungsten plates that are chosen for a fast signal and radiation hardened calorimeter. The HAD section consists of 24 layers of 15.5 mm thick tungsten plates and 24 layers of 0.7 mm diameter quartz fibers. The EM section consists of 33 layers of 2 mm thick tungsten plates and 33 layers of 0.7 mm diameter quartz fibers. The cherenkov light produced by passage of charged particles through the fibers is read by the photomultiplier tubes (PMT), see Fig. 10.16. The total depth of the combined ZDC system is 7.5 hadronic interaction lengths (λI). The ZDC sections have been studied by using both simulation and test beam facilities. From the test beam results, 300 GeV pion response of both system is given in Fig. 10.17 [10].

10.4 Conclusion

The HCAL and Very-Forward Calorimetry detector systems and some Test Beam results are discussed. All of the calorimeter systems have been studied extensively in terms of both physics and electronics. The results of the test beam are well understood. These detectors are the essential part of the CMS experiment. The construction, installation and commissioning of HCAL and part of the Very- Forward calorimetries are completed and ready for the ﬁrst beam collision in Oc- tober 2009. The construction and the structure of these detectors are the perfection of both technology and engineering. Acknowledgement This work is partially supported by the Turkish Atomic Energy Agency (TAEK).

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Fig. 10.16. Detector design and optical Fig. 10.17. The ZDC EM+HAD section re- read out system of the ZDC [11] sponses to the 300 GeV pions

References

1. CMS Physics Technical Design Report, Volume I(CMS TDR 8.1) 2 February 2006 2. The TriDAS Project, Technical Design Report, Volume 1: The Trigger Systems, CERN/LHCC 2000-38, CMS TDR 6.1 (December 2000) 3. The TriDAS Project, Technical Design Report, Volume 2: Data Acquisition and High- Level Trigger, CERN/LHCC, CMS TDR 6.2 (December 2002) 4. Physics Technical Design Report, Volume 1, CERN/LHCC 2006-001 (February 2006) 5. S. Abdullin et al. Eur.Phys.J.C55,159-171 (2008) 6. S. Abdullin et al. Eur.Phys.J.C60,359-373 (2009) 7. S. Abdullin et al. Eur.Phys.J.C57,653-663 (2008) 8. G. Bayatian et al. Eur.Phys.J.C53,139-166 (2008) 9. S. Basegmez et. al.”Performance Studies of the Full Length Prototype for the CASTOR Forward Calorimeter of the CMS Experiment”, 07 November 2008 (v2, 28 November 2008), CMS CR-2008/090 10. O.A. Grachov, et. al. ”Measuring Photons and Neutrons at Zero Degree in CMS”, April, 29, 2007, CMS CR-2007/014 11. A.S. Ayan, et. al. ”CMS Zero Degree Calorimeter Technical Design Report”, November, 9, 2006, CMS-IN-2006/054

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School of Particles and Accelerators FIRST IPM MEETING Institute for Research in ON LHCPHYSICS Fundamental Sciences (IPM) VOL. 1, NO. 1 (p. 95) Isfahan, April 20-24, 2009

11 Non-singlet QCD analysis of structure function based on associated Jacobi polynomials

Ali N. Khorramian (a,b), H. Khanpour (a), S. Atashbar Tehrani (a,b)

a Physics Department, Semnan University, Semnan, Iran b School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran

Abstract. We present the results of our non-singlet QCD analysis for the experimental data of the deep-inelastic neutrino-nucleon scattering in NLO, NNLO and N3LO. The analysis is based on the associated Jacobi polynomials technique of reconstruction of the structure functions from its Mellin moments. The ﬁt results for the non-singlet parton dis- MS 2 tribution function and their evolution are presented. Our results on ΛQCD and αs(MZ) up to N3LO are presented and compared with those obtained from deep inelastic scatter- 3 MS ing processes. In the N LO analysis, the QCD scale ΛQCD and the strong coupling con- 2 stant αs(MZ) were determined with the help of Pade-approximant.´ At the reference scale 2 2 3 Q0 = 4GeV our results of valence quark distributions up to N LO are in satisfactory agreement with the available theoretical models.

11.1 Introduction

The detailed QCD studies of the behavior of the structure functions of the non- polarized deep inelastic scattering (DIS) and parton distribution functions are still very important both from the phenomenological and theoretical points of view. In the present paper we determine the ﬂavor non–singlet parton distribu- 2 2 tion functions xuv(x, Q ) and xdv(x, Q ) using the available CCFR experimental data [1] up to the next-to-next-to leading (NNLO) and next-to-next-to-next to leading order level (N3LO). The results of the present analysis is based on the associated Jacobi polynomials expansion of the non–singlet structure function. The measurements of the CCFR collaboration provide a precise determination of the non-singlet deep inelastic scattering structure functions of neutrinos and 2 anti-neutrinos on nucleons, xF3(x, Q ). Data for xF3 in neutrino-nucleon scattering is available from the CCFR collaboration [1] . The data was obtained from the scattering of neutrinos off iron nuclei and the measurements span the ranges 1.26 ≤ Q2 ≤ 199.5 GeV2 and 0.015 ≤ x ≤ 0.75.

11.2 Theoretical Formalism

In the present analysis to start the parameterizations of the parton distributions 2 at the input scale of Q0 we choose the following parametrization for the valence

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quark densities [2] √ 2 au bu 1.5 xuv(x, Q0) = Nux (1 − x) (1 + cu x + dux + eux ) , N 2 d ed 2 xdv(x, Q0) = (1 − x) xuv(x, Q0) , (11.1) Nu

2 2 in the input scale of Q0 = 4 GeV and the normalizations Nu and Nd being ﬁxed R1 R1 by 0 uvdx = 2 and 0 dvdx = 1, respectively. By QCD ﬁts of the CCFR data for Nf=4 xF3, the seven parameters with ΛQCD will be extracted by using the associated Jacobi polynomials. The structure function is reconstructed from its moments by using the expansion in terms of orthogonal associated jacobi polynomials [3,4]

NXmax Xn 2 β α α,β (n) 2 xF3(x, Q ) = x (1 − x) Hn (x, c) cj (α, β, c) MxF3 (j + 2, Q ) (11.2) n=0 j=0

(n) where cj (α, β, c) are combinatorial coefﬁcients, given in terms of Euler Γ-functions α,β of the α and β weight parameters which have been ﬁxed, Hn (x, c) is the associated jacobi polynomials satisfy the orthogonality [5,6]

Z 1 β α (α,β) (α,β) x (1 − x) Hm (x, c)Hn (x, c)dx = δmn , (11.3) 0

and xβ(1 − x)α is the Jacobi weight function. The solution of the non–singlet evolution equation for the parton densities to 4–loop order reads [3,4,7]

NS 2 £ 2 1 2 2 2 3 2 3 ¤ 2 M (n, Q ) = 1 + as(Q )C (N) + as(Q )C (N) + as(Q )C (N) × fk(N, Q0) ± µ ¶−P^0(N)/β0 · ¸ a 1 ^+ β1 ^ 1 − (a − a0) P1 (N) − P0(N) a0 β0 β0 · µ ¶ ¸ ¡ ¢ 2 1 2 2 ^+ β1 ^( β1 β2 ^ − a − a0 P2 (N) − P1N) + + 2 − P0(N) 2β0 β0 β0 β0 µ ¶2 1 2 ^+ β1 ^ + 2 (a − a0) P1 (N) − P0(N) 2β0 β0 " µ ¶ ¡ ¢ 2 1 3 3 ^+ β1 ^+ β1 β2 ^+ − a − a0 P3 (N) − P2 (N) + 2 − P1 (N) 3β0 β0 β0 β0 # µ 3 ¶ β1 β1β2 β3 ^ + 3 − 2 2 + P0(N) β0 β0 β0 µ ¶ ¡ ¢ 1 2 2 ^+ β1 ^ + 2 (a − a0) a0 − a P1 (N) − P0(N) 2β0 β0 · µ 2 ¶ ¸ ^ β1 ^ β1 β2 ^ × P2(N) − P1(N) − 2 − P0(N) β0 β β0 0 ² µ ¶3 1 3 ^+ β1 ^ − 3 (a − a0) P1 (N) − P0(N) . (11.4) 6β0 β0

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Here, P^k denote the Mellin transforms of the (k + 1)–loop splitting functions and 2 i 2 Ci(N)(Q ) are the non–singlet Wilson coefﬁcients in O(as) [8] and as(Q ) = 2 αs(Q )/(4π) denotes the 4–loop strong coupling constant [9]

1 b ln L 1 h i a = − 1 + b2(ln2 L − ln L − 1) + b β L (β L)2 (β L)3 1 2 0 · 0 µ 0 ¶ 1 5 1 + b3 − ln3 L + ln2 L + 2 ln L − (β L)4 1 2 2 0 ¸ b − 3b b ln L + 3 , (11.5) 1 2 2

2 2 where L ≡ ln(Q /Λ ), bk ≡ βk/β0, and Λ is the QCD scale parameter. In the 3 ^+ framework of this technique the values of the terms C (n) and P3 (n) with the help of Pade-approximant´ could be expressed as [7,10,11,12]

C3(n) = [C2(n)]2/C1(n) , ^+ ^+ 2 ^+ P3 (n) = [P2 (n)] /P1 (n) . (11.6)

11.3 Results

In the QCD analysis we parameterized the strong coupling constant αs in terms 2 of four massless ﬂavors determining ΛQCD. Our results on αs(MZ) in NNLO and N3LO are presented in Table 11.1 and compared with those obtained from deep inelastic scattering processes.

2 3 Table 11.1: Comparison of αs(MZ) values in NNLO, and N LO QCD analyses. 2 αs(MZ) Ref. NNLO KA 0.1131 ± 0.0019 [4] +0.0019 BBG 0.1134 [7] −0.0021 MRST03 0.1153 ±0.0020 [14] A02 0.1143 ±0.0014 [15] Model 0.1147 ± 0.001 N3LO +0.0020 BBG 0.1141 [7] −0.0022 Model 0.1162 ± 0.0009

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98 A. Khorramian, H. Khanpour, S. Atashbar Tehrani

In Table 11.2 we summarize the NLO, NNLO and N3LO ﬁt results for the para- 2 2 Nf=4 meters of the parton densities xuv(x, Q0), xdv(x, Q0) and ΛQCD .

Table 11.2: Parameter values of the NLO, NNLO, and N3LO non-singlet QCD ﬁt 2 2 at Q0 = 4 GeV . NLO NNLO N3LO

uv Nu 2.165 3.307 3.473

au 0.618 ± 0.005 0.701 ± 0.019 0.701 ± 0.014

bu 3.300 ± 0.035 3.491 ± 0.069 3.584 ± 0.037

cu 0.923 ± 0.057 0.163 ± 0.019 −0.585 ± 0.018

du 4.589 ± 0.046 3.949 ± 0.026 6.003 ± 0.026

eu −5.257 ± 0.048 −4.125 ± 0.059 −5.332 ± 0.022

dv Nd 1.515 2.384 2.576

ed 2.281 ± 0.042 2.486 ± 0.023 2.689 ± 0.025

Nf=4 ΛQCD , MeV 311 ± 11 273 ± 17 277 ± 16 χ2/ndf 88.89/109 = 0.81 81.91/109 = 0.75 81.62/109 = 0.74

2 2 In Fig. 11.1 the parton densities xuv and xdv at the input scale Q0 = 4.0GeV at different orders in QCD as resulting from the present analysis has been shown.

11.4 Discussion

We performed a QCD analysis of the non–singlet world data up to NNLO and 3 2 2 N LO and determined the valence quark densities xuv(x, Q ) and xdv(x, Q ) in the MS–scheme. Parameterizations of these parton distribution functions were derived in a wide range of x and Q2 as fit results at NLO, NNLO, and N3LO. Nf=4 2 In the analysis the QCD scale ΛQCD and the strong coupling constant αs(MZ), were determined up to N3LO. The analysis was performed using the associated Jacobi polynomials–method to determine the parameters of the problem in a fit to the data. A new aspect in comparison with other theoretical analysis is that we determine the parton densities and the QCD scale up to N3LO by using the associated Jacobi polynomials expansion method. The benefit of this approach is the possibility to determine nonsinglet parton distributions analytically and not numerically.

References

1. W. G. Seligman et al., Phys. Rev. Lett. 79, (1997) 1213. 2. A. N. Khorramian and S. Atashbar Tehrani, JHEP 0703, 051 (2007) [arXiv:hep- ph/0610136]. 3. A. N. Khorramian, S. A. Tehrani and M. Ghominejad, Acta Phys. Polon. B 38, 3551 (2007).

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0.8

NLO xuv(x) 0.6 NNLO N3LO 0.4 2 2 Q0 = 4 GeV

0.2

-4 -3 -2 -1 10 10 10 10

0.4

NLO xdv(x) 0.3 NNLO N3LO 2 2 0.2 Q0 = 4 GeV

0.1

-4 -3 -2 -1 10 10 10 10 x 2 2 Fig. 11.1. Comparison of the parton densities xuv and xdv at the input scale Q0 = 4.0GeV at different orders in QCD as resulting from the present analysis. .

4. A. N. Khorramian and S. A. Tehrani, Phys. Rev. D 78 (2008) 074019 [arXiv:0805.3063 [hep-ph]]. 5. J. Wimp, Canadian J. Math. 39 (1987), 893-1000. 6. J. Letessier, SIAM J. Math. Anal. (1993) 7. J. Blumlein, H. Bottcher and A. Guffanti, Nucl. Phys. B 774, 182 (2007) [arXiv:hep- ph/0607200]. 8. S. Moch and J. A. M. Vermaseren, Nucl. Phys. B 573, (2000) 853 [arXiv:hep- ph/9912355]. 9. K. G. Chetyrkin, B. A. Kniehl and M. Steinhauser, , Phys. Rev. Lett. 79 (1997) 2184 [arXiv:hep-ph/9706430]. 10. A. L. Kataev, G. Parente and A. V. Sidorov, Phys. Part. Nucl. 34, (2003) 20 [arXiv:hep- ph/0106221]. 11. A. L. Kataev, G. Parente and A. V. Sidorov, Nucl. Phys. B 573, (2000) 405 [arXiv:hep- ph/9905310]. 12. A. L. Kataev, A. V. Kotikov, G. Parente and A. V. Sidorov, Phys. Lett. B 417, (1998) 374 [arXiv:hep-ph/9706534]. 13. A. L. Kataev, G. Parente and A. V. Sidorov, arXiv:hep-ph/9809500. 14. A. D. Martin, R. G. Roberts, W. J. Stirling and R. S. Thorne, arXiv:hep-ph/0307262. 15. S. Alekhin, Phys. Rev. D 68 (2003) 014002 [arXiv:hep-ph/0211096].

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School of Particles and Accelerators FIRST IPM MEETING Institute for Research in ON LHCPHYSICS Fundamental Sciences (IPM) VOL. 1, NO. 1 (p. 101) Isfahan, April 20-24, 2009

12 A Phenomenological Analysis of the Longitudinal Heavy Quark Structure Function

A. Khorramiana,b, S. Atashbar Tehranib

aPhysics Department, Semnan University, Semnan, Iran bSchool of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran

Abstract. We present the results of our QCD analysis for the heavy-quark contribution to 2 the longitudinal proton structure function FL(x, Q ). In our QCD calculations we extract light and asymptotic heavy ﬂavor contributions for the non-singlet, singlet and gluon parts due to charm to FL. Our calculations for longitudinal proton structure function based on the Jacobi polynomials method are in good agreement with very recent H1 experimental data.

12.1 Introduction

Structure functions in deep-inelastic scattering (DIS) and their scale evolution are closely related to the origins of quantum chromodynamics (QCD). DIS processes have played and still play a very important role for our understanding of QCD and of nucleon structure. In fact, DIS structure functions have been the subject of detailed theoretical and experimental investigations. Deep inelastic scattering of leptons off nucleons has been the key for our understanding of the structure of the nucleon. In the framework of the perturbative QCD inspired quark parton model, the structure functions can be directly related to the parton distribution functions (PDF’s) which are probability densities of partons existing inside proton. All calculations of high energy processes with initial hadrons, whether within the standard model or exploring new physics, require PDF’s as an essential input. The reliability of these calculations, which underpins both future theoretical and experimental progress, depends on understanding the uncertainties of the PDF’s. The assessment of PDF’s, their uncertainties and extrapolation to the kinematics relevant for future colliders such as the LHC is an important challenge to high energy physics in recent years. 2 At low Q , dominantly contributing to the cross section is F2 which is an electric-charge squared weighted sum of all ﬂavor quark PDF’s. In the low-x region, F2 is dominated by sea-quark PDF’s, and the DGLAP evolution of QCD 2 ascribes the Q -dependence of F2 (“scaling violation”) as largely owing to gluon 2 splitting into qq-pairs. At large Q , xF3 becomes signiﬁcant, and gives information on valence quark PDF’s. The structure function FL is zero in the naive quark-

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parton model, i.e. without QCD, but in leading order QCD, a finite value of FL is expected in the small x region by being directly related to the gluon PDF [1]. Since very recently, the first direct measurement of the FL at H1 using the lowered proton beam energy is extracted [2], we have enough motivation to study 2 the longitudinal structure function FL(x, Q ). In this paper we use the massive operator matrix elements, which contribute to the heavy flavor Wilson coefficients in unpolarized deeply inelastic scattering in the region Q2 >> m2 [3]. The results of the present analysis is based on the Jacobi polynomials expansion of the non-singlet structure function. This method was developed and applied for QCD analysis [4-17]. The same method has also been applied in polarized case [18-23]. Also in [24] the proton structure functions are derived in the QCD dipole picture of BFKL dynamics. The plan of the paper is to give an introduce of theoretical formalism in Sec- tion 12.2. The method of the QCD analysis of longitudinal structure function, based on Jacobi polynomials are written down in the section 12.3. Our conclusions are summarized in Section 12.4.

12.2 Theoretical formalism

2 The nucleon structure functions Fi(x, Q ) are described as Mellin convolutions j between the parton densities fj and the Wilson coefﬁcients Ci µ ¶ X Q2 F (x, Q2) = Cj x, ⊗ f (x, µ2) , (12.1) i i µ2 j j

to all orders in perturbation theory. Here µ2 denotes the factorization scale and the Mellin convolution is given by the integral

Z 1 Z 1 [C ⊗ f](x) = dx1 dx2 δ(x − x1x2) C(x1)f(x2) . (12.2) 0 0

Since the distributions fj refer to massless partons, the heavy flavor effects are contained in the Wilson coefficients only. In the perturbative predictions and in Mellin n-space, the longitudinal structure function FL consists of the light and heavy flavor contributions [25]

2 light 2 heavy 2 FL(n, Q ) = F (n, Q ) + F (n, Q ) ·L L µ ¶¸ Q2 = CNS,light(n, a ) + HNS n, a , q (n, µ2) L s L s m2 NS · µ ¶¸ Q2 + CS,light(n, a ) + HS n, a , q (n, µ2) L s L s m2 S · µ ¶¸ Q2 + Cg,light(n, a ) + HNS n, a , g(n, µ2) . (12.3) L s L s m2

We choose Q2 = µ2 as uniform factorization scale in this paper.

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2 2 i 2 In the limit Q À m the massive Wilson coefﬁcients HL up to O(αs) are given by [3] µ ¶ · µ ¶ ¸ Q2 Q2 HNS x, a , = a2 −β C(1) ln + CbNS,(2) , (12.4) L,q s m2 s 0,Q L,q m2 L,q µ ¶ Q2 HPS x, a , = a2CbPS,(2) , (12.5) L,q s m2 s L,q µ ¶ · µ ¶ ¸ Q2 1 Q2 HS x, a , = a Cb(1) + a2 Pb(0)C(1) ln + Cb(2) . (12.6) L,g s m2 s L,g s 2 qg L,q m2 L,g

S NS PS where HL,q = HL,q + HL,q. The MS coefﬁcient functions, in the massless limit, are denoted by µ ¶ µ ¶ µ ¶ Q2 Q2 Q2 Cbi = Ci ,N + N − Ci ,N , (12.7) L,q µ2 L,q µ2 L H L,q µ2 L

here NH,NL are the number of heavy and light ﬂavors, respectively. In the following we will consider the case of a single heavy quark, i.e. NH = 1. m At N LO the scale dependence of as is given by

Xm d as k+2 = β m (a ) = − a β . (12.8) d ln Q2 N LO s s k k=0

The expansion coefﬁcients βk of the β-function of QCD are known up to k = 2, i.e., N2LO [26,27]

β0 = 11 − 2/3 nf ,

β1 = 102 − 38/3 nf , 2 β2 = 2857/2 − 5033/18 nf + 325/54 nf , (12.9)

here nf stands for the number of effectively massless quark ﬂavors. The strong coupling constant up to NNLO is as following [28]

2 1 1 1 £ 2 ¡ 2 ¢ ¤ as(Q ) = − 2 b1 lnLΛ + 3 b1 ln LΛ − lnLΛ − 1 + b2 , β0LΛ (β0LΛ) (β0LΛ) (12.10)

2 2 where LΛ ≡ ln(Q /Λ ), bk ≡ βk/β0, and Λ is the QCD scale parameter. Now the moments of non-singlet, singlet and also gluon parts of longitudinal structure function FL is available by using Eq. (12.3).

12.3 The method

In this work we want to calculate the non-singlet, singlet and also gluon contributions of longitudinal structure function by using the Jacobi polynomials method.

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104 A. Khorramian, S. Atashbar Tehrani

One of the simplest and fastest possibilities in the structure function reconstruction from the QCD predictions for its Mellin moments is Jacobi polynomials expansion. According to this method one can relate the structure function with its Mellin moments [5-9]

NXmax Xn 2 β α α,β (n) 2 FL(x, Q ) = x (1 − x) Θn (x) cj (α, β)FL(j + 2, Q ) , (12.11) n=0 j=0

α,β where Nmax is the number of polynomials and Θn (x) are the Jacobi polynomi- 2 als of order n. FL(j + 2, Q ) is the moments of the longitudinal structure function which introduced in the previous section. The same method has been applied to calculate the non-singlet structure function F2 [14-17] and xF3 from their moments [10-13] and for polarized structure function xg1 [19-20]. Now it is possible 2 to determine FL(x, Q ) by having the information of massless and massive parts 2 of FL(n, Q ) in n-moment space.

0.5 Q2=30 GeV2 Q2=300 GeV2 Q2=3000 GeV2 0.4 ) 2 0.3 (x,Q L

F 0.2

0.1

10-4 10-3 10-2 10-1 x

2 Fig. 12.1. The longitudinal structure function FL(x, Q ) as a function of x and for ﬁxed Q2 = 30, 300, 3000 GeV2 values.

12.4 Conclusion

For extraction non-singlet part of longitudinal structure function FL we choose our very recently parametrization for the valence quark densities [14]. To extract singlet and gluon parts of longitudinal structure function FL we used the reported results for singlet and gluon distributions from Ref. [3]. In Fig. (12.1) we show

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12 A Phenomenological Analysis of the Longitudinal Heavy ... 105

2 2 the longitudinal structure function FL(x, Q ) as a function of x and for Q = 30, 300, 3000 GeV2. In Fig. (12.2) we present our QCD analysis for longitudinal 2 structure function FL as a function of Q . The H1 data [2,29] are at ﬁxed W = 276 GeV. We found that the Jacobi polynomial approach can describe the behavior of light and asymptotic heavy ﬂavor contributions due to charm to FL.

x 10-5 10-4 10-3 10-2

H1-2008 0.8 H1-2003(e+p) H1-2003(e-p) H1-2001 0.6 Model ) 2 0.4 (x,Q L F 0.2

-0.2 1 2 3 10 Q2 (GeV2) 10 10

2 Fig. 12.2. Longitudinal structure function FL as a function of Q .

We hope our results of QCD analysis of structure functions in terms of Jacobi polynomials could be able to describe more complicated hadron structure functions. We also hope to be able to consider the massive quark contributions for 2 F2(x, Q ) by using the structure function expansion in terms of the Jacobi polynomials.

References

1. K. Nagano [H1 Collaboration and ZEUS Collaboration], arXiv:0808.3797 [hep-ex]. 2. F. D. Aaron et al. [H1 Collaboration], Phys. Lett. B 665 (2008) 139 [arXiv:0805.2809 [hep-ex]]. 3. J. Blumlein, A. De Freitas, W. L. van Neerven and S. Klein, Nucl. Phys. B 755 (2006) 272 [arXiv:hep-ph/0608024]. 4. G. Parisi and N. Sourlas, Nucl. Phys. B151 (1979) 421; I. S. Barker, C. B. Langensiepen and G. Shaw, Nucl. Phys. B186 (1981) 61. 5. I. S. Barker, B. R. Martin and G. Shaw, Z. Phys. C19 (1983) 147; I. S. Barker and B. R. Martin, Z. Phys. C24 (1984) 255; S. P. Kurlovich, A. V. Sidorov and N. B. Skachkov, JINR Report E2-89-655, Dubna, 1989. 6. V. G. Krivokhizhin, S. P. Kurlovich, V. V. Sanadze, I. A. Savin, A. V. Sidorov and N. B. Skachkov, Z. Phys. C 36 (1987) 51. 7. V. G. Krivokhizhin et al., Z. Phys. C 48, 347 (1990). 8. J. Chyla and J. Rames, Z. Phys. C 31 (1986) 151. 9. I. S. Barker, C. S. Langensiepen and G. Shaw, Nucl. Phys. B 186 (1981) 61. 10. A. L. Kataev, A. V. Kotikov, G. Parente and A. V. Sidorov, Phys. Lett. B 417, (1998) 374 [arXiv:hep-ph/9706534]. 11. A. L. Kataev, G. Parente and A. V. Sidorov, arXiv:hep-ph/9809500. 12. A. L. Kataev, G. Parente and A. V. Sidorov, Nucl. Phys. B 573, (2000) 405. 13. A. L. Kataev, G. Parente and A. V. Sidorov, Phys. Part. Nucl. 34, (2003) 20 [arXiv:hep- ph/0106221]; A. L. Kataev, G. Parente and A. V. Sidorov, Nucl. Phys. Proc. Suppl. 116 (2003) 105 [arXiv:hep-ph/0211151].

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14. A. N. Khorramian and S. Atashbar Tehrani, Phys. Rev. D 78, (2008) 074019. arXiv:0805.3063 [hep-ph]. 15. A. N. Khorramian, S. Atashbar Tehrani and M. Ghominejad, Acta Phys. Polon. B 38, 3551 (2007). 16. A. N. Khorramian and S. Atashbar Tehrani, AIP Conf. Proc. 1006 (2008) 118. 17. A. N. Khorramian and S. Atashbar Tehrani, J. Phys. Conf. Ser. 110, 022022 (2008); S. Atashbar Tehrani and A. N. Khorramian, Nucl. Phys. Proc. Suppl. 186, 58 (2009). 18. E. Leader, A. V. Sidorov and D. B. Stamenov, Int. J. Mod. Phys. A 13, 5573 (1998). 19. S. Atashbar Tehrani and A. N. Khorramian, JHEP 0707 (2007) 048 [arXiv:0705.2647 [hep-ph]]. 20. A. N. Khorramian and S. Atashbar Tehrani, arXiv:0712.2373 [hep-ph]. 21. A. N. Khorramian and S. Atashbar Tehrani, AIP Conf. Proc. 915, 420 (2007). 22. A. Mirjalili, A. N. Khorramian and S. Atashbar-Tehrani, Nucl. Phys. Proc. Suppl. 164, 38 (2007). 23. A. Mirjalili, S. Atashbar Tehrani and A. N. Khorramian, Int. J. Mod. Phys. A 21, 4599 (2006) [arXiv:hep-ph/0608224]. 24. H. Navelet, R. B. Peschanski, C. Royon and S. Wallon, Phys. Lett. B 385, 357 (1996) [arXiv:hep-ph/9605389]. 25. A. N. Khorramian and S. Atashbar Tehrani, A. Mirjalili, Nucl. Phys. Proc. Suppl. 186, 379 (2009). 26. O. V. Tarasov, A. A. Vladimirov and A. Y. Zharkov, Phys. Lett. B 93, 429 (1980). 27. S. A. Larin and J. A. M. Vermaseren, Phys. Lett. B 303, 334 (1993). 28. A. Vogt, Comput. Phys. Commun. 170, 65 (2005) [arXiv:hep-ph/0408244]. 29. C. Adloff et al. [H1 Collaboration], Eur. Phys. J. C 30, 1 (2003) [arXiv:hep-ex/0304003]; C. Adloff et al. [H1 Collaboration], Eur. Phys. J. C 21, 33 (2001) [arXiv:hep- ex/0012053]; T. Latovika [H1 and ZEUS Collaborations], Eur. Phys. J. C 33, S388 (2004); E. M. Lobodzinska, arXiv:hep-ph/0311180.

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School of Particles and Accelerators FIRST IPM MEETING Institute for Research in ON LHCPHYSICS Fundamental Sciences (IPM) VOL. 1, NO. 1 (p. 107) Isfahan, April 20-24, 2009

13 Simulation of Resistive Plate Chamber Based on Transport Equations

L. Khosravi-Khorashada,b, M. Eskandaria, A. Moshaiia

a Department of Physics, Tarbiat Modares University, P.O. Box 14115-175, Tehran, Iran b School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran

Abstract. We have presented a streamer initiation simulation inside the gas gap of a trigger RPC with gas mixture C2F4H2/i − C4H10/SF6 96.7/3/0.3 based on simultaneous numerical solution of transport equations together with Poisson equation for electrons, negative and positive ions. The model can predict well spatial and temporal development of avalanche mode, saturated avalanche and finally streamer mode of RPC operation, under the influence of space charge field.

13.1 Introduction

Resistive Plate Chambers (RPCs) are gaseous parallel plate detectors with good time resolution and high efﬁciency used for trigger and Time-Of-Flight (TOF) applications. RPCs play an important role in the muon system of many general purpose detectors such as ATLAS and CMS [1,2]. Moreover, RPCs have extensive applications in cosmic ray detection experiments [3,4] owing to their low-cost construction and large area of detection. Although RPCs invented during 1980’s [3,4], theoretical and experimental re- searches of this detector is still under progress. In order to understand the physics of RPC and different processes happening inside the gas gap, several models have been proposed to describe the avalanche development inside the RPC gap [7,8,9,10,11,12]. Most of these simulations are dedicated to specify the growth of electron clusters in the avalanche mode operation of an RPC. However, the simulation of streamer mode suffers from the lack of extensive investigations. Here, we have presented the results of a simulation of an RPC including description of an avalanche mode operation, transition from the avalanche mode to streamer mode and ﬁnally the streamer mode operation. The simulation is based on simultaneous numerical solution of transport equations as one of the widely used methods to study parallel plate chambers [13,14].

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108 L. Khosravi-Khorashad, M. Eskandari, A. Moshaii

Fig. 13.1. Space charge electric ﬁeld of a disc charge conﬁned between the anode and cathode in over the axis of a cylinder with radius R and thickness dx including its nearest image charges.

Fig. 13.2. Townsend and attachment coefﬁcients and drift velocity of electrons for the gas mixture (C2F4H2/i − C4H10/SF6 96.7/3/0.3) derived by Magboltz at T = 296.15K and p = 1atm.

13.2 Simulation Model

The model is based on the simultaneous numerical solution of transport Eqs. (13.1-13.3) together with Poisson Eq. (13.4).

∂n (x, t) ∂(νn (x, t)) e + e = α|ν|n (x, t) − η|ν|n (x, t) (13.1) ∂t ∂x e e

∂n (x, t) + = α|ν|n (x, t) (13.2) ∂t e

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13 Simulation of Resistive Plate Chamber Based on Transport Equations 109

∂n (x, t) − = η|ν|n (x, t) (13.3) ∂t e

∂ ρ(x, t) (E ) = (13.4) ∂x sp ²

where, ρ(x, t) = e0[n+(x, t) − n−(x, t) − ne(x, t)] is the linear charge density. ne(x, t), n+(x, t) and n−(x, t) are the number densities of electrons, positive and negative ions, respectively. Here, α is the first Townsend coefficient, η is the attachment coefficient and ν is the drift velocity of electrons. The ions are assumed stationary during the short time scale of the development of the avalanche inside the gap. e0 is the absolute value of electron charge and ² is the relative permit- tivity of the gas. The charge distribution of the avalanche is supposed to be in a cylinder with radius R and length d (gas gap length), confined between the anode and cathode, with uniform distribution in the radial direction. The electric field of a disc of charge inside the cylinder, at the observation point P (Fig. 13.1) is given by [15]:

I = (E ) | 0 x discÃ0

0 where x and x are the distances of observation point and the disc of charge from cathode, respectively. Therefore by the application of image-charge method we have:

Z 0 Z x Z d Z 2d Esp = − I + I + I + I (13.6) −d 0 x d Here, the contribution of the nearest image charges to each electrode are considered in the model (Fig. 13.1). The space charge field, given by Eq. (13.1), is calculated numerically in each time step. The analytical solution of Eqs. (13.1-13.3) is impossible since they are coupled with space charge field due to electric field dependency of electron drift velocity, first Townsend and attachment coefficients. An approximate analytical solution of transport equations including photon contribution for small time intervals has been proposed in Ref. [16]. Including such mechanisms in the present model requires some experimental parameters like photo-production coefficient for the gas mixture which are not available in literature. Moreover, neglecting these effects seems not to produce a severe problem in our study. The discretized model is based on Lax finite difference scheme. The space and time are discretized by d h = N and τ denoting spatial and temporal grid spacing, respectively. The coordinates of spatial and temporal location will be depicted by: xi = (i − 1)h and tn = (n − 1)τ, where i = 1, 2, 3, ..., N and n = 1, 2, 3, ..., stept with i denotes the spatial location of a grid point and n the temporal step. Accordingly, the dis- critized form of Eqs. (13.1-13.3) are as follows:

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110 L. Khosravi-Khorashad, M. Eskandari, A. Moshaii

1 £ ¤ (n )n+1 = (1 + τ(α − η)|ν|) (n )n + (n )n e i 2 e i+1 e i−1 ντ £ ¤ − (n )n − (n )n (13.7) 2h e i+1 e i−1

1 £ ¤ (n )n+1 = (n )n + (n )n + i 2 + i+1 + i−1 1 £ ¤ + α|ν|τ (n )n + (n )n (13.8) 2 + i+1 + i−1

1 £ ¤ (n )n+1 = (n )n + (n )n − i 2 − i+1 − i−1 1 £ ¤ + η|ν|τ (n )n + (n )n (13.9) 2 − i+1 − i−1 In this case, the values of number densities of charged particles are explicitly determined from their values in earlier times.

13.3 Initial Conditions and Parameters

The Eqs. (13.1-13.3) are three ﬁrst order partial differential equations and each one needs one initial condition. We take the initial charge distribution of electrons, positive and negative ions at t = 0 in the form of Gaussian distribution:

" # µ ¶2 x − x0 ne(x, t = 0) = n0 − , σx

n+(x, t = 0) = n−(x, t = 0) = 0 (13.10)

14 −1 where σx = 300µm, x0 = 0.8mm and n0 = 10 cm . The choice of x0 and n0 is based on reducing the time of streamer formation and does not affect main characteristics of the transition of the avalanche to the streamer [17]. The parameters α, η and ν are calculated by Magboltz [18]. Figure 13.2 shows the electron drift velocity, first Townsend and attachment coefficients as a function of the electric field.

13.4 Computational Algorithm

The simulation algorithm can be summarized as follows:

d 1. Gas gap d is divided into N steps with the spatial grid spacing h = N . 2. Temporal grid spacing τ and number of time steps stept are speciﬁed representing the desired time of study t = τ (stept). 3. Initial condition is considered as in Eq. (13.10).

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Fig. 13.3. Numeric linear densities of electrons, positive and negative ions for 9ns in steps of 0.1ns for a trigger RPC with a gap length equals 2mm and a gas mixture (C2F4H2/i − C4H10/SF6 96.7/3/0.3) at HV = 10kV.

Fig. 13.4. Simulated space charge ﬁeld for a trigger RPC with a gap length equals 2mm and a gas mixture (C2F4H2/i − C4H10/SF6 96.7/3/0.3) at HV = 10kV from a) 0 − 2ns, b) 2 − 4ns, c) 4 − 6ns and d) 6 − 9ns in steps of 0.1ns.

4. Total electric field applied in the sum of external electric field and space charge field is obtained by Eq. (13.6) is calculated. 5. First Townsend coefficient (α), attachment coefficient (η) and electron drift velocity are calculated for each location (xi) at time step (tn) using the results of Fig. 13.2. 6. Number densities of electrons, positive and negative ions are computed using Eqs. (13.7-13.9). In this case, the number densities of charged species are determined in each position. 7. Space charge field Eq. (13.6) is calculated numerically in each position.

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112 L. Khosravi-Khorashad, M. Eskandari, A. Moshaii

Fig. 13.5. Numeric linear densities of electrons, positive and negative ions for 9ns in steps of 0.1ns for a trigger RPC with a gap length equals 2mm and a gas mixture (C2F4H2/i − C4H10/SF6 96.7/3/0.3) at HV = 11.14kV.

8. Total electric field is modified along the gas gap in each position using external electric field and space charge field. 9. Steps 5 to 8 are repeated stept times until the desired time of study is achieved.

The choice of spatial and temporal grid spacing (h and τ) considerably depends on stability conditions for numerical solutions of the set of Eqs. (13.7-13.9). Here, we have chosen N = 100, h = 0.02mm and τ = 0.1ns.

Fig. 13.6. Simulated space charge ﬁeld for a trigger RPC with a gap length equals 2mm and a gas mixture (C2F4H2/i−C4H10/SF6 96.7/3/0.3) at HV = 11.14kV from a) 0−2ns, b) 2 − 4ns, c) 4 − 6ns and d) 6 − 9ns in steps of 0.1ns.

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13 Simulation of Resistive Plate Chamber Based on Transport Equations 113

Fig. 13.7. Numeric linear densities of electrons, positive and negative ions for for a trigger RPC with a gap length equals 2mm and a gas mixture (C2F4H2/i − C4H10/SF6 96.7/3/0.3) at HV = 11.42kV at a) t = 0ns, b) t = 2ns, c) t = 4ns, d) t = 6ns, e) t = 8ns and f) t = 9ns.

Fig. 13.8. Simulated space charge ﬁeld for a trigger RPC with a gap length equals 2mm and a gas mixture (C2F4H2/i−C4H10/SF6 96.7/3/0.3) at HV = 11.42kV from a) 0−3ns, b) 3 − 6ns, c) 6 − 8ns and d) 8 − 9ns in steps of 0.1ns.

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114 L. Khosravi-Khorashad, M. Eskandari, A. Moshaii 13.5 Results

The simulation can well produce three modes of operation of RPC, which are avalanche, saturated avalanche and streamer mode. In addition, the existence of a pre-cursor signal to breakdown is predicted. Here, we discuss the development of each mode in details. I. Avalanche Mode: Figure 13.3 indicates the result of simulation for the trigger RPC with gas mixture C2F4H2/i−C4H10/SF6 96.7/3/0.3 at operating high voltage (HV) of 10kV during 9ns with step interval of 0.1ns. The spatial and temporal growth of electron and ion densities in the development of avalanche mode are based on the exponential growth of the Townsend mechanism. Figure 13.4 shows the simulated space charge field at four successive time intervals with steps of 0.1ns. During these four time intervals, the space charge field is not high enough to distort the applied external electric field. Hence, the electron drift velocity, first Townsend and attachment coefficients do not change considerably during the avalanche development. II. Saturated Avalanche Mode: Increasing the high voltage applied on the gap leads to transition of the mode of operation from avalanche to saturated avalanche. Figure 13.5 shows the development of particle densities at the applied high voltage of 11.14kV during 9ns time interval. Increasing high voltage results in distortion of the particle densities at the end of signal growth, near the anode electrode. The space charge development for this case is figured out in Fig. 13.6. In this case, the space charge field reaches to 15% − 45% of the external electric field and this situation corresponds to the transition from the avalanche to streamer mode usually called as ”saturated avalanche”. The reduction in the total electric field near the anode due to the space charge results in increasing the attachment coefficient in this region. This reduces the multiplication of electrons and positive ions near the anode. On the other hand, near the cathode a new signal is gradually growing due to the influence of space charge. This small signal can grow in later times to form a large streamer signal. III.Streamer Mode: The development of a streamer signal inside the gas gap can be seen when the applying high voltage increases to HV = 11.42kV. The results of simulation in this case is shown in Fig. 13.7. In this figure until the time of about 7ns, the development of the signal follows from the Townsend mechanism. At the time of t = 7.5ns (Fig. 13.7f) the exponential development is slightly distorted due to the space charge effect. In Fig. 13.7g corresponding the time of t = 8ns, we can see a complete transition from the avalanche mode to the saturated avalanche mode. In Fig. 13.7h at t = 9ns the streamer signal gradually grows and finally in Fig. 13.7i at t = 9.2ns a big streamer signal is created inside the gap. In this situation, the total electric field is extremely high so that the attachment coefficient and therefore production of new negative ions is almost negligible. Therefore, the number density of electrons and positive ions coincide with each other (Fig. 13.7i ).

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In Fig. 13.8, the variation of the space charge field during the 9ns of the development of streamer signal has been shown. At t = 9ns in Fig. 13.8 the space charge field along the gap becomes almost equal to the external field. This can be an indication of the Raether limit for the streamer initiation [19]. The results of simulation in demonstrating the transition of avalanche to saturated avalanche and saturated avalanche to streamer are in good agreement with experimental results appeared in [20].

13.6 Conclusion

The initiation of a streamer signal inside an RPC gas gap was simulated by numerical solution of the transport equations together with Poisson equation. The simulation can well reproduce both of the spatial and temporal development of the three modes of operation of an RPC: i.e. avalanche mode, saturated avalanche and the streamer mode. The obtained simulation results are in good agreement with available experimental data.

References

1. Muon Spectrometer, Technical Design Report, CERN-LHCC-97-22, ATLAS TDR 10, CERN (1997). 2. CMS, The Muon Project Technical Design Report, CERN/LHCC 97-32, (1997). 3. G. Agnetta, et al., Nucl. Instr. and Meth. A 38, 1, 64, (1996). 4. C. Bacci, et al., Nucl. Instr. and Meth. A 443, 342, (2000). 5. R. Santonico and R. Cardarelli. Development of resistive plate counters. Nucl. Instr. and Meth., 187:377-380, (1981). 6. R. Santonico and R. Cardarelli. Progress in resistive plate counters. Nucl. Instr. and Meth., A 263:20-25, (1988). 7. M. Abrescia et al. The simulation of resistive plate chambers in avalanche mode: Charge spectra and efﬁciency. Nucl. Instr. Meth., A 431:413-427, (1999). 8. M. Abrescia et al. Progress in the simulation of resistive plate chambers in avalanche mode. Nucl. Instr. Meth., B (Proc. Suppl.):459-464, (1999). 9. P. Fonte. High resolution timing of MIPs with RPCs - a model. Nucl. Instr. Meth., A 456:6-10, (2000). 10. G. Aielli. Logistic saturated avalance model. presented at the ’RPC 2001’ - 6th Work- shop on Resistive Plate Chambers and Related Detectors, 26-27 November (2001), Coimbra, Portugal. 11. W. Riegler, C. Lippmann and R. Veenhof, Nucl. Instr. And Meth. A 500, 144, (2000). 12. C. Lippmann and W. Riegler, Nucl. Instr. And Meth. A 517:54-76, (2004). 13. D Bessieres et al, A new one-dimensional moving mesh method applied to the simulation of streamer discharges, J. Phys. D: Appl. Phys. 40:6559-6570, (2007). 14. Olivier Ducasse et al, Critical Analysis on Two-Dimensional Point-to-Plane Streamer Simulations Using the Finite Element and Finite Volume Methods, IEEE TRANSAC- TIONS ON PLASMA SCIENCE, VOL. 35, NO. 5, OCTOBER 2007. 15. A. J. Davies et al., Proc. IEE, A281, p. 164, (1964). 16. P. Fonte. A model of breakdown in parallel-plate chambers. IEEE Trans. Nucl Science, 43:2135-2140, (1996). 17. S. V. Pancheshnyi et al., J. Phys. D: Appl. Phys. 34:105115, (2001).

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18. S. Biagi, Magboltz, program to compute gas transport parameters, Version 2.2, CERN. 19. H. Raether, Electron Avalanches and Breakdown in Gases, Butterworths, London, (1964). 20. R. Cardarelli, V. Makeev, R. Santonico, Avalanche and streamer mode operation of resistive plate chambers, Nucl. Instr. and Meth. A 382: 470-474, (1996).

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School of Particles and Accelerators FIRST IPM MEETING Institute for Research in ON LHCPHYSICS Fundamental Sciences (IPM) VOL. 1, NO. 1 (p. 117) Isfahan, April 20-24, 2009

14 Silicon Sensors: From basic principles to the largest Silicon detector

M. Krammer

Institute of High Energy Physics, Austrian Academy of Sciences, Vienna, Austria

Abstract. Since the invention of Silicon sensors for particle physics experiments in the early 1980ies Silicon detectors became more and more important. At present this detector technology is employed in all modern experiment. Silicon detectors were crucial for many measurements and even discoveries in the past, such as the discovery of the top quark, and will be equally important for the LHC experiments. In this presentation the principle functioning of Silicon sensors for position measurements is explained followed by some examples of their uses in particle physics experiments. These developments reached a peak in the construction of the Inner Tracker for the CMS experiment, the largest Silicon system built so far. An overview of the Inner Tracker construction and ﬁrst results from the commissioning using cosmic rays are described.

14.1 Silicon Detectors

Experiments in high energy physics investigate the elementary constituents of matter and the forces acting between them. Typical experiments examine the reactions of high energetic particles with matter or the collisions of such particles with each other. From the energy available in these reactions heavy and short- living particles are created which are the objects to study. To reconstruct the trajectories of secondary particles different detector technologies are used. In the beginning of high energy physics bubble chambers were employed. In these devices charged particles produce little gas bubbles along their trajectories in a su- perheated liquid. Photographic pictures of these bubbles were taken and then analyzed. An enormous improvement came about with the development of electronic detectors such as the multi wire proportional chamber. This type of gas detector consists of a gas-ﬁlled volume containing wires connected to high voltage. Charged particles traversing this detector are ionizing the gas molecules. The electrons and ions drift towards the wires and electrodes, respectively, inducing a signal in the electronics connected to the wires. From the wire position the position of the traversing particle is deduced and is immediately available for computational reconstruction. But this technology still has several drawbacks, such as a long dead time, low rate capability and - very importantly - a limited position resolution. Silicon detectors as position detectors in high energy physics were ﬁrst developed in the early 1980ies. They are produced from thin wafers (approximately

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300 µm thick) of high-resistivity Silicon. For most applications n-type Silicon is selected. With photolithographic methods fine-patterned p+-implants are realized on one side of the wafer forming pn-junctions. These implants are either thin strips (typically 20 µm wide with an interstrip distance of 100 µm) or small pixels (e.g. 300x300 µm2). Each implant is connected to an individual channel of the readout electronics (see Fig. 14.1). With respect to the pn-junction a reverse bias voltage is applied. This bias voltage has to be high enough to fully deplete the Silicon bulk. Charged particles traversing the detector create electron-hole pairs along their flight path. Due to the applied electrical field these electron-hole pairs are separated and drift towards the electrodes inducing signals in the closest readout channels. With a proper choice for the strip geometry a precision of a few µm can be easily achieved. By placing several Silicon detectors in the path of the charged particles the trajectories of these particles can be reconstructed.

Fig. 14.1. Schematics showing a single sided Silicon strip detector.

14.2 First Application in High Energy Physics: NA11

The ﬁrst experiment using a Silicon strip detector was the experiment NA11 at CERN in 1983 [1]. One of these detectors is shown in Fig. 14.2. The detector had a surface of approximately 24 cm2, and 1200 strips were implanted in the Silicon. The strips were separated by 20 µm. Although only every 3rd strip, respectively every 6th strip at the edges, was connected to a readout channel these connections to the discrete electronics did dominate the volume of the detector assembly, as can be seen in Fig. 14.2. The position resolution of this detector was as good as 4.5 µm. In total, the NA11 experiment employed 8 such detectors - 2 in front of the experiment’s target and 6 behind it. Particles produced by the reaction of the high energy beam hitting the target did ﬂy through the detectors and produced signals. Combining the signals from one particle the trajectory could be extrapo- lated back to the origin, i.e. the reaction point.

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14 Silicon Sensors: From basic principles to the largest Silicon detector 119

The goal of the experiment NA11 was to measure the lifetimes and the masses of D-mesons. D-mesons contain a quark of the second family of quarks, the charm quark. These D-mesons decay after a relatively short time of 4 to 10x10−13s. Con- sequently, the flight path of these mesons is in the order of a few tenth of µm only. Solely the precision of the Silicon detectors enabled the experimentalists to reconstruct the trajectories of the decay products with sufficiently good precision to identify the position of the decay point. The distance between the original interaction point and this secondary vertex is defined as the flight path of the D- meson. Collecting enough events of this type NA11 could calculate the lifetimes and the masses of the various D-mesons.

Fig. 14.2. Photograph of a Silicon detector from NA11 [1].

14.3 Progress in Electronics Integration and Detector Development

The requirements for detectors used in collider experiments are much more stringent, especially concerning the amount of material used and the geometrical arrangement around the interaction point. Before using Silicon sensors in a collider experiment, signiﬁcant progress was necessary to reduce the material intensive electronics. Finally, the development of fully custom-designed VLSI-chips made the use of Silicon detectors in collider experiments viable. These chips contain up to 128 channels of very low-noise readout electronics on a surface of a ﬁngernail. The connections of the readout channels to the strips of the Silicon sensor are produced by thin wire wedge bonding. Figure 14.3 shows a photograph of a detector module of the experiment CMS. The carbon frame holds an electronics hybrid with 6 readout chips, with 128 channels each, wire bonded to a Silicon sensor. Substantial progress was also made on the sensor technology. Starting with the most simple device as shown in Fig. 14.1 more and more sophisticated structures were developed. These new structures for example contained integrated capacitances to AC couple the signals to the readout electronics, integrated bias

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Fig. 14.3. A module for the TEC subdetector of the CMS silicon tracker.

resistors or transistor structures to apply the bias voltage to each implant and ﬁ- nally double sided Silicon sensors with implanted strips on both sides enabling two dimensional measurements with one sensor [2]. In parallel to more and more sophisticated strip detectors hybrid pixel detector were developed. The difﬁculty of such devices is the connection of the large number of pixels to the individual electronics channels. Each pixel of the sensor realized on high resistivity Silicon material has to be electrically connected to the corresponding input channel of the electronics chip. In hybrid pixel detectors this connection is done by so-called bump bonding. A schematic drawing of a cell of a hybrid pixel detector is shown in Fig. 14.4. In this drawing the Silicon pixel sensor is at the bottom. Small con- ductive bump balls connect the pixel to the input pad of the electronics chip at the top. The layout of the electronics chip has to match the pattern of the pixel sensor.

14.4 Silicon Detectors at Collider Experiments

The DELPHI experiment at the Large Electron Positron collider (LEP) at CERN was the ﬁrst collider experiment to install a Silicon vertex detector [3]. The other LEP experiments followed soon after with their own Silicon detector developments. Finally, after several steps the DELPHI collaboration installed the largest Silicon detector of this time in its experiment. This ﬁnal DELPHI vertex detector contained 888 Silicon sensors of various technologies, including newly developed double-sided Silicon sensors and hybrid pixel detectors [4]. The total area covered with Silicon was about 1.5 m2. The sensors were arranged in three concentric cylindrical layers surounding the interaction point. Additional strip

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Fig. 14.4. Schematics showing a cell of a hybrid pixel detector.

and pixel detectors were mounted on both ends to cover the low-angle region as well. The main goal of this detector in the DELPHI experiment was the identification of c-quarks, b-quarks and tau leptons by measuring their characteristic decay lengths. Figure 14.5 shows the reconstruction of a typical event seen in DELPHI. In this event two B-mesons were produced which subsequently decayed after about 1.6x10−12s. The graphics shows the three layers of Silicon detector modules and the positions were hits are recorded. The extrapolations of the tracks into the interaction region reveal that the origin of some tracks is displaced from the interaction point. The reconstruction of these secondary vertices indicates the decays of heavy quark particles - in this particular case the decays of particles containing a b-quark. The identification of a large number of such events opened a rich field of physics analysis. Detailed studies of b-quark properties became possible.

Fig. 14.5. A bb(bar) event recorded by DELPHI. In the right graph only the innermost region of the event is displayed. The two secondary vertices, from the decay of B-mesons, are visible.

The reconstruction of events at hadron colliders is however much more dif- ﬁcult. The large cross section and the high collision rate cause a high number of tracks in each event and a signiﬁcant radiation level. Especially the radiation damage affecting the Silicon sensors and the readout electronics is a challenge to i i i i i i

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be met. The first experiment at a hadron collider operating a Silicon vertex detector was CDF in 1992 [7] at the proton anti-proton collider TEVATRON located at Fermilab. For the success of CDF the operation of this detector was decisive. At the start of CDF, the main goal was the discovery of the top quark, the last missing quark of the three family model. The top quarks were expected to be produced predominantly by quark anti-quark annihilation into a gluon which subsequently decays into a top anti-top pair. The standard model of particle physics predicts further the dominant decay of the top quark into a W-Boson and a b-quark. The identification, or tagging, of these b-quarks was the domain of the vertex detector. CDF was successful and published the first evidence for the top quark in 1994 [6]. In the year 2000 CDF upgraded this Silicon system and installed the largest Sili- con detector [7] of this time. The new CDF Silicon detector including the so-called layer 00 and the intermediate Silicon layer, uses 1752 Silicon sensors in total. For the first time the signals from the Silicon detector were already used in the trigger logic to reduce the background online.

14.5 The CMS Inner Tracker

So far Silicon detectors were used to construct vertex detectors - detectors close to the interaction point. For the large tracking volumes necessary in most experiments gas detectors were employed, e.g. time projection chambers. The ﬁrst experiment which took up the challenge to develop a full Silicon tracking system was CMS (Compact Muon Solenoid) at the Large Hadron Collider at CERN. The CMS Inner Tracker [8] is geometrically divided into several substruc- tures (see Fig. 14.6) the pixel detector very close to the interaction point and the strip tracker consisting of the inner barrel detector (TIB), the inner discs (TID), the outer barrel (TOB) and the two end cap detector systems (TEC). The overall length of the Inner Tracker is 5.4 m with an outer diameter of 2.4 m. The temperature inside the tracker will be adjusted such that the maximum temperature of the silicon sensors will not exceed −10◦C. Details on the layout and the construction of the pixel and of the strip detector are explained in the following subsections.

14.5.1 The Pixel Detector Three cylindrical layers of hybrid pixel detector modules surround the interaction point at radii of 4.4, 7.3 and 10.2 cm. Two discs of pixel modules on each side complement the pixel detector. The pixel detector modules are built as hybrid pixel as- semblies containing the components described in the following. The active silicon sensors are realized on high resistance n-substrate with an implanted pn-junction and a pixel cell size of 100x150 µm2. Indium bumps are deposited onto the sensors for subsequent connection to the readout electronics. The readout electronics consists of custom ASICs fabricated in a commercial 0.25 µm process. Each chip processes the signals from 4160 pixels. Up to 16 chips are bump bonded onto one sensor wafer. On top of the sensor chip assembly is a low mass multilayer printed circuit board holding an additional control chip and other components. Figure 14.7 shows a picture of an assembled barrel pixel module. Further details on the technology used for the pixel detector can be found in [9].

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Fig. 14.6. Schematic cross section through the CMS tracker. Each line represents a detector module. Double lines indicate back-to-back modules which deliver stereo hits.

Fig. 14.7. A barrel pixel module (66.6 x 26.0 mm2).

14.5.2 The Strip Detector

The strip detector surrounds the pixel detector and adds additional 10 detector layers in the central region (4 TIB, 6 TOB). In addition 3 small and 9 large detectors discs (TID and TEC) are located on either side [10]. The basic construction element of the silicon strip tracker is a module. The supporting frame of a module is made of carbon fibre or graphite. Glued onto the frame is a Kapton layer to isolate the frame from the silicon [11] and to provide the electrical connection to the silicon backplane. A ceramic multilayer circuit (hybrid) holds the readout chips and the auxiliary chips. A glass pitch adapter is mounted between the hybrid and the first silicon sensor to match the different pitches of the chips’ input pads and of the sensor strips. Wire bond connections between the individual channels of the readout chips and the pitch adapter, between the pitch adapter and the first sensor and between the two sensors provide the electrical connections. The modules of the TIB, the TID and the four inner rings of TEC consist of only one silicon sensor, whereas the modules of the TOB

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and the three outer rings of TEC hold two sensors. All barrel modules are of rectangular shape. The modules of the discs have a wedge shape in order to form rings. Figure 14.3 shows a final module of the second ring of the TEC. The first two layers in TIB and TOB, the first two rings in TID and the rings 1, 2, and 5 in TEC are instrumented with double-sided modules. These are made of two independent single-sided modules, mounted back to back and rotated by 100 mrad with respect to each other. Table 14.1 lists some numbers illustrating the overall dimensions of the Inner Tracker strip detector.

Table 14.1. Some key parameters of the CMS Silicon strip tracker construction.

Area of active silicon ≈ 200 m2 Number of silicon sensors 24,244 Different sensor designs 15 Number of modules 15,148 Mechanically different module designs 27 Number of strips ≈ 9,300,000 Number of electronics channels ≈ 9,300,000 Number of readout chips ≈ 73,000 Number of wire bonds ≈ 25,000,000

14.5.3 Installation and Commissioning

The large strip tracker was completed at CERN using the tracker integration facility - a clean room with facilities to assemble, connect and operate part of the tracker in turn. The sealed tracker was finally transported from the integration facility to the experimental area and lifted down into the cavern. On December 15, 2007 the tracker was inserted into the final place inside the experiment CMS. After the installation of the beam pipe in CMS, the pixel detector was inserted into the tracker, completing the inner tracking system of CMS. Since summer 2008 the Inner Tracker is included in the CMS data taking. To commission the CMS experiment cosmic ray events were measured in 2008 with the CMS detector closed and the magnetic field of the superconducting magnet at the nominal operating field of 3.8 T. In this configuration more than 300 million cosmic events were recorded. The Inner Tracker was 95% of the time included in the data aquisition. About 6 million of these events had particle tracks within the Inner Tracker volume. Table 14.2 lists the percentage of hardware operating within specification for the various tracker subsystems in this first runnig period. With the only exception of the forward pixel system the percentage was between 97% and 99%. In the following winter shutdown it was possible to improve this already excellent figures. The forward pixel system was removed and repaired. Meanwhile all systems show comparable excellent performances.

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Table 14.2. Percentage of operating hardware during the cosmic ray data taking period in 2008. BPix FPix TIB/TID TOB TEC+ TEC- 99.1% 94.0% 97% 98.0% 99.2% 98.3%

The data taken was also used to test the software procedures for reconstruction and alignment. Using the standard LHC tracking software with only small modiﬁcations to take the particularities of cosmic ray events into account the achieved reconstruction efﬁciency is about 99% and in good agreement with the prediction of Monte Carlo studies. A further crucial check of the detector quality is the achieved internal alignment using this data and the software alignment procedure developed. Figure 14.8 shows the residual distribution of modules in the TIB and TOB (the barrel of the Inner Tracker) shortly after the cosmic data was taken and the alignment procedure was applied. The r.m.s. of the distributions are about 26 to 27 µm. This is an excellent result not far from the design goal to be achieved with real collisions in LHC. It proves that the detector was built with the required precision and that the software developed for reconstruction and alignment perform as expected.

Fig. 14.8. Residual distribution of modules in the TIB and TOB subsystems.

Figure 14.9 shows a typical cosmic ray event recorded in CMS. The muon entered CMS from the top, traversed all detector layers of CMS and eventually left the detector at the bottom. The right side of the ﬁgure shows a zoom of the tracker region. This particular muon did traverse all layers of the barrel tracker and the pixel detector. The reconstruction proves the functioning of all CMS detector systems. The CMS experiment is ready to record collision from the Large Hadron Col- lider!

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Fig. 14.9. A muon from cosmic ray traversing the CMS experiment. Left: Full view of the CMS detector. Right: Reconstructed track in the Inner Tracker.

14.6 Acknowledgement

I would like to thank the organizers of the First IPM Meeting on LHC Physics for the perfect organization of this conference in the beautiful city of Isfahan. I would like to thank the numerous colleagues who contributed to the design, construction and commissioning of the CMS Inner Tracker. A special thanks goes to Frank Hartmann who provided me with many details from early silicon detectors. More on the history and the development of Silicon detectors can be found in his book [12].

References

1. B. Hyams et al., Nucl. Instr. and Meth. 205 (1983) 99 2. M. Krammer, Nucl. Instr. and Methods A 379 (1996) 384 3. N. Bingefors et al., Nucl. Instr. and Meth. A 328 (1993) 447 4. P. Chochula et al., Nucl. Instr. and Meth. A 412 (1998) 304 5. W.C. Carithers et al., Nucl. Instr. and Meth. A 289 (1990) 388 6. F. Abe et al., Phys. Rev. D50 (1994) 2966 7. A. Sill, Nucl. Instr. and Meth. A 447 (2000) 1 8. CMS Tracker TDR, CERN/LHCC 98-6 CMS TDR 5 (1998) and CMS TDR Addendum, LHCC 2000-016 (2000). 9. The CMS pixel detector, A. Dominguez, Nucl. Instr. and Meth. A 581 (2007) 343. 10. Construction of the CMS silicon strip tracker, G. H. Dirkes, Nucl. Instr. and Meth. A 581 (2007) 299. 11. The Silicon Sensors for the Compact Muon Solenoid Tracker - Design and Qualiﬁcation Procedure, J.-L. Agram et al., Nucl. Instr. and Meth. A 517 (2004) 77. 12. Evolution of Silicon Sensor Technology in Particle Physics, F. Hartmann, Springer (2009)

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15 The LHC Grid Challenge

F. Malek

LPSC, Universite´ Joseph Fourier Grenoble and CNRS/IN2P3, France.

Abstract. The LHC computing is a worldwide complex machinery relying on several grid technologies such as EGEE and OSG, tens of middlewares, hundred of computing centers and is operated and used by thousands of people, engineers and physicists. This paper describes how this human adventure began and to what extent it is usable today and ready for the start up of the LHC.

15.1 The Worldwide LHC Computing Grid

The primary reason for the decision to adopt a distributed computing approach to manage LHC data was money. In 1999, when work began on the design of the computing system for LHC data analysis, it rapidly became clear that the required computing capacity was far beyond the funding capacity available at CERN. On the other hand, most of the laboratories and universities collaborating on the LHC had access to national or regional computing facilities. The obvious question was: could these facilities be somehow integrated to provide a single LHC computing service? The rapid evolution of wide area networking, the increase capacity and bandwidth coupled with falling costs made it possible. From there, the path to the Worldwide LHC Computing Grid was set. During the development of the Worldwide LHC Computing Grid, many additional benefits of a distributed system became apparent. Multiple copies of data can be kept in different sites, ensuring access for all scientists involved, independently of geographical location; It allows optimum use of spare capacity for multiple computer centers, making it more efficient; Having computer centers in multiple time zones eases round-the-clock monitoring and the availability of expert support. The cost of maintenance and upgrades is distributed, since individual institutes fund local computing resources and retain responsibility for these, while still contributing to the global effort; Independently managed resources have encouraged novel approaches to computing and analysis; The so- called ”brain drain”, where researchers are forced to leave their country to access resources, is reduced when resources are available from their desktop; It provides considerable flexibility in deciding how and where to provide future computing resources. And finally, it allows community to take advantage of new technologies that may appear and that offer improved usability, cost effectiveness or energy efficiency. The WLCG technical Design Reports [1] were issued in June 2005, describing the grid infrastructure, the common tools to be developed and the computing

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models for each of the four LHC experiments. A Memorandum of Understand- ing [2] was agreed in October 2005 between the WLCG collaboration and the participating nations and funding agencies. This MoU guarantees the resources, the quality of services and looks 5-year forward for the resource planning. The quality of services includes a guarantee of the operations 24 hours a day and 7 days a week with intervention to services essential to the running of a center in a time laps of 4 hours. For any site, the target reliability and efﬁciency to reach is 98% . The Worldwide LHC Computing Grid combines the computing resources of more than 100,000 processors from 150 institutions in 33 countries, producing a massive distributed supercomputer that will provide more than 7000 physicists around the world with near real-time access to LHC data, and the means to process it.

Fig. 15.1. The real time GridPP monitoring showing the WLCG computing facilities processing jobs and transferring data.

Fig. 15.1 shows a snapshot of the WLCG real time monitoring where the worldwide computing centers are processing data and exchanging information. The computing centers providing resources for the Worldwide LHC Comput- ing Grid are also active in other grids, in particular Enabling Grids for E-sciencE (EGEE) in Europe and Open Science Grid (OSG) in the United States, but also several national and regional grid structures such as GridPP in the UK, INFN Grid in Italy and NorduGrid in the Nordic countries.

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Fig. 15.2. LHC experiments physics simulation jobs on WLCG infrastructure in 2009.

WLCG ran around 44 million ”jobs” or tasks in 2007 and more than 65 million jobs in 2008. In preparation for LHC start-up in 2009, WLCG has been running up to 500,000 jobs per day, simulating the running conditions of the LHC, see Fig. 15.2.

15.2 The WLCG distributed computing model

The LHC will produce around 15 petabytes (15 million gigabytes) of data every year for ten to ﬁfteen years. This is enough to ﬁll 3,000,000 DVDs, every year. Viewing 3,000,000 DVDs would take around 500 years. If LHC data were to be burned to CD, a tower of CDs around 20 kilometers high would be created within a year. The WLCG infrastructure is based on three ”tiers” and 33 countries are for- mally involved:

• The Tier0 is a single site: the CERN Computing Center. All data passes through this central hub but it provides less than 20% of the total computing capacity. • The Tier1s consist of eleven sites, located in Canada, France, Germany, Italy, the Netherlands, the Nordic countries, Spain, Taiwan, the UK, and two sites in the USA. • The Tier2s consist of 140 sites, grouped into 60 federations covering countries from Australia to U.S., passing by Asia and Europe. Together, these sites will provide around 50% of the capacity needed to process the LHC data. • The Tier2 sites then feed their data to PC clusters in physics institutes around the world, such that groups of scientists and individuals can analyze LHC data from their own desks.

The CERN facility is linked to other major grid centers using 10 Gigabit per second optical wide area links, as well as to the general global education and research network infrastructure. The four LHC experiments computing models rely on the distributed computing facilities sketched on Fig. 15.3. More details i i i i i i

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Fig. 15.3. The LHC distributed computing model

can be found in the computing models described in the technical design reports for each of the experiments [3].

15.3 Computing within the LHC experiments

The Tier0 and the CAF (Cern Analysis Facility) have very much the same func- tionality for all experiments. Each LHC experiment is a Virtual Organization (VO) with a set of policies (certification, security, grid middleware, specific software, etc.). The Tier0 is the central hub where all the data passes through before they are distributed to the Tier1’s for reprocessing. The CAF is mainly used for the calibrations, first streams analysis and local users analyses. The Tier1’s have the principal role of reprocessing the data and the Tier2’s deal with the simulation and the physics analysis. As an example, the CMS computing model is sketched on Fig. 15.4. However, each of the four LHC experiment rely on its own computing model which differ somehow from the others, especially in the services (data manage- ment, data distribution, Tiers relations, etc.). For example, CMS analysis jobs in Tier2s can get data from any Tier1 while for ATLAS, the analysis jobs in Tier2s can get data only from the Tier1 within the same cloud. The clouds in ATLAS are defined as federation of Tiers within the same country or a defined region. Fig. 15.5 shows the flowchart of ATLAS clouds where eight of them are operated under EGEE, the European grid infrastructure. The IN2P3 cloud, for example, is a region which comprises the French sites and the associated ones: Japan, China and Romania. Also, CMS analysis coordination is per Tier2 while in ATLAS the coordination is done per physics group and/or cloud. The four LHC experiment rely on some common software like physics generation (Genser, HepMC, ...) or detector simulation (Geant4, Fluka, Garfield, ...).

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Fig. 15.4. CMS Data ﬂow structure.

Fig. 15.5. The ATLAS experiment Clouds infrastructure.

They also have some common core libraries and services, LCG applications packages like ROOT (Physics analysis), COOL, POOL (condition data bases) etc. But, each of the four LHC expriments has its own software infrastructure: Aliroot, Gaudi, CMSSW, Athena. The analysis tools and packages (PANDA, GANGA, ALIEN, CRAB, ...) are also quite different from one experiment to the other. All these tools should run on some 20 different platforms and operating systems. Last but not least, since the precision of calculation is an asset, the whole infrastructure must run on both 32 bits and 64 bits machines.

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132 F. Malek 15.4 Conclusion and Future challenges

The WLCG applications support and service meet with satisfaction the requirements and the baseline services are in production. There is, as expected, a continuously increasing capacity and workload and the general site reliability is improving. It has already reached a quality level of 95% for most of the Tier1s, the target value being 98% as ﬁxed by the WLCG MoU. The data and storage services remain the weak points of WLCG. Neverthe- less, sites and experiments are working well together to tackle the problems. Many data transfers, LCG services, experiment challenges are now involving most sites and the most realistic scenarii are taken into account.

Fig. 15.6. VO-wise data transfer from all sites to all sites from march 2005 to March 2009.

Combined computing readiness challenges in Feb-May 2008 (called CCRC08) and in May-June 2009 (called STEP 09) were essential to provide experience for site operations and storage systems. The infrastructure as a whole was stressed simultaneously by all four experiments. The plot on Fig. 15.6 show the results of the data transfer exercises done by the four LHC experiments since 2005. A data movement of around 2.5 petaBytes was reached in 2008. As more data is gathered from collisions inside the LHC, there will be increasing demand upon the storage and processing capacity of the Worldwide LHC Computing Grid. These challenges will include the increase of available resources in response to planned upgrades to the LHC accelerator, as well as to the increasing data requirements of the four LHC experiments. Besides this, conversion to new and evolving technologies is important. Even during the planning and design of the Worldwide LHC Computing Grid there were significant changes to available technologies. So we need to remain flexible and adaptable. Continuing to optimize the use of multi-core processors, where cores increase beyond two or four or eight processors to 16- or 32-core processors is essential. And finally, working with limitations in terms of the cooling and power requirements of large data centers, is an ongoing issue shared by large data centers all over the world.

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Fig. 15.7. Usage of the EGEE infrastructure by all scientiﬁc communities from 2008 to early 2009.

Lessons learned from the Worldwide LHC Computing Grid have driven further innovation in grids all over the world, changing the way science is done. Grids are being used in the fight against disease, climate change, air pollution and more. Any science that requires intensive simulation or calculation can benefit from grid computing. Fig. 15.7 shows the usage of the worldwide grid infrastructure EGEE. One can observe that since a year, 40% of the CPU resources are used by non HEP communities which indicates that grid infrastructures are becoming a useful tool for all scientific fields.

References

1. CERN-LHCC-2005-024, see also: http://lcg.web.cern.ch/LCG/tdr/. 2. CERN-C-RRB-2005-01. 3. ALICE-TDR-012: CERN-LHCC-2005-018; ATLAS-TDR-017: CERN-LHCC-2005-022; CMS-TDR-007: CERN-LHCC-2005-023; LHCb-TDR-11: CERN-LHCC-2005-019.

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16 Overview of the Muon System of CMS

S. Marcellini

I.N.F.N. Sezione di Bologna, Italy

Abstract. The muon system of the CMS experiment at the CERN LHC is described. The aspects and performances of their components are reviewed. The importance of the system for triggering purpose is reviewed, and the expectations for muon momentum reconstruction are discussed.

The Compact Muon Solenoid (CMS) is one of the experiments which will operate at the Large Hadron Collider (LHC) at Cern, at the center of mass energy √ s = 14 TeV. From a p-p collision rate of 40 MHz, the experiment will collect data with a maximum data-aquisition rate of about 100 Hz written on storage device, thus operating a reduction larger than 105. The detector is described in detail in [1]. The muon system is a relevant part of the apparatus. High momentum muons are produced in many Standard Model processes, like top quark, W and Z decay, and they are also an important signature of possible new physics channels, Higgs Boson decay on top of them [2]. Hence a robust and redundant muon spectrometer is needed to provide precise muon identification, good transverse momentum resolution (pT ) measurement up to momenta of several TeV, unambiguous charge identification, and excellent trigger capability. Concerning the trigger requirements, the muon system has to provide reliable momentum measurement already at trigger level, where pT threshold will be applied, to avoid feed-through of mis-measured muons from the lower part of the pT spectrum. In addition, being the di-muon rate above a given pT threshold about a factor 100 lower than the single muon rate at the same threshold, the muon ghost rate has to be kept below 0.5 %. The muon trigger system also has to assign the trigger candidate to the LHC bunch crossing (BX) at which the muon was produced. The distance between two consecutive BXs at LHC is 25 ns. The muon system, described in detail in [3], is the outermost detector of the CMS experiment, and it covers a pseudorapidity region |η| < 2.4. Figure 16.1 shows a quadrant of the detector, in the y-z plane, where z is the direction along the LHC beam. The detector is divided in two main parts: the “barrel”, in the region |η| < 1.2, and the “endcaps”, with 0.8< |η| < 2.4. The so-called “overlap region”, with 0.8< |η| < 1.2, is where muons from the interaction point cross both the barrel and the end-caps of the system. The iron of the muon detector also acts as return joke for the 4 T solenoidal magnetic field produced by the superconducting inner magnet, thus keeping the size of the CMS detector relatively small, considering the field intensity. The barrel and the end-caps will be affected by very different conditions in terms of particle rate and magnetic field intensity, during the LHC operation. In

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Fig. 16.1. Sketch of a quadrant of the CMS detector, in its longitudinal view.

the barrel the expected muon rate will be of the order of 1 Hz/cm2 or lower, and the neutron induced background is expected to be negligible. The magnetic field intensity in the active parts of the barrel detector is rather small and uniform. The only region where some relevant non uniformity is expected is the part of the inner barrel stations more distant from the interaction point, where the magnetic field lines bend rapidly from the inner magnet into the iron of the joke. In the end-caps region the environment is very different: a large muon rate, up to 1000 Hz/cm2 is expected, and the photon and neutron induced background will be also comparable. In addition, in this part of the detector the magnetic field is very non-uniform and its intensity will reach 3.5 T. These factors impose strong constraints on the choice of the active detectors to be used. In the barrel the active detectors are Drift-Tube (DT) based units, whereas the end-caps are equipped with Cathode Strip Chambers (CSC). In order to ensure redundancy and robust- ness to the triggering capability, Resistive Plate Chambers (RPCs) are also used both in barrel and end-caps, covering a region 0.8< |η| < 2.1. The DT system basic unit is a rectangular drift tube, with a section of 13x42 mm2 and a variable length, of the order of few meters, depending on its position in the detector, with an anode wire placed in the center and running along the tube’s length. Tubes are arranged in layers, which can detect the muon passage both in the r − φ transverse plane, and in the r − θ longitudinal plane. Layers are arranged in stations, which contain 8 DT layers in the r − φ and 4 layers in the r − θ view. A muon from the interaction point can cross up to four muon stations. In total 250 stations are hosted in the CMS muon barrel. The single hit resolution in the r − φ plane is between 200 and 250 µm Each station can locally reconstruct

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16 Overview of the Muon System of CMS 137

Fig. 16.2. GMT expected efﬁciency for single muons, with 3 < pT < 100 GeV, as a function of pseudorapidity, from Monte Carlo simulation.

muon segments from the TDC hits informations, and deliver the trigger primitives, which are built by dedicated on-board electronics. Then the informations from the various muon stations can be combined to perform muon track reconstruction (standalone muons) and trigger track candidates. The DT detectors are not suitable for the high particle flux in the forward region of the CMS detector, as their drift path is too large to cope with high particle rate. The end-caps are therefore equipped with CSC chambers, which are multiwire proportional detectors, with a 100 µm single hit resolution, which will sustain high particle rate and highly inhomogeneous magnetic field. Each station contains 6 gas gaps, with wires perpendicular to the cathode strips, allowing the simultaneous measurement both in the r − φ and r − θ plane. Trigger primitives are characterized by 1 mm position resolution, and the time precision of 4.5 ns unambiguously defines the BX assignment. At high pseudorapidity a muon will cross 3 or 4 stations. In order to have a redundant and robust muon trigger, an additional system, based on RPC detectors, is also hosted both in the barrel and in the end-caps of the muon detector. RPCs used in the CMS experiments are double-gap type. This allows to reach high efficiency keeping the gain lower. RPC have a very fast time response, with a time resolution of the order of 1 ns. They can therefore provide very precise BX identification, and they can work in a particle rate envi-

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Fig. 16.3. Output of the Level-1 GMT for single muon events, as a function of the pT threshold, from Monte Carlo simulation. Results are obtained for the case of high luminosity L = 1034cm−2s−1.

ronment as high as 1000 Hz/cm2. The Level-1 trigger of the CMS experiment is designed to take a fast accept/reject decision performing a rough reconstruction of the physics objects, on the basis of informations from calorimeters and muon station. This must be done for any BX, with no dead-time. To reach this goal the system is implemented using custom developed programmable hardware. Both the calorimeters and the muon systems provide triggers independently, and then the Global Trigger (GT) has the task to merge their informations and take the decision to deliver the Level-1 accept signal. The Level-1 trigger has to operate a data rejection such that the output rate will be of the order of 10-50 KHz, depending on the data taking conditions. Roughly half of this bandwidth will be dedicated to Level-1 muon trigger. All the three muon systems take part to the Level-1 trigger. DT in the barrel and CSC in the end-caps both provide very good spatial resolution, whereas excellent time resolution is obtained by the RPCs. Each system delivers the best four muon candidates (the four muons with highest transverse momentum reconstructed at trigger level) to the Global Muon Trigger (GMT), which selects the best four muon candidates to be sent to the GT, with a logic which takes into account a proper matching between the various detectors. The GT can set pT threshold in a range which can vary from 0 to several tens of GeV, on single muons and di-muons, to cope with different LHC conditions in terms

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16 Overview of the Muon System of CMS 139

Fig. 16.4. Transverse momentum resolution, as expected from Monte Carlo simulation as a function of the muon transverse momentum. The cases when track is reconstructed with tracker system only, with muon system only, or both, are shown separately.

of luminosity and background. Figure 16.2 shows the Monte Carlo expected trigger efficiency at the output of the GMT, as a function of the pseudorapidity of the muon. The efficiency for the three separate muon subsystems are superimposed. The regions of lower efficiency are due to geometrical acceptance, and they are mostly recovered at the output of the GMT. Figure 16.3 shows the Monte Carlo Level-1 single muon trigger rate at the output of the GMT, as a function of the transverse momentum pT, expected for the high luminosity case L = 1034cm−2s−1. The observed rate at is higher than the generated one due to the feed-through of low momentum muons (whose production rate is very high) which fill the higher momenta bins due to momentum mis-measurement. A GMT rate of about 20 Hz is obtained with a pT threshold of few tens of GeV. At lower luminosity this threshold can be lowered. At the LHC startup, when the luminosity will be more than 2 orders of magnitude lower, and √ the center of mass energy will be s = 10 TeV, the single muon pT threshold will be as low as 3 GeV, which is the minimum momentum a muons must have to reach the outer part of the muon detector. The muon system will provide an independent way to measure muon momentum. For muons with pT < 200 GeV, the momentum measurement is essentially given by the tracker only. Above this value, the inclusion of the muon system in the determination of the particle momentum becomes more and more im-

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portant, due to the high lever arm provided by the muon detector hits, which are placed several meters away from the interaction point. An accurate calibration, and a precise knowledge of the alignment of the detector are mandatory to reach the best performance. Figure 16.4 shows the transverse momentum resolution in the central part of the CMS detector, with and without the inclusion of the muon detector informations, as expected from Monte Carlo simulation. Single proton beams of 900 GeV energy were injected in the LHC machine at September 10, 2008, at the accelerator startup. In the few days before the LHC incident occurred, and which caused the machine stop for major interventions, the muon appartus detected very clearly and very efﬁciently off-beam muons and muons produced by beam splash against the collimators placed several meters before interaction points. These muons typically cross the detector longitudinally, and were used to test the detector trigger, the synchronization of the various parts, and the alignment procedures in the end-caps. The experiment is now in a re-commissioning phase, and it will be ready to collect data from LHC interactions scheduled late in 2009.

References

1. S. Chatrchyan et al., The CMS Collaboration, The CMS Experiment at LHC, JINST 3 (2008) S08004 2. CMS Collaboration, CMS Physics, Technical Design Report,Volume II, Physics Perfor- mance, CERN/LHCC 2006-21 3. CMS Collaboration, The Muon Project, Technical Design Report, CERN/LHCC 97-32

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17 Target mass correction and its effect in polarized deep inelastic scattering

A. Mirjalilia,b, H. Mahdizadeh Saffara

a Physics Department, Yazd University, P.O.B 89195-741, Yazd, Iran bSchool of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran

Abstract. We use phenomenological valon model to extract polarized parton densities and ﬁnally polarized proton structure function. The comparison of the used model with available experimental data indicates that the used model is adequate. Since the results at low Q2 and large x values, did not pass well through the curve which obtains from the model, we employ target mass correction in our calculations. Considering these corrections, the improvement of the results are impressive.

17.1 Introduction

Lepton Scattering from nucleon targets plays an essential role in getting our insights from proton as a combined particle which consists from quarks and gluons. Experimental data which are resulted from electron scattering at high Q2, deep inelastic scattering (DIS), are used to extract parton distributions. By increasing the variety of data and also their precisions, it is necessary to improve the theoretical analysis. This can be done by adding some corrections to the analytical expressions which exist. One of the most important corrections, is the target effect which is M2 j in terms of powers of ( Q2 ) , where M is the mass of target and Q is the energy which ascribe to an intermediate particle which probe the nucleon. In this case we have an expansion which its coefﬁcients indicates the different orders of twist. Other coefﬁcients of expansion are proportional to higher twist. They enter in calculation where partonic correlation and appearance of gluon are considered. M2 j The theoretical point view of ( Q2 ) expression is contained in OPE (Operator Product Expansion) theorem which was initiated by K.G.Wilson[1].

17.2 Theoretical framework

In considering the target mass correction (TMC), we encounter with the production of two currents. The currents which take place inside the nucleon and are very close each other, so as we can consider them in one place. This production is indicated by jµ(x)jν(y) which is used in calculation the amplitude of compton scattering:

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142 A. Mirjalili, H. Mahdizadeh Saffar

Z 4 iqx Tµν = i d xe < PS|T(Jµ(x)Jν(0))|PS > . (17.1)

The imaginary part of this amplitude is related to hadronic tensor:

1 W = ImT . (17.2) µν 2π µν

Calculating the jµ(x)jν(y) production at very close distances, will yield some divergencies and to avoid them we need to restore to OPE. According to OPE, commutation of two A(x) and B(x) ﬁelds are expressed as:

→− →− X →− →− [A(x0, x ),B(x0, y )] = Dn( x − y )On(x). (17.3) n →− →− On(x) is indicating a summation of operators in x and Dn( x − y ) is representing Dirac Delta functions or its derivatives. In OPE, time ordered product of two operator which are taken place almost at the same place, is expressed as follows[2]:

Z 4 iqx i d xe < PS|T(Jµ(x)Jν(0))|PS > X n = cn,i(q, M) < PS|Oi |PS > . (17.4) n,i

n The matrix elements < PS|Oi |PS > is relating to experimental data and are completely independent of q as renormalization or factorization scale. The q-dependance is entering just through cn,i(q, M) and the mass of nucleon is also appearing by this quantity. The simultaneous dependence to Q2 and M2 in M2 cn,i(q, M) will cause the appearance of different powers of Q2 in expansion of current products and ﬁnally will yield some expression for mass effect correction. TMC ic nominated mostly at medium of Q2 and large x-values while in these regions, there are not good agreement between theoretical results of polarized parton distribution and experimental data. The present difference between theoretical predictions and experimental data for polarized parton structure function, is the main motivation to consider TMC which we pay attention to it here. In DIS, the Bjorken variable, x, is introduced as:

Q2 Q2 x = = ( ) . (17.5) 2P.q 2Mν rest

Here P and q are the four momentum of target particle and photon propaga- tor. ν is the energy difference between incoming and outgoing particle.

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17 Target mass correction and its effect in polarized deep inelastic scattering 143

By considering the mass of target particle, while quarks are massless, instead of Bjorken variable, x, we will have Natchmann variable as:

2x 2x ξ = q ≡ . (17.6) 4x2M2 1 + r 1 + 1 + Q2

It can be seen easily that the Natchmann variable at large values of Q2 is converted to x variable. 2 Mass effect correction to polarized structure function g1(x, Q ), in terms of moment of matrix elements of second and third twist operator while we are at third order of mass approximation, can be written as follows[3]:

M2 n(n + 1) gTMC(n, Q2) = a + (na + 4d ) 1 n Q2 (n + 2)2 n+2 n+2 M2 n(n + 1)(n + 2) +( )2 (na + 8d ) Q2 2(n + 4)2 n+4 n+4

M2 n(n + 1)(n + 2)(n + 3) + ( )3 (na + 12d ).(17.7) Q2 6(n + 6)2 n+6 n+6

The an and dn quantities are obtained in the following way. From the product expansion of simultaneous currents and according to the OPE theorem, The σµ1...µn−1 λσµ1...µn−2 operators like R1 and R2 can be written as:

σµ1...µn−1 σµ1...µn−1 < PS|R1 |PS >= −2ManM1 , (17.8)

λσµ1...µn−2 λσµ1...µn−2 < PS|R2 |PS >= MdnM2 . (17.9)

σµ1...µn−1 M1 is a symmetric tensor of order n. It is constructed by spin four λσµ1...µn−2 σµ1...µn−1 vector, S, and n − 1 four vector of P. M2 is deﬁned like M1 with the difference that it is antisymmetric under the exchange of λ and σ indices while are symmetric under the exchange of other indices. These two operators are traceless. σµ1...µn−1 The quantities an and bn are reduced matrix elements of R1 and λσµ1...µn−2 R2 operators. These operators are in fact representation of second and third order of twist. Calculation of an and dn are very hard but it has been done in [4], using the Natchmann variable and the the related expressions for them, are:

Z 1 n+1 2 2 ξ x n M 2 an = dx 2 {[ − 2 2 xξ]g1(x, Q ) 0 x ξ (n + 2) Q M2 4n − x2 g (x, Q2)}, Q2 n + 2 2

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(n = 3, 5, ...), (17.10)

Z 1 n+1 ξ x 2 dn = dx 2 { g1(x, Q ) 0 x ξ n x2 n M2 +[ − x2]g (x, Q2)}, n − 1 ξ2 n + 1 Q2 2

(n = 3, 5, ...). (17.11)

2 The structure function g2(x, Q ) in above equations, can be calculated in 2 terms of g1(x, Q ) as follows:

Z 1 2 2 2 g1(y, Q ) g2(x, Q ) = −g1(x, Q ) + dy. (17.12) x y

17.3 Polarized structure function and TMC

To follow the calculation to obtain TMC effect, we need ﬁrst to calculate the po- p larized structure function g1 . According to the quark model, in the LO approxi- p mation, g1 can be written as a linear combination of δq and δq [5,6], 1 X gp(x, Q2) = e2 [δq(x, Q2) + δq(x, Q2)] , (17.13) 1 2 q q

where eq are the electric charges of the (light) quark-ﬂavours q = u, d, s. Here the sum usually runs over the light quark-ﬂavours q = u, d, s, since the heavy quark contributions (c, b,...) could preferably be calculated perturbatively from the intrinsic light quark (u, d, s) and gluon (g) partonic-constituents of the nucleon.

p 2 Within the MS factorization scheme the NLO contributions to g1 (x, Q ) are ﬁnally given by [5]

1 X © α (Q2) ª gp(x, Q2) = e2 δq(x, Q2)+δq¯ (x, Q2)+ s [δC ⊗(δq+δq¯ )+2δC ⊗δg] , 1 2 q 2π q g q (17.14)

with the convolutions deﬁned as Z1 dy x (C ⊗ q)(x, Q2) = C( )q(y, Q2) . (17.15) y y x One can relate the polarized structure function with its Mellin moments, based on hyper geometrical expansion [7]. In this way, extraction of the unknown parameters which exist in the phenomenological valon model can be done. We p obtained polarized proton structure function, xg1 , based on this method. This structure function in the LO and NLO approximations can now be presented.

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17 Target mass correction and its effect in polarized deep inelastic scattering 145

p 2 2 Fig. 17.1. The plot of xg1 in terms of x variable at Q = 2 GeV , in the NLO approximation. Comparison with the experimental data is also indicted.

p 2 2 The results for xg1 in the NLO approximations as a function of x at Q = 2 GeV is depicted in Fig. 16.1. A comparison with experimental data [8,9] have also been done. 2 p 2 Since we access to xg1(x, Q ) , we can obtain obtain g2 (x, Q ) function, using Eq. (17.12) and then using Eqs.(17.10-17.11), we can calculate an and dn quan- 2 tities. Due to very complex form of g1(x, Q ) which is obtained in constituent quark model (Valon-model)[10], the Mathematica software is not able to calcu- R 2 1 g1(y,Q ) late directly the integral 0 y dy. To do this integral, we substitute it with a polynomial function of y while there are some unknown parameters which will be obtained by ﬁtting. To do the integral in Eq. (17.10) and Eq. (17.11) we need to use from the numerical solution and among them, the Newton-Cotes is the one which we use it. using this method, we will be able to calculate an and dn quantities and target mass correction can be obtained. The results are depicted in Fig. 16.2 at Q2 = 2Gev2 in the NLO approximation. The comparison with usual case while we do not employ TMC, are also done. As can be seen there are a shift toward up for top 2 of g1(x, Q ) when we employ TMC and the agreement with experimental data is increased.

17.4 Conclusions

Employing TMC had a noticeable effect at large value of x and low values of Q2. It has an effective improvement at the mentioned ranges. But as it can be seen in Figs. 16.1,16.2 the corrected structure function has not enough precision at the low-x values and do not cover the experimental data at these values of x. Further-

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p TMC 2 2 Fig. 17.2. Comparison between xg1 and xg1 (x, Q ) in terms of x variable at Q = 2 GeV2 in the NLO approximation. Experimental data are also included.

TMC 2 more the surface area under the plot of the xg1 (x, Q ) function is more than 2 the surface area which is related to xg1(x, Q ). This is in contradiction to the existence constrains. To obey the constrains, we need to extract the unknown parameters from a structure function which involves the TMC correction beforehand. TMC 2 This means we should fit xg1 (x, Q ) over the experimental data rather than 2 xg1(x, Q ). This fitting procedure is based on using the hypergeometric polynomials. Due to multiple integrals which appear in this way, the calculations will not be easy and we should find a numerical way in which the following of the calculations is possible. This can be done as a new research job in future.

References

1. K.G. Wilson, Phys. Rev. 179 (1969) 1499. 2. H. Georgi and H. D. Politzer, Physical Review D 14 (1976) 1829. 3. Y. B. Dong, Physics Letters B 653 (2007) 18-22. 4. S. Wandzura, Nuclear Physics B 122 (1977) 412; S. Matsuda, T. Uematsu, Nuclear Physics B 168 (1980) 181. 5. G. Altarelli and Parisi, Nucl. Phys. B126, 298 (1977); B. Lampe and E. Reya, Phys.Rept. 332,(2000) 1. 6. G. Altarelli, Phys. Rep. 81,(1982) 1. 7. A. L. Kataev, G. Parente and A. V. Sidorov; Phys. Part. Nucl. 34(2003) 20. 8. E143 Collaboration, K. Abe et al., Phys. Rev. D58,(1998) 112003 ; Airapetian et al., Phys.Lett.B442 (1998) 484. 9. Spin Muon Collaboration, D. Adams et al., Phys. Rev. D 56,(1997) 5330. 10. B. Lampe and E. Reya, Physics Reports 332 (2000) 1-163.

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18 Single Top Production at the LHC with CMS Detector

M. Mohammadi Najafabadi

School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran

Abstract. The detection of single-top events with the CMS detector with center of mass energy of 14 TeV of colliding protons is discussed. The selections are proposed, aimed to measure single top production in the Standard Model t- channel, s-channel and tW- channel. The perspectives of the measurements for an integrated luminosity of 10 fb−1 are described. The results are based on detailed detector simulations, either based on GEANT4, or on faster techniques. The reconstruction procedures developed by the CMS Collabora- tion are utilized.

18.1 Introduction

1 In the Standard Model (SM) the top quark is a spin- 2 fermion with electric charge 2 − 3 e, the weak isospin partner of the quark, and a color triplet. Even within the SM the top quark is a very special object. Indeed, the top quark is much heavier than all other quarks in the SM and the top Yukawa coupling is surprisingly −24 close to one. The top quark lifetime, τt = 0.4 × 10 s, is much smaller than the typical time for the formation of QCD bound states. Therefore, the top quark decays long before it can hadronize, providing a very clean source for fundamental information. At the LHC the top quarks are expected to be produced either in pair or singly. Due to strong interactions of the top quarks with gluons, the top pair production mechanism dominates the top quark production rates. Single top production at the LHC can classiﬁed by the virtuality of the involved W-boson: 2 2 2 2 t-channel production (qW < 0), s-channel (qW > 0) and tW-channel (qW = MW ). The Feynman diagrams for these processes are shown in Fig.18.1. Recently the CDF and D0 experiments at Tevatron pp¯ collider both provided a 5σ observation of the single top [7,2]. The largest source of single top at the LHC in the center of mass energy of 14 TeV is t-channel with the total cross section of 240 pb. The cross section of tW- and s-channels are 66 pb and 10 pb, respectively. It is important to note that the cross section of top pair production is 833 pb which is much larger than single top. The study of single top quark production provides a unique possibility to investigate several features of the top quark and the SM. The cross sections of all three processes are directly proportional to the squared of the CKM matrix Vtb which allows to a direct measurement of this quantity and thus for a further

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148 M. Mohammadi Najafabadi

test of the SM. In particular the assumption that only three quark families exist can be probed via the study of single top production processes. The structure of Wtb vertex and the top quark FCNC (Flavor Changing Neutral Current) can be investigated using single top events. The existence of heavy charged gauge boson W0 and charged Higgs bosons can deviate the cross sections of t- and s- channel

of single top processes from the SM expectations [3].

¼ ¼

Õ Õ Õ Õ Õ

b Ø g Õ b

Ø¹chaÒÒeÐ ×¹chaÒÒeÐ

ØÏ ¹chaÒÒeÐ

b Ï Fig. 18.1. Feynman diagrams for single top quark production at the LHC.

18.2 Searches for single top quark at LHC with CMS detector

All single top production modes have been studied in the CMS, considering leptonic final states for the t- and s-channel and both the semi-leptonic and the di- leptonic decays in the tW-channel. The results here are aimed for an integrated luminosity of 10 fb−1 in the low luminosity regime of LHC. In the simulation, no artificial misalignment has been considered, but the systematic uncertainties from the knowledge of the jet energy scale and b-tagging efficiency have been taken into account. The single top signal samples have been generated using SingleTop (based on CompHEP) and TopReX with PYTHIA for the showering and hadronization steps. PYTHIA , TopReX and Alpgen were used for generation of background events. The results are based on detailed detector simulations, either based on GEANT4, or on faster techniques. The reconstruction procedures developed by the CMS Collaboration are utilized.

18.2.1 t-channel single top

The t-channel ﬁnal state for leptonic W decays is characterized by one isolated lepton, missing transverse energy from the neutrino, one b-jet from the t quark decay and one further jet with a broad |η| spectrum extending up to |η| ∼ 5. In the analysis of CMS only muonic decay of the W-boson is considered which is expected to be cleaner. Events are selected requiring a single isolated muon (pT > 19 GeV/c and |η| < 2.1), ET,miss > 40 GeV, one central b-tagged jet (pT > 35 GeV/c and |η| < 2.5) and one forward jet (pT > 40 GeV/c and |η| > 2.5).

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18 Single Top Production at the LHC with CMS Detector 149

The purity of the selected sample was increased cutting on the transverse mass of the reconstructed W boson, the mass of the top quark and the sum of the transverse momentum vectors of all reconstructed objects ΣT = pT,µ +ET,miss +ET,jets. A full description of the reconstruction and selection can be found in [4]. The expected yield is 2389 signal events and 1785 background events. The signal-to- background ratio is 1.4 and the dominant backgrounds are tt¯ and W + jj. The systematic uncertainty on the cross section has been computed taking into account theoretical uncertainties (PDF, masses of b and t quarks, ...), the uncertainty on the jet energy scale, the uncertainty on b-tagging and the uncertainty due to luminosity. The resulting uncertainty is: ∆σ = 2.7%(stat) ⊕ 8%(syst) ⊕ 5% = 10%. (18.1) σ

18.2.2 tW channel The tW associated production is a more challenging channel because a robust jet counting is necessary to reduce the large background from top pair events. Back- ground normalization using control samples extracted from data is also necessary to avoid introducing large systematic uncertainties, as the achievable S/B ratio is rather poor. Two analysis strategies have been developed, one for the semi-leptonic events (tW → bWW → bljj) and one for the di-leptonic events (tW → bWW → blνl0ν0). Information from the reconstructed tracks and jet shape variables were used in order to make jet counting more robust against calorimetric noise and pile-up. In the semi-leptonic decays, events are selected requiring one isolated lepton and exactly three jets, exactly one of which must be b-tagged; a cut on the missing transverse energy has also been applied to suppress QCD background. Additional selection cuts are applied to the transverse mass of the leptonically decaying W, on the mass of the two light jets and on the reconstructed top quark mass; the b ←→ W pairing was done combining in a Fisher discriminator angular variables, pT (top) and the charges (using for the jets the pT weighted sum of the charges of the tracks in the jet cone). A control sample dominated by tt¯ events was selected by requiring one additional jet. In the di-leptonic case: Two high pT isolated leptons are required, opposite in ﬂavor (e + µ) to suppress the Z/γ∗ → l+l− process, and a single jet, b-tagged. To normalize the dominant background from di-leptonic tt¯ a control sample was selected requiring one additional jet; the jet is required to be b-tagged to avoid signal contamination in this sample. The expectations in the semi-leptonic channel are 1700 signal events and 8734 background events for 10 −1, with S/B = 0.2; the dominant background is tt¯ (83%). In the di-leptonic case the expected yield is 562 signal events and 1488 background events (96% tt¯), corresponding to S/B = 0.4. Many sources of systematic uncertainties have been considered, both theoretical (PDFs, background cross sections) and experimental (jet energy scale, b-tagging efﬁciency, amount of pile-up). The expected accuracy on the cross sections is: ∆σ ∆σ (1l) = 19% , (2l) = 25% (18.2) σ σ i i i i i i

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The dominant systematic uncertainties are from the jet energy scale (both channels), b-tagging efﬁciency (di-leptonic) and amount of pile-up (semi-leptonic).

18.2.3 s-channel single top

At LHC the expected s-channel single top cross section is 10 pb, an order of magnitude smaller than t-channel and almost a factor 100 smaller than tt¯ The analysis has been done using W → eν and W → µν events together, and requiring two b tags. The s-channel selection requires one isolated high pT lepton, two b-tagged jets and missing transverse energy should be greater than 30 GeV. The W-boson is reconstructed from lepton and MET by imposing the mass constraint, and the top quark is reconstructed by combining the W with b-jet with most opposite jet charge. After reconstruction additional cuts are applied to the kinematic observables such as transverse mass of W, top mass, |Σ¯ T | and HT (scalar sum of the ET of all reconstructed objects including neutrino). Finally, the expected number of signal events passing all selection cuts is 273, together with 2045 background events (dominant contributions: 62% tt,¯ 31% t-channel single top), leads to S/B = 1.3. In order to reduce the systematic uncertainties on the background normalization, two control samples extracted from data are used, one enriched in semi- leptonic tt¯ and one in di-leptonic tt¯. Nevertheless, there is still a large systematic uncertainty, mostly arising from the knowledge of the jet energy scale. The relative uncertainty on cross section measurement is 41%.

18.3 Conclusions

All single top production channels have been studied by the CMS experiment, and the expected uncertainties are in reasonable agreement. The t-channel production, thanks to the large expected cross section (240 pb) should be observable with the ﬁrst few fb−1 of integrated luminosity. The tW associated production, invisible at Tevatron but sizable at LHC (σ = 66 pb), is more challenging but should be in reach with 10-20 fb−1. Observing the s-channel production appears to be much harder, and will probably require even more data and advanced analysis techniques.

References

1. The CDF Collaboration, First Observation of Electroweak Single Top Quark Production, arXiv:0903.0885v2[hep-ex]. 2. The D0 Collaboration, Observation of single top quark production, arXiv:0903.0850[hep-ex]. 3. T.M.P. Tait, C.-P. Yuan, Single Top Production as a Window to Physics Beyond the Stan- dard Model, Phys.Rev.D63:014018 (2001), arXiv:hep-ph/0007298. 4. CMS physics technical design report, volume II: Physics performance, CMS Collabora- tion, CERN-LHCC-2006-021, J. Phys. G, 34 (2007) 995.

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19 Constraints on the Masses of Fourth Generation Quarks

M. Mohammadi Najafabadia, S. Hosseini, Y. Radkhorramib

aSchool of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran bPhysics Department, Tarbiat Modares University, Tehran, Iran

Abstract. We study the one loop contribution of the down type quark of the SM-like fourth generation (b0) on the top quark electric dipole moment. Using the known limits on the top quark electric dipole moments (EDM), we place limits on the b0 mass. Then from the estimated ratio for the masses of the fourth generation of quarks from other stud-

ies and the achieved bound from top quark EDM on mb0 , we obtain a limit for the up type quark of fourth generation (t0) mass.

19.1 Introduction

The Standard Model (SM) of particle physics is in a very good agreement with present experimental data. Nonetheless, it is believed to leave many questions unanswered, and this belief has resulted in numerous theoretical and experimental attempts to discover a more fundamental underlying theory. Various types of experiments may expose the existence of physics beyond the SM, including the search for direct production of exotic particles at high energy colliders. A complementary approach in hunting for new physics is to examine its indirect effects in higher order processes. As mentioned, the SM with three generations of quarks and leptons is in excellent agreement with the current experimental data. However, the SM does not explain the fermion mass hierarchy and it also is not able to explain why there are precisely three families. Several models have been proposed to solve the shortcomings of the SM through the introduction of new generations of quarks and leptons. While some models beyond SM, such as Grand Unified Theories (GUT), predict the new generations of quarks or leptons. The strong CP problem is solvable by requiring additional quarks. The weak CP violation may be accommodated through the KM mechanism, while the strong CP issue can be solved in a model with two additional flavor of quarks by spontaneous CP violation. Another motivation for fourth generation is that in the literature it has been shown that a non-supersymmetric model with four generations can have successful unification of gauge couplings at the unification scale. In the scenarios of gauge mediated supersymmetry breaking additional generations of quarks and leptons arise automatically. More details can be found in [1],[2], [3] and references

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therein. It should be mentioned that the fourth generation of quarks and leptons can be a chiral doublet (SM-like fermion generation) or non-chiral doublet (also known as vector-like). For example, in Grand Uniﬁed Theories all types of additional fermions are possible. While in models which attempt to solve the strong CP problem only non-chiral doublet of quarks are considered. There have been already many indirect and direct studies on the fourth generation of quarks. For example, the effects of a vector-like fourth generation of quarks on the width of Z boson and forward-backward asymmetry has been studied in [4]. Bounds on the mixing of the SM down type quarks with new vector-like singlet quarks derived in [5]. In [6], the pair production of t0 quarks at Tevatron has been studied. It has been shown that the production cross section for t0t¯0 at hadron colliders could be considerably higher than QCD prediction if a gluon-prime (a massive color octet vector boson) is present in the theory. In [7], using a data sample corresponding to 2.8 fb−1 of integrated luminosity recorded by CDF experiment in proton anti- proton collisions, a limit was set on the production cross section of t0t¯0. From this limit a lower limit of 311 GeV/c2 was derived for a new heavy top-like quark. Since top quark is far more massive than other SM fermions, its interactions may be quite sensitive to new physics originating at higher scale [8],[9],[10]. Hence, the study of interactions of fourth generation of quarks with top quark might give interesting results about the fourth generation. In this article, our aim is to constraint the mass of the down type quark of the fourth generation (b0) using the one loop contribution of the b0 in the electric dipole moment (EDM) of top quark. In the analysis, we will use the estimated bounds on the EDM’s of top quark to constraint the mass of b0. In [2], it has been shown that for the chiral doublet of (t0, b0) the ratio of masses is 1.1 or less (mt0 /mb0 ≤ 1.1). Using this value, the bound on mt0 is also estimated.

19.2 The Contribution of the b0 in the Top Quark EDM

In this work, we examine the properties of masses of fourth generation of quarks. Similar to the interaction of Wtb, a general effective Lagrangian for the interaction of Wtb0 can be written in the following form:

g µ 0 LWtb0 = √ tγ¯ (gLPL + gRPR) b Wµ (19.1) 2

where PL(PR) are the left-handed (right-handed) projection operators. The gL, gR coefficients are complex in general. This signifies the CP violating effects. These coefficients include the mixing factor between the fourth family and the top quark (Vtb0 ) in the generalized CKM matrix. For the interaction of Wtb, these factors have been estimated from different studies. For example, from the B decay processes −3 −3 −2 the limits on gL, gR are: Re(gR) ≤ 4×10 , Im(gR) ≤ 10 and Im(gL) ≤ 3×10 [11],[12],[13]. The introduced Lagrangian in Eq.19.1 induces an electric dipole moment for the top quark at the one loop level via the Feynamn diagrams shown in Fig.19.1. After calculation of the one loop corrections to the vertex of ttγ¯ shown in Fig.19.1, we find some terms with different structures. The coefficient of the structure of

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19 Constraints on the Masses of Fourth Generation Quarks 153

ν ν σµνγ5q gives the top quark electric dipole moment where q is the four momentum of photon [14]. It should be mentioned that this structure arises via radiative corrections and does not exist at tree level.

γ γ

b' b' W W

tW t t b' t

Fig. 19.1. Feynman diagrams contributing to the on shell ttγ¯ vertex.

After all calculation, the top EDM is found as follows:

e 3α mb0 1 ∗ Re(dtop) = − (V1(xb0 , xW ) + V2(xb0 , xW ))Im(gLgR), (19.2) mW 32π mW 3

2 2 where xa = ma/mt . The V1,2 are the functions stand for the contribution of the Feynman diagram where the photon emerges from the W boson and the b0 quark line, respectively. They have the following forms:

¡ 2 2 ¢ V1 = − (4xW − xb0 + 1) f(xb0 , xW ) − xb0 + 4xW − 5xb0 xW − 3xW − 2xb0 + 1 g(xb0 , xW ) ¡ 2 2 ¢ V2 = − (4xW − xb0 + 1) f(xW , xb0 ) + xb0 + 4xW − 5xb0 xW − 3xW − 2xb0 + 1 g(xW , xb0 ) (19.3)

where the functions of f and g are as follows: µ ¶ µ ¶ q Ã √ ! 1 + a − b b 2 ab f(a, b) = log + (1 − a − b)2 − 4ab × ArcSech + 2 2 a a + b − 1 µ ¶ Ã √ ! 1 b 1 + a − b 2 ab g(a, b) = − log − p × ArcSech 2 a (1 − a − b)2 − 4ab a + b − 1

19.3 The Limits on mt0 , mb0

In [15], the authors have predicted an upper bound for the top quark EDM. In that paper, a source of CP violation mediated by WWγ vertex has been analyzed using the effective Lagrangian technique and its implications on the CP-odd electromagnetic properties of the Standard Model particles have been studied. The contribution of WWγ vertex to the EDM of charged leptons and quarks has been calculated. Their estimate for the top quark EDM is 1.6 × 10−22 e.cm. In Eq.26.3, ∗ −3 a reasonable assumption is to set Im (gLgR) to a value around 10 [16]. Under

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this assumption and by using the bound of the top EDM, the lower limit of 268 GeV/c2 is achieved for the mass of the down type quark in the fourth family of quarks. Fig.19.2 presents the dependency of the top quark electric dipole moment ∗ −3 on the mb0 for Im (gLgR) = 10 . ∗ Obviously, this lower limit depends on the quantity of Im (gLgR). However, ∗ ∗ −3 it is not highly dependent on Im (gLgR). When Im (gLgR) changes from 10 to 1, the lower limit on the mb0 varies only up to 3%. One of the recent estimated 2 lower bound on the mb0 is 199 GeV/c [17]. Hence, the constraint obtained in the current study is compatible with other studies and the lower bound on the mb0 is slightly increased. For the chiral doublet of (t0, b0), the electroweak precision measurements predict that mt0 ≤ 1.1. Combining this with the bound obtained from top EDM mb0 on the mass of b0 immediately gives the lower limit of 294.8 GeV/c2 on the mass of t0. This value also conﬁrms the achieved constraint from other studies (311 GeV/c2) which mentioned in the introduction [7].

Re Hdt L, e . cm

-22 5. ´ 10 -22 4. ´ 10 -22 3. ´ 10 -22 2. ´ 10 -22 1. ´ 10 mb ' , GeV c2 220 240 260 280 ∗ −3 Fig. 19.2. The real part of top electric dipole moment versus mb0 when Im(gLgR) = 10 .

19.4 Conclusion

In this paper, we tried to extract a limit on the mass of the down type quark of the SM-like fourth generation (b0) by employing a general Lagrangian for the interaction of W − t − b0 with complex left-handed and right-handed couplings. This general Lagrangian produces an electric dipole moment for the top quark at one loop level which contains mb0 . From the estimated upper limit on the top quark EDM, a lower limit of 268 GeV/c2 predicted for the mass of b0. From electroweak precision data, other studies have been shown that for the chiral doublet of (t0, b0) the ratio of masses is 1.1 or less. It turns out that the lower bound on the mass of t0 is 294.8 GeV/c2. These results are regular and compatible with those obtained from other studies and the bound on mb0 is slightly increased.

References

1. P. H. Frampton, P. Q. Hung and M. Sher, Phys. Rept. 330 (2000) 263, [arXiv:hep- ph/9903387]. 2. P. H. Frampton and P. Q. Hung, Phys. Rev. D 58 (1998) 057704, [arXiv:hep-ph/9711218].

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3. V. Barger and Roger J.N. Phillips, Collider Physics (Frontiers in Physics). 4. T. Yoshikawa, Prog. Theor. Phys. 96, 269 (1996) [arXiv:hep-ph/9512251]. 5. L. Lavoura and J. Silva, Phys. Rev. D 47 (1993) 1117. 6. B. A. Dobrescu, K. Kong and R. Mahbubani, arXiv:0902.0792 [hep-ph]. 7. A. Lister [CDF Collaboration], arXiv:0810.3349 [hep-ex]. 8. M. Beneke et al., arXiv:hep-ph/0003033. 9. M. Mohammadi Najafabadi and N. Tazik, arXiv:0902.0441 [hep-ph]. 10. M. Mohammadi Najafabadi, arXiv:0902.0059 [hep-ph]. 11. A. Abd El-Hady and G. Valencia, Phys. Lett. B 414 (1997) 173, [arXiv:hep-ph/9704300]. 12. F. Larios, M. A. Perez and C. P. Yuan, Phys. Lett. B 457 (1999) 334, [arXiv:hep- ph/9903394]. 13. B. Grzadkowski and M. Misiak, Phys. Rev. D 78 (2008) 077501, [arXiv:0802.1413 [hep- ph]]. 14. M. Pospelov and A. Ritz, Annals Phys. 318 (2005) 119, [arXiv:hep-ph/0504231]. 15. H. Novales-Sanchez and J. J. Toscano, Phys. Rev. D 77 (2008) 015011, [arXiv:0712.2008 [hep-ph]]. 16. W. S. Hou, M. Nagashima and A. Soddu, Phys. Rev. D 72 (2005) 115007, [arXiv:hep- ph/0508237]. 17. C. Amsler et al., Phys. Lett. B 667 (2008) 1.

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School of Particles and Accelerators FIRST IPM MEETING Institute for Research in ON LHCPHYSICS Fundamental Sciences (IPM) VOL. 1, NO. 1 (p. 157) Isfahan, April 20-24, 2009

20 Study of Top Quark FCNC using Top and Charm Quarks electric dipole moments

M. Mohammadi Najafabadia, N. Tazikb

aSchool of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran b Physics Department, Semnan University, Semnan, Iran

Abstract. We study the one-loop contribution of the effective ﬂavor changing neutral couplings (FCNC) tcZ on the charm quark electric dipole moment. Using the known limits on the top and charm quarks electric dipole moments, we place limits on these FCNC anomalous couplings.

20.1 Introduction

The standard model (SM) is in very good agreement with present experimental data. Nonetheless, it is believed to leave many questions unanswered, and this belief has resulted in numerous theoretical and experimental attempts to discover a more fundamental underlying theory. Various types of experiments may expose the existence of physics beyond the SM, including the search for direct production of exotic particles at high energy colliders. A complementary approach in hunting for new physics is to examine its indirect effects in higher order processes. Since top quark is far more massive than other SM fermions, its interactions may be quite sensitive to new physics originating at higher scale [1]. If there are any deviations from the SM expectations in the properties of the top quark, they may indirectly lead to modiﬁcations in the anticipated branching fractions. In the SM, due to the Glashow-Iliopoulos-Maiani (GIM) mechanism, the top quark Flavor Changing Neutral Current (FCNC) interactions are absent at tree level and are extremely suppressed at loop level since such FCNC interactions are induced by the W boson charged current Cabbibo-Kobayashi-Maskawa (CKM) transitions involving down-type quarks in the loops which are much lighter than the top quark. In models beyond SM such as minimal supersymmetric standard model (MSSM) or Technicolor theory, although the top quark FCNC interactions are also induced at loop level, they can be greatly enhanced relative to the SM predictions. For example in MSSM, in addition to the W boson loops, there are four kinds of loops contributing to the top quark FCNC interactions. In MSSM, charged Higgs, chargino, gluino and neutralino loops contribute to the top quark FCNC interactions. Theoretical branching ratios of FCNC top quark decays in various models are presented in Table 20.3 [2],[3]. It is worth mentioning that at the LHC, the branching franction for top FCNC decay, BR(t → Zq), can be

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measured with the precision of 6.1 × 10−5 and 3.1 × 10−4 with the integrated luminosity of 100 fb−1 and 10 fb−1, respectively [4],[5]. There are several studies on the top quark FCNC which some of them can be found in: [6],[7],[8],[9],[10],[11], [12]. In this article, our aim is to constraint the top quark FCNC anomalous couplings, in the process of t → Zc, using effects induced by the electric dipole moment (EDM) of top quark on the one loop induced EDM of the charm quark. In the analysis, we will use the estimated bounds on the EDM’s of top and charm quark to constraint the anomalous couplings.

20.2 Effective FCNC Lagrangian

One tool that is often used to describe the effects of new physics at an energy scale of Λ, much higher than the electroweak scale, is the effective Lagrangian method. If the underlying extented theory under consideration only becomes important at a scale Λ, then it makes sense to expand the Lagrangian in powers of Λ−1: X ci L = LSM + Oi (20.1) Λni−4

where LSM is the standard model Lagrangian, Oi’s are the operators containing only the SM ﬁelds, ni is the dimension of Oi and ci’s are dimensionless parameters [13],[14],[15]. In the top quark sector, the lowest dimension operators that contribute to FCNC with the Ztc¯ vertex can be written as [16]: h i g µ µ Leff = − κLZ tγ¯ µPLc + κRZ tγ¯ µPRc + h.c. (20.2) 2 cos θW

where g is the coupling constant of SU(2)L, θW is the Weinberg mixing angle and κL,R are free parameters determining the strength of these anomalous couplings. In the above relation, PL,R are the left-handed and right-handed projection operators. The top FCNC anomalous interaction leads to the following branching fraction for the t → Zc (in the limit of zero mass of b, c quarks): Γ(t → Zc) BR(t → Zc) ≡ = (20.3) Γ(t → Wb) (κ2 + κ2 ) (m2 − m2 )2(m2 + 2m2 ) L R t Z t Z ' 0.5(κ2 + κ2 ) 2 2 2 2 2 L R 2 (mt − mW ) (mt + 2mW ) Recent upper bound from CDF experiment for branching fraction of t → Zq, (q = 2 2 u, c), is 3.7% (with 95% C.L.)[17]. Therefore, one can conclude κL + κR < 0.074.

20.3 Estimation of the Constraints

We consider the effective interaction of the quarks with on-shell photons to make prediction of the acceptable range for the FCNC parameters (κL, κR)[18],[19],[20]: i L = − d qγ¯ σ qFµν (20.4) eff 2 q 5 µν i i i i i i

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Title Suppressed Due to Excessive Length 159

µν where F is the electromagnetic ﬁeld tensor and dq is the top quark electric dipole moment (EDM) which is a real number by hermiticity. One should note that this is a CP violating term. Therefore, a non-vanishing value for EDM of a fermion is of special interest as it signiﬁes the presence of CP violating interactions. In the SM, top quark can not have an EDM at least to three-loops. The SM prediction for the top EDM is 10−31 − 10−32 e-cm which is too small to be observable. In contrast, in extensions of SM, such as MSSM, this situation changes sharply and the top quark EDM can arise at the one-loop. In beyond standard model theories the typical top EDM is of order of 10−18 − 10−20 e-cm which is larger than the SM prediction by more than 10 orders of magnitude [19],[20].

Model SM MSSM Technicolor BR(t → cZ) ∼ 10−14 ∼ 10−6 ∼ 10−4

Table 20.1. Theoretical branching ratios of FCNC top quark decays in various models.

The contribution of FCNC to the on-shell ccγ¯ coupling is given through the diagram shown in the left side of Fig.20.1. Using the introduced effective interactions and after some algebra, the respective one-loop vertex can be written as: Z g2 d4k Γµ = − 2 × dt × 4 × 4 cos θW (2π) h ¡ ¢ i 2 2 2 2 ν ... + mt(κL + κR)(p/2 − p/1) − 4κLκR(k.(p1 + p2) − p1.p2 + mt − mZ) γ5σµνq 2 2 2 2 2 2 (k − mZ)((p1 − k) − mt )((p2 − k) − mt ) (20.5)

One should note that there are contributions to both magnetic and electric dipole moments of the charm quark which we have kept only the terms contributing to EDM. After evaluating the integral over k:

α 2 2 dc = × dt × [(κ + κ )f(xt, xc) + κLκRg(xt)] (20.6) 2 2 L R 4π sin θW cos θW where √ xtxc 1 + 3xt(xt − 4/3) − 2(2xt − 1) log(xt) f(xt, xc) = × 3 (20.7) 2 2(xt − 1) xt − log(xt) − 1 g(xt) = xt − 1

2 2 mt mc where xt = 2 and xc = 2 . In obtaining the above relation, we have ignored mZ mZ 2 2 of the terms proportional to (mc/mZ), which in fact is a negligible quantity. In [21], the authors have estimated the upper bound of 7 × 10−21 on the top and 1 × 10−27 on the charm quark electric dipole moments using the experimental bound on neutron electric dipole moment. The combination of these

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bounds and Eq.20.6 leads to the exclusion contour shown in the right side of Fig.20.1. However, in this exclusion contour another parameterization for top FCNC anomalous coupling has been used which are related to the parameters of Eq.20.2 by: κR,L ≡ gV ± gA. If we combine our result with that obtained by CDF experiment, which mentioned before, the bounds on κR,L are estimated as: −3 κL < 3 × 10 , κR < 0.27. These values are compatible with the ones estimated −2 in the other studies [16]. The obtained upper bound on κL in [16] is 5 × 10 . Hence, the allowed region for κL from the present work is one order of magnitude smaller than the one obtained in [16].

0.04 g A 0.03

A q 0.02

0.01

0 t t k -0.01 Z -0.02 p 1 c p c 2 -0.03

-0.04 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 g V Fig. 20.1. Left: The FCNC one-loop contribution to the vertexccγ ¯ , Right: The exclusion contour on top FCNC anomalous couplings.

20.4 Conclusion

In this article, within the framework of the effective Lagrangian approach, we performed a calculation of the radiative corrections induced on the charm quark electric dipole moment by the effective FCNC vertex tcZ. Using the present upper bounds on the top and charm quark EDM’s, the new constraints on the top −3 FCNC anomalous couplings were estimated: κL < 3 × 10 , κR < 0.27. These constraints are regular and comparable with the ones obtained in the past studies and the estimated limit on κL is slightly better.

References

1. M. Beneke et al., arXiv:hep-ph/0003033. 2. J. M. Yang, arXiv:0801.0210 [hep-ph]. 3. J. A. Aguilar-Saavedra, Acta Phys. Polon. B 35, 2695 (2004). 4. J. Carvalho et al. [ATLAS Collaboration], Eur. Phys. J. C 52, 999 (2007). 5. W. Bernreuther, J. Phys. G 35, 083001 (2008),arXiv:0805.1333 [hep-ph]. 6. G. A. Gonzalez-Sprinberg and R. Martinez, arXiv:hep-ph/0605335. 7. J. J. Zhang, C. S. Li, J. Gao, H. Zhang, Z. Li, C. P. Yuan and T. C. Yuan, arXiv:0810.3889 [hep-ph]. 8. J. Cao, Z. Heng, L. Wu and J. M. Yang, arXiv:0812.1698 [hep-ph]. 9. R. A. Coimbra, P. M. Ferreira, R. B. Guedes, O. Oliveira, A. Onofre, R. Santos and M. Won, arXiv:0811.1743 [hep-ph].

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10. F. Larios, R. Martinez and M. A. Perez, Phys. Rev. D 72 (2005) 057504, arXiv:hep- ph/0412222. 11. A. A. Ashimova and S. R. Slabospitsky, Phys. Lett. B 668 (2008) 282, arXiv:hep- ph/0604119. 12. Yu. P. Gouz and S. R. Slabospitsky, Phys. Lett. B 457 (1999) 177, arXiv:hep-ph/9811330. 13. R. D. Peccei and X. Zhang, Nucl. Phys. B337, 269 (1990). 14. Z. Han, arXiv:0807.0490[hep-ph]. 15. W. Buchmuller and D. Wyler, Nucl. Phys. B 268, 621 (1986). 16. T. Han, R. D. Peccei and X. Zhang, Nucl. Phys. B 454, 527 (1995). 17. T.Aaltonen,et al. [CDF Collaboration], arXiv:0805.2109 [hep-ex]. 18. J. L. Hewett and T. G. Rizzo, Phys. Rev. D 49, 319 (1994). 19. M. Pospelov and A. Ritz, Annals Phys. 318, 119 (2005), arXiv:hep-ph/0504231. 20. M. Raidal et al., arXiv:0801.1826 [hep-ph]. 21. H. Novales-Sanchez and J. J. Toscano, Phys. Rev. D 77, 015011 (2008).

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21 Progress in Experimental Activities on RPC Detector in Iran

A. Moshaiia,c, K. Kavianib,c M. Eskandaria, L. Khosravi-Khorashada,c

a Department of Physics, Tarbiat Modares University, P.O. Box 14115-175, Tehran, Iran b Al-Zahra University, Tehran, Iran c School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran

Abstract. This paper reports about the main activities performed to establish a particle detector laboratory in Iran. The laboratory includes a cosmic telescope system using two long scintillator counters, a gas mixing system with controllable digital ﬂowmeters, and a simple data acquisition system, which are all described in details. Also, the results obtained from construction and test of some prototype glass resistive plate chamber (RPC) detectors in this lab are explained too.

21.1 Introduction

Development of experimental particle physics in the last three decades was mainly achieved due to success in construction of large scale high energy physics experiments. Especially, LHC at CERN, the world largest physics experiment is the most complete and the earliest one of such large scale experiments designed to include a very huge accelerator along with four main complexes of detectors, i.e. ATLAS [1], CMS [2], ALICE, and LHCb. Each one of these detector complexes, usually known as experiment, is constructed by collaboration of many institute and universities from different countries. The Compact Muon Solenoid (CMS) is one of the experiments which will operate in LHC. More than 36 countries are collaborating in construction of CMS, in which Iran is one of them. Iran has involved at CERN since 2001 and started his contribution by constructing a special huge table used in the forward region of hadronic calorimeters of CMS. The collaboration has been continued by contribution in development of simulation and reconstruction of CMS. However, the lack of any area for experimental collaboration of Iran in CMS intreagues people to ﬁnd a simple and attractive area for experimental involvement. The idea of collaboration of Iran in production and test of a relatively simple detector i.e; Resistive Plate Chambers (RPCs) for upgrade stage of CMS promotes this line to the establishment of a detector laboratory in Iran at IPM. The lab was physically formed after importing some basic experimental equipments and measurement facilities.

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164 A. Moshaii, K. Kaviani, M. Eskandari, L. Khosravi-Khorashad

From the beginning of the year 2008, the particle detector laboratory was officially established in Larak site of IPM (Fig. 21.1). The laboratory has an area of about 35 m2 equipped with an office room beside the lab. Here we report about the main activities performed in this lab since last year. The laboratory now includes a cosmic telescope system using two long scintillator counters, a gas mixing system with controllable digital flowmeters, and a simple data acquisition system. We describe these systems in details. In addition, the results of construction and test of some prototype glass RPCs, which are made by normal window glass in this lab are explained too.

Fig. 21.1. A picture of particle detector laboratory in Larak garden at IPM in Tehran.

21.2 Cosmic Hodoscope

The cosmic hodoscope is included from two long scintillator counters (with about 2m long) which are mounted by two Philips photomultiplier tubes (PMTs). The PMTs are supplied by a DC high voltage of around 2 kV. The signal taken from a PMT is displayed by a digital 200 MHz Tektronix oscilloscope. When an ionized cosmic muon goes through the scintillating crystal, it creates a number of photon inside the crystal. These photons can be detected by a sensitive layer of PMT and a number of photons are created which are subsequently accelerated by a line of high voltage. The hit of the electrons to the anode of scintillator creates a very fast signal (with duration of about 5ns) and this signal can be detected by the oscilloscope. Figure (21.2 left) shows the system of cosmic hodoscope of the lab. This hodoscope uses the concept of coincidence for detection of muon. The up and down scintillators have about 1.5m distance. Therefore, giving c as the speed of light, there will be about 4.5 ns time interval between the signals created by the two PMTs from up and down scintillators. This interval can be tuned by a coincidence electronics NIM module and an average of a lot of passage of muons, giving us the sample of data shown in Fig. (21.2 right). As we see in this ﬁgure, the number of count is relevance to the distance between the two scintillators and the time interval of the coincidence unit. Usually for better measuring the signals and counts, a speciﬁc delay of about 20 ns is put on the way of one of scintillators.

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Fig. 21.2. Left: A picture of cosmic hodoscope assembled in the lab. Right: The plot of data registration of coincidence between two scintillators.

21.3 Glass RPC Prototypes

Fig. 21.3. Graphite coating of the ﬁrst glass RPC with 40cm × 50cm plates.

RPC is a gaseous particle detector [3] and [4] which is highly used in the muon system of general purpose detector in LHC, like CMS and ATLAS. Here, we present the result of construction of two different glass RPC prototype made in the lab together with the experimental measurements related to these two detectors. The first prototype consists of 40cm × 50cm glass with 2mm thickness as the high resistive plates. We also used long spacers with 2mm thickness made with same glass of the resistive plate materials. The outer surface of the plates, as shown in Fig. 21.3, are coated with graphite sprays in order to create the electrodes for applying the high voltage. In addition, the plates stick together with aquarium glue. Mylar sheets are placed on the graphite coating as insulators (Fig. 21.4 left), and read-out strips are lied on them (Fig. 21.4 right). We have used cop- per strips with approximately 2.5cm − 3cm width as the readout strips. The final stage, as indicated by Fig. 21.5, is to cover all the parts with a thick aluminium foil as the Faraday cage to reduce the effect of ambient noise on the detector. The induced signal taken from the first prototype glass RPC is shown by (Fig. 21.6). The signal is due to cosmic muons, and taken by the oscilloscope from one

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Fig. 21.4. Mylar sheets placed on the graphite coating (left) and Read-out strips (right).

Fig. 21.5. Faraday cage for the constructed RPC detector.

Fig. 21.6. Induced signal of the ﬁrst RPC prototype from one of the read-out strips observed by oscilloscope at HV = 9kV.

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of the strips with applying HV = 9kV on the electrodes. We also made a second RPC prototype consists of 100cm × 29cm glass plates with 2mm thickness. The construction procedure of the second prototype is all the same as the ﬁrst one except that we have used 1mm thickness glass spacers to increase the electric ﬁled inside the gap of detector and in order to get a higher signal from incoming cosmic muons at lower voltages. Figure 21.7 shows the current variation of the second prototype RPC with respect to change in its applying high voltage. As indicated by the Fig. 21.7 distinct signals are observed on the oscilloscope with applying HV = 3.5kV. Comparison of the results of Figs. (21.6) and (21.7) shows that the applied high voltage to get a good signal has been reduced with the reduction of the spacer thickness.

Fig. 21.7. Current of the second prototype RPC with respect to its high voltage. Distinct signals are observed at HV = 3.5kV.

21.4 Gas Mixing System

The gas mixing system used for RPC is shown by Fig. (21.8). It has three gas entries for C2F4H2/i−C4H10/SF6. The gas mixing system separately displays the entrance pressure of each kind of the gases entering to the system. Additionally, it shows the pressure of gas mixture which goes through flow meters. Flow meters show the flow of the gas mixture which are finally gone through to the RPC. The system contains a series of bubblers showing flow of exhausted gases. The system can be connected to a digital mass flow controller in order to specify the precise percentage of each gas in the gas mixture. Before using the gas mixing system, the flowmeters have to be calibrate with a separate trustable flow-meter for a gas. We did the calibration procedure with

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Fig. 21.8. Gas mixing system used for RPCs.

the argon gas for the three inlets of C2F4H2 i − C4H10 and SF6. The results of calibration is depicted in Fig. (21.9).

Fig. 21.9. Calibration plots for the three inlets of C2F4H2, i − C4H10 and SF6 in the gas mixing system using argon as the calibration gas.

21.5 Conclusions

A brief report about three main activities performed in the particle detector laboratory at IPM in Iran was presented. The laboratory, which is now equipped with a cosmic telescope system and a dedicated gas mixing system is ready to take a responsibility in construction of RPCs for the upgrade stage of CMS.

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21 Progress in Experimental Activities on RPC Detector in Iran 169 References

1. Muon Spectrometer, Technical Design Report, CERN-LHCC-97-22, ATLAS TDR 10, CERN (1997). 2. CMS, The Muon Project Technical Design Report, CERN/LHCC 97-32, (1997). 3. R. Santonico and R. Cardarelli. Development of resistive plate counters. Nucl. Instr. and Meth., 187:377-380, (1981). 4. R. Santonico and R. Cardarelli. Progress in resistive plate counters. Nucl. Instr. and Meth., A 263:20-25, (1988).

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22 Search for SUSY in CMS

S. Paktinat Mehdiabadi

School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran

Abstract. Search for SUSY is one of the main goals of the CMS experiment. To ﬁnd this new physics, a good knowledge of the detector and Standard Model backgrounds is necessary. This note is a short review of what the collaboration has done recently to be ready to search for SUSY as soon as data is ready.

22.1 Introduction

Supersymmetry (SUSY) [1] is one of the most promising extensions of the Stan- dard Model (SM) of the elementary particles which can solve both Hierarchy and quadratic divergences by introducing new symmetry between the bosonic and fermionic degrees of freedom. CMS experiment [2] which is going to start data taking before the end of this year has an extensive program to search for SUSY in different channels. Here we report only the recent activities which are newer than what was reported in the Physics TDR-II [3]. In these new analysis, the emphasis is to have some data driven methods to estimate the backgrounds and the Monte Carlo based methods are avoided. On the other hand the analysis are optimized for the early data where we do not have a good knowledge of detector systematic uncertainties. There are different phenomenological models for SUSY breaking which makes a mass difference between the SM particles and their supersymmetric partners. In this note, the focus is on the mSUGRA [1] scenario where the gravity is the responsible for supersymmetry breaking. Since the R- parity is assumed to be conserved, SUSY particles are generated in pairs and the Lightest Supersymmetric Particle (LSP) is stable. LSP appears at missing transverse energy (MET) which is a very important signature for SUSY. SUSY particles depending on their mass can decay via a long chain, leading to a multi-particle (lepton, jet) topology plus a large MET.

22.2 Past Activities

The results of the physics studies before 2006 were documented in a large book, called “CMS Physics: Technical Design Report” [3]. The emphasis in that time was to use a complete detector with good knowledge of the systematic uncertainties according to 1, 10 and 30 fb−1 of integrated luminosity in 14 TeV center of mass

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Fig. 22.1. mSUGRA parameter space. The lines indicate the ranges reachable by different signatures with 1 fb−1 of integrated luminosity.

energy. SUSY group had an important contribution in that document and different channels were examined to search for SUSY. Figure 22.1 shows the range of the parameter space which can be scanned with 1 fb−1 of data in different channels. It can be seen that the main part of the parameter space is reachable even with 1 fb−1 of data. Since LHC is going to run in the center of mass energy of 10 TeV and early data needs very special treatment to control the backgrounds and detector systematics, it is necessary to repeat the previous analysis in a new framework. In the following some of these new analysis are reviewed.

22.3 SUSY in Dijet Final States

Following a phenomenological article [4], researchers in CMS experiment have studied the dijet final states coming from SUSY events [5]. The QCD dijet background has a very high cross section and can hide the signal easily. Using some special variables can help to isolate the signal. One of the most important variables is αT which is defined as the ratio of the transverse energy of the second jet and the transverse mass of the first two leading jets.

j2 ET αT = (22.1) j1j2 MinvT Figure 22.2 shows the distribution of this variable for different samples. It can be seen that cut on this variable can remove almost all QCD dijet backgrounds. Other cuts which are used in this analysis are as follows:

• Dijet Trigger: At least two jets with PT > 150 GeV/c. i i i i i i

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Fig. 22.2. The ditribution of αT for different samples. QCD background has a completely different shape with a sharp edge.

• At least two jets with PT > 50 GeV/c and Electromagnetic fraction < 0.9. This cut removes the electrons faking jets. • Third jet with PT > 50 GeV/c is vetoed. It reduces the effect of the higher order corrections. • ∆φ(MHT, jet1,2,3) > 0.3 rad (MHT is the negative of the vector sum of the first two leading jets in the transverse plane). This is a cut against the badly measured jets. • |η| of the leading jet < 2.5. • lepton veto: no electron or muon with PT > 10 GeV/c. • HT > 500 GeV. (HT is defined as the scalar sum of the transverse momentum of the first two leading jets). • ∆φ between the first two leading jets must be less than 2π/3. Two jets from QCD are almost back-to-back, but in SUSY they can be in each direction due to the presence of two LSP’s. • αT > 0.55 After applying these cuts, the signal over background is 5.6 and the QCD multi jet sample is completely suppressed. It is shown that the result is robust against the systematic uncertainties. Some data driven methods are introduced to measure the background contribution in the signal region.

22.4 SUSY Parameter Estimation

If SUSY is discovered, its spectroscopy is a challenging task for the LHC experiments. Since in SUSY events always there are at least two missing objects (LSP), it is impossible to make the invariant mass distribution and see the peak on top of the pole mass. An interesting method to ﬁnd the mass of the SUSY particles is

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to look for some endpoints and by measuring the endpoints put some constraints between the involved masses. If we can have endpoints as many as the unknown masses, it would be possible to extract the masses or at least put some boundaries for their allowed masses. One of the cleanest endpoints is the endpoint in the invariant mass distribu- 0 tion of two leptons which come from the decay of a second neutralinoχ ˜ 2

0 ±˜∓ ± ∓ 0 χ˜ 2 → l lR → l l χ˜ 1 (22.2)

0 This endpoint happens when two leptons are back-to-back in theχ ˜ 2 rest frame ˜∓ and the intermediate sparticles, lR is on-shell.. In an analysis in CMS [6] this decay is considered and the endpoint reconstruction and measurement is examined. The position of the endpoint is related to the masses of the involved particles by the following relation: v u u(M2 − M2 )(M2 − M2 ) χ0 lR lR χ0 Mmax = t 2 1 (22.3) ll M2 lR

Measuring this endpoint value can provide a first constraint towards sparticle mass measurements. The analysis is targeting at integrated luminosity of 1 fb−1. The physics background of the signal decay chain comes both from SUSY and SM processes with at least two opposite-sign same-flavor leptons and is estimated using different-flavor dilepton pairs. The final set of requirements imposed in the analysis are summarized:

+ − + − • At least two opposite-sign and isolated leptons (e e or µ µ ) with PT > 10 GeV/c and |η| < 2.4. • At least three jets with ET > 30 GeV and |η| < 3. j1 j2 • ET > 120 GeV and ET > 80 GeV. miss • Missing ET cut: ET > 200 GeV. Figure 22.3 shows the invariant mass distribution of dileptons. An unbinned maximum likelihood ﬁt is performed on the distribution and the endpoint value as well as the number of signal and background events are obtained. The theoretical value for the endpoint is 78.15 GeV/c2. The extracted value from the ﬁt is consistent with this value within the uncertainties. A detailed study is done to evaluate the statistical and systematic uncertainties on dielectron and dimuon endpoints separately. The result is as follows:

max 2 mee = 77.90 ± 1.07(stat.) ± 0.36(syst.)GeV/c (22.4) max 2 mµµ = 78.03 ± 0.75(stat.) ± 0.18(syst.)GeV/c

As it was expected the uncertainties on dielectron endpoint is worse than the dimuon endpoint. The uncertainty even with 1 fb−1 of integrated luminosity is about 1 GeV/c2.

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22 Search for SUSY in CMS 175

Fig. 22.3. Unbinned likelihood ﬁt of the dilepton invariant masses for 1 fb−1 of integrated luminosity; the Signal PDF (red), the ﬂavor-symmetric Background PDF (green) components are shown superimposed, as extracted from the Fit. Z-peak is visible close to its nominal mass.

22.5 Conclusion

The recent activities of the CMS collaboration was reviewed briefly. The collaboration has plans both to search for SUSY from the first day of the data taking and do spectroscopy when the sufficient data is ready if the existence of SUSY is approved.

22.6 Acknowledgment

The author would like to thank the organizers of the conference for their help and hospitality during the conference in Isfahan.

References

1. S. P. Martin, “A Supersymmetry Primer”, hep-ph/9709356 v3 7 Apr 1999. 2. CMS Collaboration, “The CMS experiment at the CERN LHC”, JINST 3:S08004, 2008. 3. CMS Collaboration, “CMS technical design report, volume II: Physics performance”, J. Phys. G34, 995 2007. 4. L. Randall, D. Tucker-Smith, “Dijet Searches for Supersymmetry at the Large Hadron Collider”, Phys.Rev.Lett.101:221803, 2008. 5. CMS Collaboration, “SUSY searches with dijet events”, PAS-SUS-08/005 2008. 6. CMS Collaboration, “Dilepton + Jets + MET channel : Observation and Measurement 0 0 ofχ ˜ 2 → χ˜ 1ll”, PAS-SUS-08/001 2008.

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23 Two constraints kinematic ﬁt and top quark extraction

S. Paktinat Mehdiabadi1, A. Mirjalili2,1, S. A. Moosavy2

1 School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran 2Physics Department, Yazd University, P.O.B 89195-741, Yazd, Iran

Abstract. The precision measurement of produced jets in final state of proton collisions at Large Hadron Collider (LHC) can be increased by employing a proper kinematical assumption on the produced events. The suggested kinematical constrains through La- grangian multiplier will be used in minimal Chi square method in an event to event way. Here a constrained kinematical fitting is employed to extract a top quark in a multi-jets environment. Different fitting methods are considered. We use and improve a new algorithm (partition matrix) which are based on kinematical fitting and constrain of jet energies. The precision measurement for energy of top quark and w-boson through the fitting has an improvement with respect to reconstructed top quark and w-boson.

23.1 Introduction

To extract top quark in multi-jet events, it is required to remove much combinatorial background. To optimize the extraction, we use the constrained kinematical ﬁtting. Since the aim is not to measure the mass of top quark, we use this mass as a constrain. So in hadronic decay, there are two constraints: W mass: invariant mass of two light jets should be equal to w-boson mass. Top mass: invariant mass of two previous jets and b-jet should be equal to top quark mass. In this article, a new method is introduced which is based on constrained kinematical ﬁtting. Here the value of χ2 is periodically minimized and the constrained will appear through the Lagrangian multipliers.

23.2 Top quark extraction

In every event, the different combinations of jets are ﬁtted and the minimum value for each combination will be obtained. Each combination contains two light jets and one b-jet. Among the combinations which have convergence ﬁtting, the combination whit minimum χ2 is chosen as the best combination. This method is called partition matrix. The Fig. 23.1 indicates different distributions of the chosen combinations. The χ2 distribution has a peak at zero. These events have large χ2.

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This can be resulted from uncorrected combination of jets or a mistake in uncertainties of measurements. These events whit low probability will be eliminated by a cut on the χ2 (χ2 > 0.05). Different distributions of the chosen combinations, after applying the cut , are shown by thick lines. This cut will remove the combinations with large mass.

χ2 ConChi2 χ2 Probability with 2 d.o.f ProChi2 Entries 4945 Entries 4945 Mean 5.376 Mean 0.2371 RMS 5.25 RMS 0.317

Events 250 Events 103 200 Partitioned Matrix

150 102 100

50 10 0 0 2 4 6 8 10 12 14 16 18 20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 χ2 χ2 probability

Rec W InvMass jjWFristTopHighPro jjWUsedFristTop Rec top InvMass bjjHighProFrist bjjUsedFristTop Entries 2425 Entries 4945 Entries 2425 Entries 4945

2 Mean 86.5 2 Mean 130.5 Mean 183.2 Mean 237.4 RMS 14.2 RMS 90.49 RMS 22.46 RMS 99.24 500 250 All (from fit) All (from fit)

2 χ2 Prob(χ ) > 0.05 400 Prob( ) > 0.05 200 Events / 6 GeV/c Events / 6 GeV/c

300 150

200 100

100 50

00 100 200 300 400 500 600 00 100 200 300 400 500 600 2 2 mW (GeV/c ) mt (GeV/c )

Fig. 23.1. The distribution of minimum χ2 in every event (left handed on top) and probability distribution (right handed on the top) . The plots at the second row are relating to invariant mass of w-boson and top quark. The results of ﬁtting with cut ( thick lines ) and without cut (dashed lines) on the probability χ2 are compared.

In Fig. 23.1 RecTop denotes to the fitting which at least is convergence for a combinationp of jets. The GenTop is representing the extracted top quarks in a distance ∆R = ∆η2 + ∆φ2 < 1. These quarks have hadronic decays and all their partons satisfy the jet cuts ET ≥ 300GeV and | η ≤ 2.5 | . The number of these quarks are 3063 in 2767 events (some events have two or three top quarks). Since in each event just one top quark is extracted, to find the efficiency, the number of GenTop is divided over 4508. The purity degree is defined as a ratio of extracted top which is matched whit a produced top. The results before after the applying cut on the probability χ2 are tabulated respectively in Table 23.1 and Table 23.2.

23.2.1 Fitting effect on the kinematic property of reconstructed top quark

The main aim to use kinematic ﬁtting is to eliminate the background combination and to do the best chosen for jets to reconstruct the top quark and w-boson. This kind of ﬁtting is also able to improve the effects related to errors in measuring the

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RecTop GenTop Matched Purity Efﬁciency 3683 4508 1166 34% 25%

Table 23.1. Number of the obtained quarks, degree of purity and efﬁciency. The method of partition matrix without applying the cut is presenting.

RecTop GenTop Matched Purity Efﬁciency 935 4508 362 38% 8% Table 23.2. Number of the obtained quarks, degree of purity and efﬁciency after applying the cuts over the probability χ2 .

energies. It is because that in fitting, the real mass of w-boson and top quark are entered and real partons are appeared like jets ( true or false of the jet assump- tions, are reflected in χ2 value). To investigate this effect, the energy of top quark before and after the fitting is compared to energy of produced top. In every event, if the probability for optimized combination is more than 0.05 and the produced top quark is placed at distance less than 1 from extracted top quark, energy of the extracted and fitted top quark is compared whit the energy of produced top quark. The improvement of energy is defined as σRec−σFit It is seen σRec that the algorithm of partition matrix will improve the result of measurement for w-boson and top quark whit amount of 3% and 24% respectively (See Fig. 23.2). This improvement, will be important in making precisely reconstruction and the mass of top quark.

23.3 Repetition of analysis without b-jet tagging

It is possible that LHC, at the beginning, is not able to distinguish the b-jet , from light jets. In fact to distinguish the b-jet, it is necessary to reconstruct exactly the trace of charged particles. It will not happen at beginning for the LHC because of the mistakes which will occur for the place of pieces. Therefor we repeat the analysis for the state where the top quark consists the three jets.

23.3.1 The result of top quark extraction

In this case in every event, different combinations have been fitted and minimum of χ2 will be found for each combination. When the fitting is convergence, a combination with minimum χ2 is chosen as the proper combination. Figure 23.3 indicates different distributions for these combinations. By comparison Fig. 23.1 and Fig. 23.3, we see that when there is not b tagging, the results will be better. In this case, there is no error in distinguish the b-jet. As we know, we can choose the first top quark as the best top quark which has the minimum χ2. By this condition, the efficiency, purity and the number of top quark without any cut and with the cut can be summarized respectively as in Table 23.3 and Table 23.4.

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The quantities which were used in Table 23.4 are similar to previous analysis.

DelthaERecW DelthaERecW DelthaEFitW DelthaEFitW Entries 2551 Entries 2551 Mean -1.238 Mean 9.196 50 RMS 93.17 40 RMS 91.78 Events Events 35 40 30

25 30 20

20 15

10 10 5

-200 -150 -100 -50 0 50 100 150 200 -200 -150 -100 -50 0 50 100 150 200 Gen Rec Gen Fit EW - EW (GeV) EW - EW (GeV)

DelthaERecTop DelthaERecTop DelthaEFitTop DelthaEFitTop Entries 2551 Entries 2551 Mean -16.4 60 Mean 1.17 35 RMS 94.91 RMS 87.81 Events Events 50 30

25 40

20 30

15 20 10 10 5

-200 -150 -100 -50 0 50 100 150 200 -200 -150 -100 -50 0 50 100 150 200 Gen Rec Gen Fit Et - Et (GeV) Et - Et (GeV)

Fig. 23.2. The energy difference of reconstructed/ﬁtted for w/top and the produced for w(top) with applying cut over χ2 probability.

Comparing Table 23.3 and 23.4 with Table 23.1 and 23.2, we see that the purity has been improved. This is because we do not have any constrain for b-jet.

Rectop Gen Top Matched purity Efﬁciency 4945 4508 1864 37% 40%

Table 23.3. The efﬁciency, purity and the number of top quarks, without applying the cut on the probability distribution when the b-jet is not distinguishable.

Rectop Gen Top Matched purity Efﬁciency 2425 4508 1094 45% 24%

Table 23.4. The efﬁciency, purity and the number of top quarks, after applying the cut on the χ2 probability.

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23 Two constrained kinematic ﬁttings and top quark extraction 181

χ2 ConChi2 χ2 Probability with 2 d.o.f ProChi2 Entries 3386 Entries 3386 Mean 7.601 2200 Mean 0.1083 RMS 5.613 RMS 0.2234 2000

Events 50 Events 1800 1600 40 1400 1200 30 1000 800 20 600 400 10 200

0 0 2 4 6 8 10 12 14 16 18 20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 χ2 χ2 probability

Rec W InvMass Rec top InvMass bjjHighProFrist bjjUsedFristTop jjWFristTopHighPro 2 240 jjWUsedFristTop 2 Entries 935 Entries 3386 Entries 935 Entries 3386 Mean 184 Mean 251.9 220 Mean 87.65 Mean 138.3 120 RMS 24.17 RMS 104.6 200 RMS 15.93 RMS 90.72

180 100 All (from fit)

160 All (from fit) Prob(χ2) > 0.05 Events / 6 GeV/c Events / 6 GeV/c 140 Prob(χ2) > 0.05 80 120 60 100 80 40 60

40 20 20 0 0 0 100 200 300 400 500 600 0 100 200 300 400 500 600 2 2 mW (GeV/c ) mt (GeV/c )

Fig. 23.3. The distribution of minimum χ2 in every event (left handed on top) and probability distribution (right handed on the top). The plots at the second row are relating to invariant mass of w-boson and top quark. The results of ﬁtting with cut ( thick lines ) and without cut (dashed lines) on the probability χ2 are compared.

Here the number of events which contain one top quark is 4508. The efﬁ- ciency and purity are as previous analysis. In fact we consider the constrain of b-jet due to error of QCD. It is because the particles which are coming from QCD, can be replaced instead of b-jets. We see that by applying this constrain, we will no better results. It is because by applying this constrain on the b-jet the probability of avoiding the real jets is more.

23.3.2 The effect of ﬁtting on the kinematic of reconstructed top quarks

As it was said, the main aim of kinematic fitting is to find the top quark by reducing the combinatorial background. Moreover to reconstruct the other particles, including the particles which are coming from scalar top quark, the kinematic fitting can give us better results. In this case, Fig. 23.4 indicates the result of comparison between the energy before and after the fitting for top quark and w-boson. It is seen that the algorithm of partition matrix will improve the result of measurement respectively with 11% and 4%.

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182 S. Paktinat Mehdiabadi, A. Mirjalili, S. A. Moosavy

DelthaERecW DelthaEFitW DelthaERecW DelthaEFitW 70 Constant 58.45 80 Constant 66.2 Events Events 60 Mean -13.86 70 Mean -3.776 50 60 Sigma 78.5 Sigma 69.47 50 40 40 30 30

20 20

10 10

0 -200 -150 -100 -50 0 50 100 150 200 -200 -150 -100 -50 0 50 100 150 200 Gen Rec EGen - EFit (GeV) EW - EW (GeV) W W

DelthaERecTop DelthaEFitTop DelthaEFitTop DelthaERecTop 80 70 Constant 62.82 Constant 53.43 Events 70 Events 60 60 Mean 2.296 50 Mean -1.944 50 Sigma 74.9 40 Sigma 78.65 40

30 30

20 20

10 10

-2000 -150 -100 -50 0 50 100 150 200 -200 -150 -100 -50 0 50 100 150 200 Gen Fit Gen Rec Et - Et (GeV) Et - Et (GeV)

Fig. 23.4. The energy difference for reconstructed (ﬁtted) w (top quark) and produced w (top quark). The combination of ﬁtted jet are passed through the probability cut. The central of distributions (-105,105), for emphasizing and improvement, are chosen as Gaussian distributions (thick line)

23.4 Conclusion

To extract the top quark in an environment full of jets, it is required to eliminate a huge volume of combinatorial backgrounds which cover the signal. In this connection, a new algorithm which is based on kinematic ﬁtting for jet energies, using two improved constrains were introduced. Then a mathematical framework which is useful for running this algorithm was deﬁned. The result of extraction for top quark for two cases that b-jets are distinguishable or not, were considered. It was observed when there is not b-jet tagging, the results will be better. Because there is not any error to distinguish b-jets. The algorithm of partition matrix to measure the energy of w-boson and top quark for b-jet tagging were improved respectively 3% and 24%. For the case we can not distinguish b-jet, the results were improved respectively 11% and 4%.

References

[1] S. Paktinat, CMS Internal Note 2005/005, ”2C Kinematics Fit in stop to top Decays”, December 19, 2005. [2] S. Paktinat Mehdiabadi, Phd Thesis, CERN, CMS/TS2007-002.

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24 CMS commissioning with cosmic muon data

G. Pugliese

Dipartimento Interateneo di Fisica, Bari, Italy

Abstract. The status of the Compact Muon Solenoid experiment and the commissioning strategy is reviewed. The detector performance measured with cosmic muon data is summarized. Particular emphasis is given to the results obtained with the large sample of data collected during 2008.

24.1 Introduction

The Compact Muon Solenoid (CMS) experiment is a multi purpose experiment with excellent particle identification capability able to capitalize on the rich physics program of the LHC, the new CERN 14 TeV proton proton collider. The CMS overall capability for LHC physics studies is discussed in [1]. The CMS [2] basic design concept is a super-conducting solenoid that allows a strong magnetic 4 T field; the tracker and the calorimetries are within the field volume, while outside in the iron yoke, it is located the muon spectrometer for a fast trigger and precise muon tracking. A schematic view of the CMS experiment and its components is shown in Fig. 24.1. Its length of 22 m and diameter of 15 m, and weighs 12.500 tonnes give an idea of its magnitude. The CMS tracker is the biggest all silicon detector in the word. It has been specif- ically designed to provide a precise and efficient measurement of the trajectories of charged particles emerging from the LHC collisions, as well as a precise reconstruction of secondary vertices. It consists of an inner ”pixel” detector and an outer ”strip” detector. The pixel detector consists of 3 barrel layers and 2 endcap disks and has a total of 66 million channels. The strip tracker is composed of more than 15.000 sensor modules (11 million channels) covering over 200 m2 of surface area and divided into several major compartments: inner and outer barrel structures (4 and 6 layers, TIB and TOB respectively), and inner and outer disks (3 and 9 disks respectively, TID and TEC). Calorimetry is provided by 76000 lead tungstate crystals for electromagnetic showers (ECAL) and a 70000 brass-scintillator plate calorimeter for the barrel and endcap regions for hadronic showers (HCAL). Both calorimeters are placed inside the volume of the solenoid and the barrel and endcap compartments cover the range in pseudorapidity η < 3. An hadron outer detector composed of scintillator is placed outside the barrel HCAL region for penetrating shower detection. A quartz very forward calorimeter system provides for coverage in the region 3 < η < 5. ECAL has been designed to obtain an energy resolution of better than

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0.5 % above 100 GeV. HCAL,√ when combined with the ECAL, measures jets with a resolution ∆E/E ≈ 100 %/ E ⊕ 5 %. The muon spectrometer plays a crucial role in CMS: processes including muons are powerful signatures of interesting events over the high background rate expected at the LHC with full luminosity. It is divided into 5 separate wheels in the barrel and 4 independent disks both in the positive and in the negative endcap. It is equipped with a redundant muon system based on Drift Tubes Chambers (DT) and Cathode Strip Chamber (CSC) respectively in the barrel and endcap regions for precise position measurement. In addition, Resistive Plate Chambers (RPC) are used for bunch crossing identiﬁcation and preliminary measurement of the muon transverse momentum. Each barrel wheel is divided into 12 sectors covering the full azimuthal angle, one sector consisting of four layers of DT chambers and 6 layers of RPCs. The innermost DT chambers are made of 3 groups of four layers of tubes (so called ”Super Layers”) able to locally reconstruct 3D segments up to 8 hits in r-φ plane and up to 4 hits in r-z plane. The outer-most DT layer provides a 2D segment in r-φ plane. In particular, the CMS muon system is one of the largest ever built detector employing RPC: 912 chambers for a total of 3500 m2 of active surface and 150000 electronic channel. The muons are measured in the pseudorapidity window |η| < 2.4. Matching the muons to the tracks measured in the silicon tracker results in a transverse momentum resolution between 1 and 5 %, for pT values up to 1 TeV/c.

Fig. 24.1. Schematic view of the CMS experiment

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24 CMS commissioning with cosmic muon data 185 24.2 CMS commissioning strategy

CMS is the first high energy physics collider detector assembled and cabled on the surface experimental hall, from the 2001 to the 2006. The commissioning activity started in 2005, in parallel with the installation of the detector, by testing the func- tionality of each single piece of sub-detector with provisional electronics readout. In the summer 2006, for the first time, the CMS detector was closed and the magnet was ramped up to its nominal value for commissioning and field mapping. A slice composed by portions of all systems was operated under cosmic rays with the purpose to study the global CMS behavior by combining information from different sub-detectors. Also prototypes of the final readout, data acquisition and control system protocols were employed. The test, called the Magnet Test and Cosmic Challenge (MTCC), provided important commissioning and operational experience, and magnet field mapping [3]. The lowering of the heavy elements of CMS into the cavern began in November 2006, starting with the forward calorimeters and followed by the different CMS slices, disks and barrel wheels, onto which the muon detectors are mounted. Several data taking campaigns known as ”global runs”, with at that time available detectors, took place in the last years. Figure 24.2 shows the fraction of the detector participating in data taking with sub-detectors and trigger beeing considered separately. In August 2008, all CMS detectors, with exception of the negative RPC disks and the pre-shower detector, were in read out. A total of about 350 million events were collected between May and August 2008 during the four periods of data taking called CRUZETs (Cosmic RUn at Zero Tesla). Between October and November 2008, the CMS experiment performed a period of continuously data taking for about one month called CRAFT (Cosmic Run At Four Tesla), with magnetic field at nominal value collecting approximately 300 million cosmic muon events. All global runs were an useful benchmark to complete the CMS commissioning. For each sub-detector, it was important to study the detector efficiency and to improve the performance measuring calibration and alignment constants. Moreover, the monitor tools such as the Data Quality Monitoring (DQM) and De- tector Control System (DCS), were tested and largely used from the shifters in control room in order to understand and safety control the detector. Finally, they were a good exercise data transfer off-site to CAF (CMS Analysis Facility) and to Tiers for prompt reconstruction, alignment and calibration. On November 2008, CMS was opened for the winter showdown. The installation and commissioning of pre shower detector toke place, together with the comple- tion and commissioning of the negative side of RPC disks. All sub detectors have taken advantage to repair faulty channels and possibly replace bad functioning components.

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Fig. 24.2. Fraction of CMS detector systems participating in global commissioning as a function of time (the box size represents approximate fraction included: 25%, 50%, 75%, 100%).

24.3 CMS performance with cosmic data

Detector performance results obtained during the 2008 data taking are summarized in the following paragraphs. More details can be found elsewhere [4]. Fig- ure 24.3 shows a typical event display of a single cosmic muon leaving tracking hits in the DT and RPC muon systems and associated energy deposits in ECAL and HCAL, with magnetic ﬁeld. This demonstrates the good inter-synchronization of the full system.

24.3.1 Silicon tracker

Cosmic muon data were used to evaluate the silicon strip and pixel tracker performance. The signal-to-noise ratio was estimated considering only clusters associated to a reconstructed track and the total cluster signal was corrected for the incident angle of the cosmic muon. For the strip tracker, the average value of the signal-to-noise ratio is between 25-30 (it depends on the silicon thickness in each sub-system) in good agreement with expectations from previous measurements. The track hit finding efficiency was measured and found higher than 99%, with some regions with lower efficiency, that corresponds to known hardware problems or failures that should be fixed in the shutdown period. The large number of cosmic events with a tracker track allowed detailed alignment studies. Figure 24.4 shows the mean values of the residuals distributions for the strip tracker inner and outer barrel and disks. They are consistent with 0, and the best resolution obtained, 10 µm in the barrel, is significant better with respect to both not aligned and CRUZET geometries. The results are comparable with what was expected after about 25pb−1 of integrated luminosity. The drift motion of the charge carriers is affected by the Lorentz force (deflected at Lorentz angle) in the magnetic field. To determine the value of the Lorentz An- gle, the spread of the drifting charge distribution is measured as a function of the

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24 CMS commissioning with cosmic muon data 187

Fig. 24.3. An event display of a cosmic muon recorded during the CRAFT data taking with a track reconstructed using the DT and RPC muon system data and with associated energy deposits in the HCAL and ECAL.

track incidence angle. The minimum corresponds to the Lorentz Angle. For the barrel silicon tracker the value of 24.60 is found (see Fig. 24.5).

24.3.2 Calorimeters

Figure 24.6 shows the stopping power (deposited energy divided by the path length in the crystal) of cosmic muons traversing ECAL as a function of the muon momentum, as measured in the tracker. Experimental data (dots) are compared to the theoretical curve of total stopping power (dE/dx) in PbWO4 (black continuous line). The dashed lines are the contributions due to collision loss, in red, and bremsstrahlung radiation, in blue. The good agreement shows that both the tracker momentum and the ECAL energy scale are correct. Similar results were also obtained for the HCAL. In Fig. 24.7 the measured energy loss (in blue) and the Monte Carlo prediction (in red) are reported as a function of the muon momentum. Good agreement is found also with 2006 test beam measurements.

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Fig. 24.4. Mean of residual distributions for silicon strips tracker

Fig. 24.5. Spread of the drifting charge distribution measured as a function of the track incidence angle

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24.3.3 Muon Spectrometer

The cosmic data have been used to study the performance of the muon reconstruction and identification algorithms, commissioning the whole software apparatus for online and off-line reconstruction. The first reconstruction step is the local reconstruction of track segments at the level of single chambers, starting from the one-dimensional hits in the cells. For each tube traversed by a muon track, the expected position was compared with the hit position in order to estimate the efficiency. For each super layer, the efficiency is calculated as the average efficiency of its tubes. In Fig. 24.8 the distribution of the average efficiency for all super layer is reported. Lower values correspond to groups of temporary disconnected channels. The resolution on the position of the single hit is also measured and found between 200 µm and 260 µm, with a satisfactory agreement between data and Monte Carlo data. The worst resolution values were obtained in the innermost station on the external wheels (W+2 and W-2) where the magnetic field has larger radial field (which gives a maximum difference in drift velocity of about 3%). The redundancy of the muon system is an useful feature to have unbiased cross- checks of sub detector performance. RPCs performance can be studied making use of the local reconstruction of the DT hits at a chamber level. The extrapolation of DT segment on the RPC plane allows to study the RPC performance at a local level. Following the segment extrapolation on the RPC surface, the fired RPC strips are searched in a region of ± 2 strip width around the impact point. For each chamber, both the global efficiency and the map of local efficiency have been estimated in order to spot inefficient points and to study the uniformity. Moreover in order to optimized the detector performance the efficiency has been studied at different applied voltage. In Fig. 24.9 the distribution of maximum efficiency for all the RPCs is shown. The tail at lower efficiency values is due to

Fig. 24.6. ECAL stopping power for cosmic muons measured as a function of the muon momentum. (Errors on the vertical scale are statistical only; error bars on the momentum represent the bin width).

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Fig. 24.7. Energy lost in HCAL for cosmic muons as a function of the muon momentum measurement in the tracker, measured from CRAFT and Monte Carlo data.

Fig. 24.8. Distribution of the average single cell efﬁciency in each Super Layer.

hardware problems as dead gaps and swapped cables; most of them were ﬁxed during the shut-down period.

24.4 Conclusion

The CMS commissioning is in its ﬁnal phase. In the last years, a large amount of cosmic muon data collected with and without magnetic ﬁeld were very useful to evaluate the detector performance and to calculate calibration and alignment constants with unexpected accuracy. Thanks to all global runs and local data taking,

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24 CMS commissioning with cosmic muon data 191

Fig. 24.9. Distribution of maximum efﬁciency for barrel RPCs

each sub-detector has reached a good level of knowledge. The system is ready and looking forward to exploring the physics of LHC data in fall 2009.

References

1. CMS CERN/LHCC 2006-001, CMS Collaboration ”Physics Technical Design Report, Vol- ume 1: Detector Performance and Software”; J. Phys. G: Nucl. Part. Phys. , 34 (2007) 995, CMS Collaboration, ”CMS Physics Technical Design Report, Volume 2: Physics Performance”. 2. JINST 3:S08004,2008, CMS Collaboration, ”The CMS experiment at the CERN LHC”. 3. CMS Note 2007/005, CMS Collaboration, ”The CMS Magnet Test and Cosmic Challenge (MTCC Phase I and II)” 4. CMS Collaboration, in preparation.

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25 QCD Physics Potential of CMS

K. Rabbertz

Institut fur¨ Experimentelle Kernphysik, University of Karlsruhe, Germany

Abstract. In view of the approaching LHC operation the feasibility and accuracy of QCD measurements with the CMS experiment at the Large Hadron Collider (LHC) involving hadrons and jets are discussed. This summary is based on analyses performed at CMS for center-of-mass energies of 10 as well as 14 TeV assuming event numbers ranging from some days of data taking up to 100 pb−1 of integrated luminosity with proton-proton collisions.

25.1 Introduction

With the advent of the LHC, a completely new regime in centre-of-mass energy for hadron-hadron collisions will be explored. While the main interest of the LHC is to unravel the nature of electroweak symmetry breaking, a detailed understanding of the detector performance and the Standard Model processes is a must. QCD, the theory of the strong interaction, describes one of the four fundamental forces of nature and in particular the hard interactions between coloured quarks and gluons and how they bind together to form hadrons. Due to the huge cross sections of QCD reactions involved, the most outstanding feature of events at the TeV energy scale is therefore the abundant production of jets, i.e. collimated streams of hadrons that are supposed to originate from a common initiator. A profound understanding of hadron production and jet physics therefore poses the foundation for the physics commissioning and monitoring of the CMS experiment [1] and is a mandatory step in order to re-establish the Standard Model and to set the stage for the search of new phenomena. In the next section analyses dealing with first measurements of hadron production and of the Underlying Event (UE) activity based on jets formed from tracks of charged particles are presented. The following section then concentrates on jet physics before finishing this report with an outlook. Photon physics which in CMS is included in the QCD working group as well had to be left out. The latest results from CMS can be found in [2] and [3]. Details on the performance of the CMS experiment with respect to track reconstruction, alignment, jet finding and calibration can be found elsewhere in these proceed- ings.

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194 K. Rabbertz 25.2 Tracks and Hadrons

25.2.1 Charged Hadron Production Charged particle multiplicity distributions from hadron-hadron collisions have been studied already in other experiments [4,5]. A measurement of the distribution in pseudorapidity η = − ln tan(θ/2) with θ being the polar angle, dNch/dη, can be carried out with a few thousand events collected by the CMS detector and will be one of the first measurements at the LHC. Since one has to integrate over the transverse momentum spectrum for each pseudorapidity region, however, one needs to extrapolate the measurable pT range to small momenta due to the limitation of track finding in the low pT limit. To reduce unavoidable modeling systematics three different methods to reach as low in pT as possible are foreseen in CMS [6,7,8]. The first consists of a hit-counting technique [9] where charged particles are only required to reach the first layer of the CMS pixel detector, hence pT & 30 MeV. The advantage of this method is its relative insensitivity to detector misalignment, however, it depends on details of the simulation of the pixel response. The results from all three pixel layers (with different reaches in low pT) can be compared. To reduce the sensitivity to the detailed detector response simulation, tracklets consisting of two-hit pixel tracks in consecutive layers are employed as suggested in [10]. Finally, a track-reconstruction method with pixel hit triplets working down to pT ≈ 100 MeV is proposed which requires a more careful study of the tracker alignment. The three techniques exhibit different sensitivities to the diverse sources of systematic uncertainty and complement each other. Simulation results for all three are shown in Fig. 25.1.

Fig. 25.1. Simulation results for charged particle densities in pseudorapidity using the √ √ methods of pixel hit counting (left, s = 14 TeV), pixel tracklets (middle, s = 10 TeV) √ and track reconstruction with pixel triplets (right, s = 10 TeV) including estimates of the systematic uncertainties of ≈ 7 − 10% are shown together with input predictions from PYTHIA.

25.2.2 Underlying Event Measurements

Another analysis [11] exploits the standard track reconstruction for pT > 900 MeV with the silicon strip tracker of CMS. After triggering on Minimum Bias or jet

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25 QCD Physics Potential of CMS 195

events with different jet pT thresholds, all the tracks are investigated with respect to the difference in azimuth towards the leading jet constructed from these tracks. In other experiments [12,13] it could be shown that the transverse region of 60◦ < |∆φ| < 120◦ with respect to the leading jet is most sensitive to the Under- lying Event, i.e. every collision product not coming directly from the hard scatter. Extrapolations of the UE contributions to events at LHC energies vary widely such that an early determination of its size and the tuning of the MC generators is an important start-up measurement. Figure 25.2 presents the composition of the total charged particle distribution in ∆φ for all trigger streams on the left and the resulting pT dependence of the charged particle density in the transverse plane reconstructed from simulations with PYTHIA tune DWT on the right. For comparison the MC predictions of PYTHIA with various tunes and from HERWIG without model for multiple parton interactions are shown as well. Already with the assumed 10 pb−1 of integrated √ luminosity at s = 14 TeV it will be possible to differentiate between the extrapolations of some models to LHC energies. Using tracks with a lower limit of pT > 500 MeV the sensitivity can be further increased as demonstrated in [11].

Fig. 25.2. Composition of the total charged particle distribution in ∆φ for all trigger

streams (left) and the resulting pT dependence of the reconstructed charged particle density in the transverse plane together with predictions of various PYTHIA tunes and from −1 √ HERWIG assuming 10 pb of integrated luminosity at s = 14 TeV.

25.3 Jet Physics

In contrast to the last section where jets were used at most in order to ﬁx the basic orientation of an event, they are the primary topic now. Instead of looking after global event properties like the numbers of produced hadrons or the general ﬂow of momentum in an event, one would like to establish a closer connection to the hard process which is described theoretically in terms of partons, i.e. quarks, anti-quarks and gluons. Since it is impossible to unambiguously assign bunches of observed hadrons to the originating partons, jet algorithms are employed that

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define a distance measure between objects and uniquely determine which of them are sufficiently close to each other to be considered to come from the same origin and hence to combine them into a jet. In CMS three jet algorithms with in total five different jet sizes R (or D) are in use: The Iterative Cone algorithm with R = 0.5 as implemented in the trigger of the CMS experiment [14], the SISCone algorithm [15] with R = 0.5 or R = 0.7, and the kT algorithm [16,17,18] with D = 0.4 or D = 0.6. For SISCone and kT the implementation of [19] has been employed. It has to be noted that the Iterative Cone is not collinear and infrared-safe. For safe jet algorithms the following theoretical uncertainties in approximate order of importance have to be considered when comparing pQCD results to experimental data: The uncertainty inherent in the determination of the parton density functions (PDFs) of the proton, the precision in perturbative QCD (leading order LO, next-to-leading order NLO, . . . ) 1, non-perturbative corrections, the dependence on the PDF parameterizations, the knowledge of αS(MZ), and for very high jet transverse momenta potentially electroweak corrections. On the experimental side the dominant uncertainties are due to the jet energy calibration JEC (including the treatment of electronic noise and of collisions from different proton bunch crossings, i.e. pile-up), the luminosity determination, the jet energy resolution JER, trigger efficiencies, the spatial resolutions in azimuthal angle φ and in pseudorapidity η, and non-collision background. Depending on a particular jet analysis the sensitivity to one or another effect might be reduced. For example in the case of normalized observables like the dijet azimuthal decor- relation and event shapes or in cross-section ratios like the dijet production ratio in pseudorapidity and 3-jet to all-jet ratios, the luminosity uncertainty is eliminated and the uncertainty due to the JEC is reduced. The inclusive jet cross section, which will be discussed first, is a particularly challenging measurement and requires all uncertainties to be under control.

25.3.1 Inclusive Jets

In [20] a plan for the measurement of the differential inclusive jet production cross section for rapidities up to |y| = 2.5 with CMS assuming 10 pb−1 of inte- √ grated luminosity at a center of mass energy of s = 10 TeV is presented.2 The reach in jet transverse momentum is already beyond any previous collider experiment [22,23,24] and the TeV scale of jet physics can be probed. The analysis is performed on fully simulated CMS events which are adopted as pseudo data. Jets are reconstructed from calorimeter energy depositions with the inclusive kT (D = 0.6) and the SISCone (R = 0.7) algorithm. Events accepted by the trigger simulation are combined to the inclusive jet pT spectrum in such a way that each pT bin receives contributions from exactly one fully efﬁcient trigger. Subsequently, each jet is subjected to a JEC that corrects on average the observed jet energy to the energy of the ﬁnal state particle jet [25]. Lacking collision

1 The uncertainty of a pQCD calculation is conventionally estimated by varying the renormalization and factorization scales. √ 2 Forward jets with 3 < |η| < 5 have been investigated in [21] for s = 14 TeV .

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data the JEC is currently derived from Monte Carlo truth by matching reconstructed jets with generated particle jets. Due to the fact that the QCD jet pT spectrum is steeply falling an additional unsmearing step becomes necessary. There are more jets migrating to higher transverse momenta than in the opposite direction because of the finite jet energy resolution. To remove this distortion from the measured spectrum the Ansatz Method is used, which has been employed suc- cessfully at the Tevatron [26,24]. The corrected¯ ³pT,jet spectra´¯ (times K factors) for ¯ ¯ three regions in absolute rapidity |y| = ¯ 1 ln E+pz ¯ are compared to theory 2 E−pz predictions (times non-perturbative corrections) in Fig. 25.3 left. The smeared Ansatz Function which has been fitted to the measured spectrum is also used to derive the uncertainties associated with a flat (in pT,jet) 10% jet energy scale uncertainty as well as a 10% variation relative to the nominal value of the JER as estimated in [27]. The result including an assumed initial 10% uncertainty on the luminosity is shown in Fig. 25.4 left together with a summary of the associated theory uncertainties on the right. The latter have been evaluated using NLOJET++ [28] and fastNLO [29] for the PDF (CTEQ6.5 [30]) as well as scale uncertainties and the difference between PYTHIA [31] and HERWIG++ [32] for the non-perturbative corrections. Despite rather large experimental uncertainties initially, some signals of new physics like contact interactions would be observable already at start-up in jet cross sections at transverse momenta beyond Tevatron energies. This is demonstrated in Fig. 25.3 right where a contact interaction term corresponding to a com- positeness scale of Λ+ = 3 TeV is drawn in addition to a pure PYTHIA QCD prediction.

Fig. 25.3. Comparison between the corrected measured spectra and the theory predictions

for the kT algorithm (left). For better visibility the spectra have been multiplied by factors of 8, 16 and 32. Fractional difference of a PYTHIA QCD+3 TeV contact interaction term and pure PYTHIA QCD in comparison to the experimental and theoretical uncertainties (right).

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Fig. 25.4. Fractional experimental (left) and theoretical (right) systematic uncertainties at

central rapidity for the kT jet algorithm. For better visibility the y-axis ranges have been chosen differently.

25.3.2 Dijets Another possibility to search for new phenomena already at start-up with about 100 pb−1 of integrated luminosity is to look for resonances in the dijet mass spectrum e.g. from the decay of spin-2 Randall-Sundrum gravitons, spin-1 Z0 bosons √ or spin-1/2 excited quarks q∗ as presented in [33] for s = 14 TeV. Since these resonances exhibit a more isotropic decay angular distribution than dijets from QCD, it is possible to reduce or eliminate the sensitivity to the dominant sources of experimental uncertainty from the JEC respectively the luminosity determination by examining only the ratio of the cross section in two different regions in pseudorapidity. Figure 25.5 left shows the resulting ratios of σdijet(|ηj| < 0.7) to σdijet(0.7 < |ηj| < 1.3) for three different resonance masses which come out to be signiﬁcantly larger than for QCD. Figure 25.5 right illustrates for three different masses of a potential q∗ resonance the observable dijet mass spectrum in comparison to QCD including statistical uncertainties as expected for 100 pb−1.

25.3.3 Dijet azimuthal Decorrelations In the study [34] of the normalized dijet cross section 1 · dσdijet emphasis is σdijet d∆ϕdijet put on the angular correlation in azimuth between the two leading jets reconstructed from simulated energy depositions in the calorimeters. Angular quantities in general can be measured more precisely than the energy of jets as here the JEC uncertainty only affects the classiﬁcation of events into different bins of the leading jet pT. The remaining total systematic uncertainty including effects of the JER and the required unsmearing using different MC generators is estimated to vary approximately linearly from 5% at ∆ϕdijet = π to 10% at ∆ϕdijet = 5π/9. In Fig. 25.6 the corrected ∆ϕdijet distributions from simulated PYTHIA events are compared in several bins of leading jet pT with the predictions of several MC generators and with LO as well as NLO pQCD.

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25 QCD Physics Potential of CMS 199

Fig. 25.5. Dijet cross-section ratios in pseudorapidity versus resonance mass for spin-2 Randall-Sundrum gravitons, spin-1 Z 0 bosons, spin-1/2 excited quarks q∗ and QCD (left). Dijet ratio versus resonance mass for three different excited quark masses compared to QCD (right) with statistical uncertainties as expected for 100 pb−1 of integrated luminos- √ ity at s = 14 TeV.

Fig. 25.6. Corrected ∆ϕdijet distributions reconstructed from simulated energy depositions in the calorimeters (black symbols) are presented in several bins of leading jet pT together with the statistical uncertainties as expected for 10 pb−1 of integrated luminosity √ at s = 10 TeV. In addition, the distributions are compared to the particle jet predictions from PYTHIA (full), HERWIG++ (short-dashed), MADGRAPH (dotted), and the predictions from LO (dash-dotted) and NLO pQCD (long-dashed line).

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25.3.4 Event Shapes Normalized hadronic event shape distributions of e.g. central transverse thrust τ⊥,C [35] which have been analyzed in [36] are somewhat similar to the previous observable in the sense that they characterize the geometric momentum flow within an event. Only they usually exploit the complete four-vectors of the measured objects. The sensitivity to the JEC is then reduced by normalizing the quantity derived from the four-vectors to the momentum sum. In general, event shapes, which have also been measured in e+e− and ep collisions, do not necessarily require the use of jet algorithms. In this study, however, the shape defining objects have been chosen to be jets reconstructed from simulated energy depositions in the calorimeters with pseudorapidities up to |η| < 1.3. Figure 25.7 shows the τ⊥,C distribution for kT jets with jet size D = 0.6 including statistical and systematic uncertainties from JEC and JER for assumed 10 pb−1 of integrated lu- √ minosity at s = 14 TeV together with the MC predictions from PYTHIA and ALPGEN. With higher transverse momenta more events approach thrust values corresponding to a dijet configuration (τ⊥,C → 0) as can be seen from a comparison of the distributions for two different minimal transverse energies of the leading jet in Fig. 25.7 left and right. Early measurements of event shapes allow to study differences in the modelling of QCD multi-jet production and are a valu- able input to MC generator tuning.

Fig. 25.7. The central transverse thrust distribution (τ⊥,C, in logarithmic scale) reconstructed from simulated energy depositions in the calorimeters (black points) is presented cor cor for ET,1 > 80 GeV (left) and ET,1 > 500 GeV (right) together with the statistical and dominant systematic uncertainties as expected for 10 pb−1 of integrated luminosity at √ s = 14 TeV. A trigger pre-scale of 100 is assumed in the left plot. In addition, the distributions are compared to the generator predictions of PYTHIA (dashed) and ALPGEN (dotted line).

25.3.5 Jet Shapes As the last topic to be covered in this note jet shapes look into the internal structure of jets. Two observables are suggested in [37] and [38]: The fractional transverse momentum 1 − ψ(R) of a jet outside the jet core with a radius of R = 0.2

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25 QCD Physics Potential of CMS 201 ® 2 and the second central moment of the jet transverse proﬁle δRc . To explore the largest jet pT range possible, the ﬁrst quantity has been evaluated for the two leading calorimeter jets from QCD dijet production and is compared in Fig. 25.8 with the MC prediction of PYTHIA for quark and gluon jets. The total uncertainty is dominated at low pT by systematic uncertainties due to the JEC, non-linearities of the calorimeter and fragmentation model dependencies estimated using PYTHIA and HERWIG++. At high p the uncertainty due to lack of statistics with only √ T 10 pb−1 at s = 14 TeV takes over. To reduce the sensitivity to the® JEC and non-linearities in the calorimeters 2 the second central moment δRc has been calculated for jets where the tracks of charged particles (pT > 1 GeV) associated with a jet are used to correct the calorimetric energy determination [39]. The jet substructure then is derived from tracks respectively the charged particles alone. Instead of 10% JEC uncertainty in the former study® only ≈ 5% are assumed in the latter. Figure 25.9 compares the 2 result for δRc with the MC prediction of HERWIG++ for quark and gluon jets. Both observables will serve as input for tuning MC generators, in particular with respect to fragmentation models, and may allow an extraction of the quark- gluon jet fraction.

2 Fig. 25.8. The fractional transverse Fig. 25.9. The second central moment δRc momentum of a jet outside R=0.2, of the jet transverse energy distribution is

1 − ψ(0.2), is presented versus pT,jet presented versus pT,jet for jets reconstructed for jets reconstructed from simulated from tracks (black points) in the pseudora- energy depositions in the calorime- pidity region |η| < 1 including statistical un- ters (black points) in the rapidity re- certainties as expected for 10 pb−1 of inte- √ gion |y| < 1 including statistical grated luminosity at s = 10 TeV. The to- and systematic uncertainties as ex- tal systematic uncertainty is indicated by the pected for 10 pb−1 of integrated lu- √ shaded region. In addition, HERWIG++ pre- minosity at s = 14 TeV. In addi- dictions using charged particles are shown tion, PYTHIA (tune DWT) predictions for quark (dashed) and gluon initiated jets are shown for quark initiated (dash- (dash-dotted line). dotted), gluon initiated (solid), and for all particle jets (dashed line).

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202 K. Rabbertz 25.4 Outlook

A number of QCD analyses involving charged particle tracks and jets possible already after a few days of data taking or after accumulating roughly 10 to 100 pb−1 of integrated luminosity have been presented. A rich program of new physics measurements re-establishing the Standard Model and preparing the arena for searches for new phenomena will be possible. CMS is well prepared and ﬁrst proton-proton collisions at the LHC are eagerly awaited.

25.5 Acknowledgements

I would like to thank the conference organizers for the kind invitation and for the overwhelming hospitality I had the occasion to encounter. I would also like to thank Kirsti Aspola for her kind organizational help.

References

1. CMS Collaboration, “The CMS experiment at the CERN LHC,” JINST 0803 (2008) S08004. 2. CMS Collaboration, “CMS technical design report, volume II: Physics performance,” J. Phys. G34 (2007) 995–1579. 3. P. Gupta, B. C. Choudhary, S. Chatterji, and S. Bhattacharya, “Study of direct photon √ plus jet production in CMS experiment at s = 14-TeV,” Eur. Phys. J. C53 (2008) 49–58. 4. UA5 Collaboration, G. J. Alner et al., “Scaling of Pseudorapidity Distributions at c.m. Energies Up to 0.9-TeV,” Z. Phys. C33 (1986) 1–6. 5. CDF Collaboration, F. Abe et al., “Pseudorapidity distributions of charged particles √ produced inpp ¯ interactions at s = 630 GeV and 1800 GeV,” Phys. Rev. D41 (1990) 2330. 6. CMS Collaboration, “Pseudorapidity distributions of charged hadrons in √ minimum-bias p-p collisions at s = 14 TeV,” CMS Physics Analysis Summary CMS-PAS-QCD-08-004 (2008). 7. CMS Collaboration, “Measurement of charged hadron spectra in proton-proton √ collisions at s = 14 TeV,” CMS Physics Analysis Summary CMS-PAS-QCD-07-001 (2007). 8. CMS Collaboration, “Study of Charged Hadron Multiplicity in Minimum Bias p+p √ Collisions at s = 900 GeV and 10 TeV,” CMS Physics Analysis Summary CMS-PAS-QCD-09-002 (2009). 9. PHOBOS Collaboration, B. B. Back et al., “Charged particle pseudorapidity density √ distributions from Au+Au collisions at sNN = 130-GeV,” Phys. Rev. Lett. 87 (2001) 102303. 10. PHOBOS Collaboration, B. B. Back et al., “Charged particle multiplicity near mid-rapidity in central Au + Au collisions at S(1/2) = 56-A/GeV and 130- A/GeV,” Phys. Rev. Lett. 85 (2000) 3100–3104, 11. CMS Collaboration, “Measurement of the Underlying Event in Jet Topologies using Charged Particle and Momentum Densities,” CMS Physics Analysis Summary CMS-PAS-QCD-07-003 (2007). 12. CDF Collaboration, A. A. Affolder et al., “Charged jet evolution and the underlying event in pp¯ collisions at 1.8 TeV,” Phys. Rev. D65 (2002) 092002.

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25 QCD Physics Potential of CMS 203

13. CDF Collaboration, D. E. Acosta et al., “The underlying event in hard interactions at the Tevatronpp ¯ collider,” Phys. Rev. D70 (2004) 072002. 14. D. Acosta, M. Della Negra, L. Fo, A. Herv, and A. Petrilli, eds., “CMS Physics: Technical Design Report, Volume I: Detector Performance and Software”, volume LHCC-2006-001 of Technical Design Report CMS. CERN, Geneva, 2006. 15. G. P. Salam and G. Soyez, “A practical Seedless Infrared-Safe Cone jet algorithm,” JHEP 05 (2007) 086, 16. S. D. Ellis and D. E. Soper, “Successive combination jet algorithm for hadron collisions,” Phys. Rev. D48 (1993) 3160–3166, 17. S. Catani, Dokshitzer, L. Yuri and B. R. Webber, B. R., “The K-perpendicular clustering algorithm for jets in deep inelastic scattering and hadron collisions” Phys. Lett. B285 (1992) 291-299. 18. Catani, S. and Dokshitzer, Yuri L. and Seymour, M. H. and Webber, B. R., “Longitudinally invariant K(t) clustering algorithms for hadron hadron collisions,” Nucl. Phys. B406 (1993) 187-224. 19. M. Cacciari and G. P. Salam, “Dispelling the N**3 myth for the k(t) jet-finder,” Phys. Lett. B641 (2006) 57–61, 20. CMS Collaboration, “Initial Measurement of the Inclusive Jet Cross Section at 10 TeV with CMS,” CMS Physics Analysis Summary CMS-PAS-QCD-08-001 (2009). 21. CMS Collaboration, “Jet reconstruction in the CMS Forward Hadron (HF) calorimeter √ in proton-proton collisions at s = 14 TeV,” CMS Physics Analysis Summary CMS-PAS-FWD-08-001 (2008). 22. CDF Collaboration, T. Aaltonen et al., “Measurement of the Inclusive Jet Cross Section at the Fermilab Tevatron p-pbar Collider Using a Cone-Based Jet Algorithm,” Phys. Rev. D78 (2008) 052006. 23. Abulencia, A. and others, Measurement of the Inclusive Jet Cross Section using the √ kT algorithminpp Collisions at s = 1.96 TeV with the CDF II Detector, ” Phys. Rev. D75 (2007) 092006. 24. D0 Collaboration, V. M. Abazov et al., “Measurement of the inclusive jet cross section √ in pp¯ collisions at s = 1.96TeV,” Phys. Rev. Lett. 101 (2008) 062001. 25. CMS Collaboration, “Plans for Jet Energy Corrections at CMS,” CMS Physics Analysis Summary CMS-PAS-JME-07-002 (2008). √ 26. D0 Collaboration, B. Abbott et al., “High-pT jets inpp ¯ collisions at s = 630 GeV and 1800 GeV,” Phys. Rev. D64 (2001) 032003. 27. CMS Collaboration, “Measurement of the Jet Energy Resolutions and Jet Reconstruction Efficiency at CMS,” CMS Physics Analysis Summary CMS-PAS-JME-09-007 (2009). 28. Z. Nagy, “Three-jet cross sections in hadron hadron collisions at next-to-leading order,” Phys. Rev. Lett. 88 (2002) 122003. 29. T. Kluge, K. Rabbertz, and M. Wobisch, “Fast pQCD calculations for PDF fits, http://www.arXiv.org/abs/hep-ph/0609285. 30. W. K. Tung et al., “Heavy quark mass effects in deep inelastic scattering and global QCD analysis,” JHEP 02 (2007) 053. 31. T. Sjostrand, S. Mrenna, and P. Skands, “PYTHIA 6.4 physics and manual,” JHEP 05 (2006) 026. 32. M. Bahr et al., “Herwig++ Physics and Manual,” Eur. Phys. J. C58 (2008) 639–707. 33. CMS Collaboration, “CMS Search Plans and Sensitivity to New Physics using Dijets,” CMS Physics Analysis Summary CMS-PAS-SBM-07-001 (2007). 34. CMS Collaboration, “Dijet Azimuthal Decorrelations in pp Collisions at √ s = 10 TeV,” CMS Physics Analysis Summary CMS-PAS-QCD-09-003 (2009).

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35. A. Banﬁ, G. P. Salam, and G. Zanderighi, “Resummed event shapes at hadron hadron colliders,” JHEP 08 (2004) 062. 36. CMS Collaboration, “Study of Hadronic Event-Shape Variables,” CMS Physics Analysis Summary CMS-PAS-QCD-08-003 (2008). 37. CMS Collaboration, “Transverse Momentum Distribution within Jets in pp Collisions at 14 TeV,” CMS Physics Analysis Summary CMS-PAS-QCD-08-005 (2008). 38. CMS Collaboration, “Study of jet transverse structure using the second moment of √ the jet proﬁle in transverse momentum in pp collisions at s = 10 TeV,” CMS Physics Analysis Summary CMS-PAS-QCD-08-002 (2009). 39. CMS Collaboration, “Jet Plus Tracks Algorithm for Calorimeter Jet Energy Corrections in CMS,” CMS Physics Analysis Summary CMS-PAS-JME-09-002 (2009).

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School of Particles and Accelerators FIRST IPM MEETING Institute for Research in ON LHCPHYSICS Fundamental Sciences (IPM) VOL. 1, NO. 1 (p. 205) Isfahan, April 20-24, 2009

26 Study of the Top Quark Anomalous Wtb couplings using the Top Electric Dipole moments

N. Roodi

Science and Research Branch, Islamic Azad University, Tehran, Iran

Abstract. Studying top quark is particularly interesting for several practical reasons. In- deed due to its large mass the electroweak gauge symmetry is broken maximally by top quark and it may be the ﬁrst place in which the non-SM effects could be appeared. In this paper, it is shown that the most general Lagrangian for the interaction of W with top and bottom quarks which consists of V-A and V+A structure with in general complex couplings produces an Electric Dipole Moment (EDM) for the top quark at one loop level. By using the upper bound on the top quark electric dipole moment we place limits on the Wtb anomalous couplings.

26.1 Introduction

1 2 The top quark is, according to the Standard Model (SM), a spin- 2 and charge- 3 fermion, transforming as a colour triplet under the group SU(3) of the strong interactions and as the weak-isospin partner of the bottom quark. None of these quantum numbers has been directly measured so far, although a large amount of indirect evidence supports these assignments. The analysis of Electroweak ob- 0 2 servables in Z decays requires the existence of a T3 = 1/2, charge- 3 fermion, with a mass in the range of 170 GeV/c2, consistent with the direct Tevatron measurements. The measurement of the total cross section at the Tevatron, and its comparison with the theoretical estimates, are consistent with the production of a spin-1/2 and colour-triplet particle. The LHC should provide a direct measurement of the top quantum numbers. A complementary approach in hunting for new physics is to examine its indirect effects in higher order processes. Since top quark is far more massive than other standard model fermions, its interactions may be quite sensitive to new physics originating at higher scale . If there are any deviations from the SM expectations in the properties of the top quark, they may indirectly lead to modiﬁcations in the anticipated branching fractions [1],[2]. In this work, We consider the effective interaction of the quarks with on- shell photons to make prediction of the acceptable range for the anomalous Wtb couplings.

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206 N. Roodi 26.2 Top Electric Dipole Moment and Anomalous Wtb couplings

A non-vanishing value for the EDM of a fermion is of special interest as it signifies the presence of CP-violating interactions. Since the top is such an unusual fermion, in fact so heavy that it is very unlikely to exist as a bound state with another quark, it is clearly important to ask: What is its EDM? It is a well known fact that the only source of CP violation in the SM, namely, the Cabbibo Kobayashi Maskawa (CKM) phase, has an negligible effect on flavor diagonal processes such as the EDM of elementary particles . In the SM quarks cannot have an EDM at least to three loops level but the Top Dipole Moment can arise at the 1-loop. The EDM of light fermions has been long studied both theoretically and experimentally (the EDM of light quarks via the neutron and proton) those of the heaviest quarks still require more attention. In fact, the top quark may be more sensitive to new sources of CP violation since it is the only known fermion with a mass of the size of the electroweak symmetry breaking scale. Since the dipole moment char- acterizes the effective coupling between the spin of the fermion and the external gauge field, to extract the dipole moment one needs information on the spin polarization of the top quark. Fortunately, the left handed nature of the weak decays of the top allows us to determine its polarization quite readily. The most general ttγ¯ vertex function is given by:

µν Γµ = it¯(Qtγµ + iσ qν(a + dtγ5))t (26.1)

where Qt is the electric charge of the top quark, a is its Magnetic Dipole Moment (MDM), and dt is its Electric Dipole Moment (EDM). Here qµ is the photon four 2 momentum. At tree level Qt = 3 e, whereas a and dt arise via radiative corrections. In general, the vertex of Wtb can be in the form of:

g µ µ LWtb = √ t¯(aLγ PL + aRγ PR)Wµb + h.c. (26.2) 2

Where g is the weak interaction coupling constant, PL, PR are the left, right handed projection operators and aL, aR are in general complex. In the Standard Model case aL = Vtb = 1 and aR = 0.0. The anomalous Wtb coupling of the above Equa- tion induces an EDM for the top quark through the Feynman diagrams shown in Fig. 25.1, where all the particles are taken on-shell. After some calculation via the unitary gauge, one can extract the coefﬁcient of the dt term from the ttγ¯ vertex function. This leads to

µ ¶ e 3α mb 1 ∗ dt = − V1(xb, xW ) + V2(xb, xW ) Im (aLaR) (26.3) mW 32π mW 3

mi with xi = mt ,Nc = 3, Qb = −1/3, and QW = −1. The FW and Fb functions stand for the contribution of the Feynman diagram where the photon emerges from the W boson and the b-quark line, respectively. They are given by:

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Title Suppressed Due to Excessive Length 207

¡ 2 2 ¢ V1 = − (4xW − xb + 1) f(xb, xW ) − xb + 4xW − 5xbxW − 3xW − 2xb + 1 g(xb, xW ) ¡ 2 2 ¢ V2 = − (4xW − xb + 1) f(xW , xb) + xb + 4xW − 5xbxW − 3xW − 2xb + 1 g(xW , xb) (26.4)

Once the Equation of dt is numerically evaluated, one obtains:

−19 dt = −2.6 × 10 Im(aLaR) e.cm (26.5)

In the literature one of the estimated upper bound on the top EDM is 1.6 × 10−22 iφ e.cm [3]. We can set: aL = 1, aR = κRe R By combining the bound on the Top EDM and using the deﬁned parameterization for aL and aR we have the following upper bound on the right handed coupling aR:

−4 κR sin φR < 6 × 10 (26.6) In conclusion, we can say the top EDM is sensitive to the Wtb anomalous couplings and it provided a very tight bound on the right handed coupling in Wtb vertex.

γ γ

b b W W

t W t t b t Fig. 26.1. Feynman diagrams contributing to the on-shell ttγ¯ vertex.

References

1. M. Beneke, et al, arXiv:hep-ph/0003033. 2. Werner Bernreuther, arXiv:0805.1333. 3. H. Novales-Sanchez, J.J. Toscano, arXiv:0712.2008.

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27 Searching for purely hadronic top decays from SUSY

B. Safarzadeha,b, S. Paktinat Mehdiabadib

aScience and Research campus Islamic Azad university bSchool of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran

Abstract. A search for SUSY in a low mass mSUGRA test point by looking for purely hadronic top decays in the ﬁnal states is presented. Missing transverse energy for early data is not under control, using a kinematic variable Meff, to suppress the dominant background from QCD and standard model events is under study.

27.1 Introduction

Supersymmetry scenarios provide a promising extension for the standard model solving the quadratic divergencies and hierarchy problems. Supersymmetry imposes a new symmetry between bosonic and fermionic degree of freedom [1]. In this note, we will focuss on supersymmetry breaking scenarios in which the squarks are heavier than the gluino and the third generation squarks are lighter than those of the two ﬁrst generations and also gluino. In this case, the gluino will dominantly decay into top(bottom) quarks. Top quarks decay either hadronically, t → Wb → bqq¯0 q, q 0 = u, d, s, c, or leptonically t → Wb → b`ν ` = e, µ, τ. In this note hadronic channel of top decays is used to look for supersymmetry signals. The structure of this note is as follows, ﬁrst of all we will review an approved analysis[2], which is based on 14 TeV simulated data. In the second part a new strategy will be introduced which can be applied on early data assuming the center of mass energy of 10 TeV.

27.2 Inclusive search for SUSY in top quark ﬁnals states in CMS

In CMS an inclusive search for SUSY in LM1 point [3] as a test point, is done by looking for events with a top quark in the ﬁnal states [2]. In this point, the top quark can be produced inclusively in the decays of t˜, b˜ andg ˜ accompanied by a neutralino, which appear as a large missing transverse energy(MET). Hence in the ﬁnal state there is at least one top quark plus a large MET. The approach is to use this feature to look for an excess in the number of the extracted top quarks, when a hard cut is applied on the missing transverse energy. To extract the top quark in a multi-jets environment requires eliminating the huge combinatorial

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210 B. Safarzadeh, S. Paktinat Mehdiabadi

background which can hide signal. In order to select real combinations of the jets originated from a top quark, a two constraint kinematical ﬁt [4] is utilized. Since the purpose of the study is not to measure the top mass, the W an top mass are used as constraints. This approach for some reason are useful, at ﬁrst it has a quantitative feature to reject fake top quarks (χ2 probability, Fig. 27.1), and also it can improve the kinematics features of the reconstructed top quark.

χ 2 Probability with 2 d.o.f

1 TotalSusy CMS Susy(withTop) Events Susy(noTop) 10-1 tt

10-2

10-3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 χ2 probability

Fig. 27.1. χ2 probability distribution for 200K events of the inclusive LM1 sample and 100K events of the inclusive tt¯ sample. All plots are normalized to 1 to make the shape comparison easier. The fake top quarks (SUSY events without a generated top quark ‘Susy(noTop)’) are concentrated in the low probability region.

In Fig. 27.2 the difference between the energy of the reconstructed (ﬁtted)

900 400 Constant 401.5 Constant 714.5

Events 800 Events 350 Mean -10.27 700 Mean -4.179 300 Sigma 26.92 600 Sigma 250 14.11 500 200 400 150 300 100 200 50 100 0 0 -100 -80 -60 -40 -20 0 20 40 60 80 100 -100 -80 -60 -40 -20 0 20 40 60 80 100 Gen Rec Gen Fit Et - Et (GeV) Et - Et (GeV) Fig. 27.2. The difference between the energy of the reconstructed/fitted top and the generated top. Fitted jet combinations pass the probability cut(χ2 probability > 0.05). The central parts of the distributions(-30,30) are fitted with a gaussian function(thick-blue lines) to emphasize and quantify the improvement in the resolution. The fit improves the resolution of the energy of the W and top quark by 37% and 48%, respectively. It also improves the bias. Distributions are made by 100k events of the inclusive tt¯ sample.

top quark and thep generated top quark, when the generated top quark which is closer than ∆R = ∆η2 + ∆φ2 = 0.5 to the reconstructed top quark (generated top decays hadronically and all its three partons have ET > 30 GeV and |η| < 2.5) is shown.

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27 Searching for purely hadronic top decays from SUSY 211

One of the main background is semileptonic tt¯ when there is a potentially high value for missing energy and a hadronically decaying top quark. To suppress these events one can use this fact that missing energy(MET) and the ﬁtted top quark are almost back to back in the transverse plane. The cuts optimization was done to suppress the SM background as well as increase the ratio of the SUSY events with a generated top quark ‘SUSY(withTop)’ against the SUSY events without a generated top quark ‘SUSY(noTop)’. In order to achieve these mains the following cuts are applied:

miss 1. The ﬁrst level trigger [5] (a central jet with ET > 88 and ET > 46 GeV). miss 2. The High Level Trigger (a central jet with ET > 180 and ET > 123 GeV). miss 3. ET > 150GeV, as shown in Fig. 27.3.

4 TotalSUSY 10 -1 SUSY(withTop)METStopMETStop CMS 1 fb METSingletMETWWjMETSusyhnew1METSinglethnew1METZWj SUSY(noTop)EntriesMETWWjMETZWj METtt 327864 48191 Entries 48191 327864 279673 700 193 EntriesMeanMeanMETSusy 5348 272.4 29113 191.9146 tt MeanEntries 272.4140.3 193 5348700 RMSMeanEntriesRMS 242.7 279673 113242.7 277.5 84.24 WWjMeanRMS 169.3 191.9 64.08 113 14667.28 RMSMean 99.54 277.5169.3 3 ZWjRMS 90.03 99.54 84.24 114.4 RMS 67.28 114.4 10 SingleRMS Top 90.03

Events / 30 GeV 10

0 100 200 300 400 500 600 700 MET (GeV)

Fig. 27.3. MET distributions for different samples. Events are required to pass the Level 1 and High Level Trigger.

raw 4. at least 4 jets, with at least one of them b-tagged, jets with ET > 30 GeV and |η| < 2.5. 5. to increase the ratio of SUSY(withTop) against the SUSY(noTop), convergent ﬁt with χ2 probability > 0.1 is applied. miss 6. ∆φ between the ﬁtted top quark and the ET < 2.6. Figure 27.4 shows the distribution of this quantity for different samples. 7. To suppress the QCD multi-jet backgrounds every event is required to have at least one isolated electron or muon with PT > 5 GeV/c and |η| < 2.5.

After applying these cuts, the only remaining background is tt¯. The ratio of the SUSY signal against the SM background is 11, when almost 70% of the extracted SUSY events have a generated top quark ‘SUSY(withTop)’. Figure 27.5 shows the distributions of missing transverse energy and the extracted top quark for different samples. It can be seen that the SUSY signal is well above the standard model (tt¯) background. Including the systematic uncertainties on the background the estimation for the minimum integrated luminosity for a 5σ discovery is ∼0.25 fb−1. Note that the analysis uses uncertainties that are realizable with 1 fb−1 of data.

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212 B. Safarzadeh, S. Paktinat Mehdiabadi

TotalSUSY SUSY(withTop)PhiFitTopMetWWjPhiFitTopMetSinglethnew2 6 EntriesEntries EntriesPhiFitTopMettt 0 2 1646 SUSY(noTop)MeanMean PhiFitTopMetSusy PhiFitTopMetStop0 0.2826 MeanEntries 1.822 994 113 RMS Mean 0.2669 1.79 Events RMS Entries 0 652 RMSRMS 0.8824 0.8976 tt MeanMean 1.871 2.668 5 Single TopRMSRMS 0.8562 0.6914

0 0 0.5 1 1.5 2 2.5 3 ∆φ(FittedTop, MET)

Fig. 27.4. The ∆φ between the ﬁtted top and the missing transverse energy. The distributions are made after applying the cut 5.

2 8 -1 TotalSUSY TotalSUSY hnew6 bjjtt Entries bjjSusy 526 METSingletMETWWj EntriesMeanEntries 165 187.3 11 CMS 1 fb METStopMETSusy bjjStop METSusyhnew1METSinglet SUSY(withTop)MeanRMSMean 189.7bjjWWj 16.78 186.8 Entries 361 METStop RMSEntries 17.76 0 10 METttEntriesMETWWjMETZWjEntries 165 0 MeanRMS 186.3 10.63 Entries 361 165 526 RMSMean 16.2 0 SUSY(withTop)Entries EntriesMean 361METZWj11EntriesMean 0262 0 0 RMS 0 Mean Entries 262Entries 0 0 7 SUSY(noTop) RMSEntries 0 87.59 Mean Mean 200.5255.1 255.1 257.2MeanRMS 0 0 0 RMS 87.59Mean 0 RMS Mean 75.48RMSMean 0 0 0 RMS 83.3283.32 SUSY(noTop)RMS RMS 84.73 0 tt RMSRMSRMS 0 0 8 6 tt CMS 1 fb-1 5

Events / 30 GeV 6

Events / 6 GeV/c 4

4 3

2 2 1

0 0 150 200 250 300 350 400 450 500 550 600 650 700 0 50 100 150 200 250 300 350 400 2 MET (GeV) mt (GeV/c ) Fig. 27.5. Missing transverse energy (left) and the extracted top quark (right) after applying all cuts.

27.3 Implementation of the analysis on early data

There are some limitations on early data which restrict applying previous analysis • The calorimeter deposit based missing energy might not be reliable during the early phase of data taking. • Errors on jet energies might not be well known. It is however possible to define kinematic variables that can discriminate between signal and background without relying on the missing energy. Based on the three leading jets two additional variable are defined [6] and P [7], HT as the scalar sum of the two on more leading jet P ’s, HT = Pji and P T i T ji missing PT (MHT) of the event calculated as MHT = − i PT Typical observable that separate signal and background events is the effective mass (Meff), which is defined as Meff = HT + MHT. Figure 27.6 shows the distribution of (Meff) for different samples. As expected, the backgrounds tend smaller values than the SUSY signal. Hopefully Meff looks to be a efficient parameter for suppression of standard background mainly QCD and tt¯ events applying this cut for early data is under study.

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27 Searching for purely hadronic top decays from SUSY 213

-1 2 10 lm0 lm1 lm2 lm3 10 lm4 lm5 events/100 pb events/100 all Bkg.

CMS preliminary 1

10 -1 500 1000 1500 2000 2500 3000 Meff

Fig. 27.6. The Meff of all background and different benchmark points.

27.4 Acknowledgment

I would like to thank conference organizer for their hospitality during the conference time in Isfahan.

References

1. S. P. Martin, “A Supersymmetry Primer”, (hep-ph/9709356 v3 7 Apr 1999). 2. S. Paktinat, L. Pape, M. Spiropulu, “Search for SUSY in top ﬁnal states in the mSUGRA scenario at CMS”, J.Phys.G34:N13-N22, 2007,CMS Note 2006/102. 3. J.Ellis, J.S.Hagelin, D.V.Nanopoulos,K.Olive, M.Srednicki, Nucl.Phys.B238(1984)453. 4. J. D’Hondt et al. “Fitting of Event Topologies with External Kinematic Constraints in CMS”, CMS Note 2006/023. 5. The CMS Collaboration, “ The Trigger and Data Acquisition project”, Volume II, CERN/LHCC 2002-26,CMS TDR 6.2, 15 December 2002. 6. The CMS Collaboration, “ SUSY Searchs with dijet events”,CMS PAS SUS-08-005. 7. CMS Collaboration, “Search strategy for exclusive multi-jet events from supersymmetry at CMS”,CMS PAS-SUS-09-001.

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School of Particles and Accelerators FIRST IPM MEETING Institute for Research in ON LHCPHYSICS Fundamental Sciences (IPM) VOL. 1, NO. 1 (p. 215) Isfahan, April 20-24, 2009

28 Search for Supersymmetry in Top Final States at CMS

N. Salimia,b, S. Paktinat Mehdiabadib

aTarbiat Modares University, Tehran, Iran bSchool of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran

Abstract. A search for SUSY using the top quark plus missing transverse energy(MET), in a low mass mSUGRA test point is performed. A two -constraints kinematic ﬁt is utilized to extract the top quark. It is shown that for point LM1 , a 5σ excess can be observed with 30pb−1. The ﬁnal signal over background ratio, is 12.0.

28.1 Introduction

Supersymmetric scenarios [1] provide a very promising extension for the standard model (SM) solving the quadratic divergences and hierarchy problem. Su- persymmetry imposes a new symmetry between the fermionic and bosonic degrees of freedom.In this analysis we focus on mSUGRA, where gravity is responsible for soft supersymmetry breaking.Top can be produced inclusively in the decay of heavy squarks or gluinos accompanied by a neutralino. Hence in the ﬁnal state there is at least a top quark plus a large missing transverse energy(MET). The approach to use this feature is looking for an excess in the number of the extracted top quarks in the tail of the MET distribution from the tt¯ events. The analysis is optimized to have a pure sample as signal. We study the potential of SUSY discovery in CMS by this signature.

28.2 The Data Samples and Reconstruction Algorithms

The main sample (referred as LM1-stop sample) used to study the kinematic ﬁt in section 27.3 was produced for the scalar top quark search in point CMS-LM1 2 2 (mSUGRA scenario,m0 = 60GeV/c ,m12 = 250GeV/c ,A0 = 0.0, tan(β) = 10 and µ > 0). Every event is required to have at least one scalar top quark that decays as follows: ˜ 0 ∼ 0 t1→t + χ2→t + lR + l→t + l + l + χ1

The t˜1 is produced inclusively. The sample that contains 6629 events was generated and reconstructed using CMSSW-1-6-12 that is called CSA07 at CMS [2].

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216 N. Salimi, S. Paktinat Mehdiabadi 28.3 2C Kinematic Fit for Top Quark Extraction

Extracting the top quark in a multi-jets environment requires eliminating the huge combinatorial background which can easily hide the signal. Since the purpose of the study is not to measure the mass of the top, its mass is used as a constraint. So in a hadronic decay of a top, we have two constraints:

mw: The invariant mass of two non b-jets must be equal to the known mas of the W boson.

mtop: The invariant mass of these two jets and a b-jet must be equal to the mass of the top quark.

28.3.1 Result for Top Extraction For every event we fit each combination of two non b-tagged jets and non b- tagged jet, and compute the χ2. If the fit converges, the combination with the least χ2 is selected as the right combination. Figure 28.1 shows different distributions for these selected combinations. The χ2 probability distribution in Fig. 28.1 (top-right), has a peak in the low probability region.These events have a large χ2 either because the tested hypothesis is wrong or because the uncertainty on the jet resolution used in the fit is not correctly estimated[3]. To remove the effect of these ’low probability’ events, a cut on the χ2 probability is introduced and combinations with a χ2 probability less than 0.05 (χ2 > 6) are rejected. Figure 28.2 show the comparison between the energy resolution before and after the fit for both the top and W. The energy resolution of the top and W are improved by 3% and 24% respectively after using the fit.(They are shown by ImpEwRes and ImpEtRes in Table 28.1).

Table 28.1. The results for top extraction

Algorithm Rec Top Matched Purity Eff ImpEW Res ImpETopRes Partition Matrix 3386 1166 34% 25% - - Part Mat ( χ2 < 6 ) 935 362 38% 8% 3% 24%

Table 28.1 shows results of top extraction. ’RecTop’ stands for the number of events for which the fit converges for at least one jet combination. ’Matched’p refers to the number of the extracted top quarks that are closer than ∆R = ∆η2 + ∆ϕ2 ≤ 1 to a generated top quark that decays hadronically and all of its partons pass the kinematic cuts of the jets ( Et ≥ 30GeV and | η |≤ 2.5 ). The generated top quark in our sample is 4508. Since we select one top quark per event, to find the efficiency (shown in table as ’Eff’) the ’Matched’ number is divided by 4508. The ’purity’ is defined as the percentage of the ’RecTop’ that are ’Matched’.

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28 Search for Supersymmetry in Top Final States at CMS 217

DelthaERecW DelthaERecW DelthaEFitW DelthaEFitW χ2 ConChi2 χ2 Probability with 2 d.o.f ProChi2 Entries 2551 Entries 2551 Stop Entries 3386 Entries 3386 Mean -1.238 Mean 9.196 Mean 7.601 Mean 0.1083 RMS 93.17 RMS 91.78 RMS 5.613 RMS 0.2234 50 40

50 Events Events Events Events 103 35 40 40 30

2 25 10 30 30 20

20 15 20 10 10 10 10 5 1 -200 -150 -100 -50 0 50 100 150 200 -200 -150 -100 -50 0 50 100 150 200 0 2 4 6 8 10 12 14 16 18 20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 EGen - ERec (GeV) EGen - EFit (GeV) χ2 χ2 probability W W W W DelthaERecTop DelthaERecTop DelthaEFitTop DelthaEFitTop Rec W InvMass Rec top InvMass Entries 2551 Entries 2551 bjjHighPro jjWUsed bjjUsed Mean -16.4 Mean 1.17 2 2 60 240 jjWHighPro EntriesAll (from 935 fit) AllEntries (from fit) 3386 Entries 3386 35 RMS 94.91 RMS 87.81 220 EntriesMean 935138.3 Mean 251.9 184 RMS 90.72 120 Mean 87.65 RMS 104.624.17 Events Events 200 RMS 15.93 50 Prob(χ2) > 0.05 30 180 Prob(χ2) > 0.05 100 160 25 40 Events / 6 GeV/c Events / 6 GeV/c 140 80 20 120 30 60 100 15 80 20 40 60 10

40 20 10 5 20 0 0 0 100 200 300 400 500 600 0 100 200 300 400 500 600 -200 -150 -100 -50 0 50 100 150 200 -200 -150 -100 -50 0 50 100 150 200 2 m (GeV/c2 ) Gen Rec Gen Fit mW (GeV/c ) t Et - Et (GeV) Et - Et (GeV)

Fig. 28.1. The distribution of the least Fig. 28.2. The differrences between χ2solution in every event (top-left) and the energy of the reconstructed/fitted distribution of its probability (top-right). W(top)and the generated W(top).Fitted The dijet and bjj invariant masses for the jet combinations pass the probability leastχ2 are shown in the second row. cut. The central parts of the distributions (-105, 105)are fitted with a Gaussian function (thick-blue lines) to emphasize and quantify the improvement in the resolution. Thefit improves the resolution of the energy of the W and top quark by 3% and 24% respectively.

28.4 Analysis Path

In this note our strategy to search for SUSY is to look at the number of extracted top quarks for 100pb−1. Different cuts and selections used in this analysis are as follows:

28.4.1 MET≥ 200GeV

Figure 28.3 compares the MET distribution from different samples. To increase the ratio of the SUSY events to ttbar and other SM backgrounds, a cut on MET is introduced.

28.4.2 at least 5 jets

We looking for a hadronically decaying top candidates. Figure 28.4 shows the multiplicity distribution. The events with less than 5 jets are rejected to suppress the SM background.

28.4.3 at least 1 b-jet

The top quark almost always decays to a b-tagged jet plus a W, so in every event at least one jet must be tagged as a b-tagged jet.

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218 N. Salimi, S. Paktinat Mehdiabadi

Missing Transverse Energy SUSY(With Top) nj1 MET5MET4 SUSY(noTop) EntriesEntries MET2MET1MET3 10679853471 MeanUSY(noMean Top) 34.12 34.64 nj2nj5nj3nj4nj1 4 EntriesRMSRMS 140133 2436094512 32.01 30.56 SUSY(WithTop) 10 UnderflowUnderflow 0 0 OverflowOverflow 0.289 1.516 Entries 1073249923 290666383 MeanIntegraltt~Integral 2.699e+04260.6246.645.55 5150 tt~

Events Skewness 3.991 Mean 7.0373.9485.0925.371 3.65 RMSKurtosis 134.3134.535.41 31.06 WW Events RMSWW 2.058 2.3212.014 2.262.06 WZ WZ 102 103

102 10

10 1

1 10-1 0 100 200 300 400 500 600 700 0 2 4 6 8 10 12 14 16 18 MET (Gev) Jet Multiplicity

Fig. 28.3. MET distributions for different Fig. 28.4. The jet-multiplicity in the events samples. that pass the cut on MET.

28.4.4 a convergent ﬁt with a χ2probability > 0.05

To find a top quark, the best jet combination is found by the kinematic fit. A cut on the χ2 probability is applied to increase the purity of the selected top quarks.Table 28.2 shows the number of remaining events after every cut. Table 28.2 shows the number of the remaining events after each cut. These cuts were optimized to increase the ratio of SUSY(withTop)/SUSY(noTop) and decrease the SM backgrounds simultaneously, whilst keeping the significance sufficiently high.The significance is defined as follows [4]: √ √ significance = 2 × ( S + B − B)

where S and B are the member of the remaining events after all cuts, respectively. We try to ﬁnd the minimum integrated luminosity to achieve a 5σ discovery. Using S and B for 100pb−1 ,the minimum integrated luminosity can be found by solving the equation: p √ √ 5 = minIL/100 × 2 × ( 39 + 4 − 4) ⇒ minIL/100 = 0.30pb−1 ⇒ minIL = 30pb−1

For this integrated luminosity, the corresponding number of events for signal and background are 12 and 1, leading to 100% statistical uncertainty on the background which is larger than systematic uncertainty [5], so the latter can be neglected.

28.5 Results

In the events extracted as signal 28/(28 + 11) = 71% are from SUSY events which have a top quark at the generator level.

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28 Search for Supersymmetry in Top Final States at CMS 219

Table 28.2. Effect of different samples. In every row, the number of the remaining events 100pb−1 after that cut is shown. Nev shows the number of events used in this analysis.Nev is the same number after normalizing to the cross section times 100pb−1 and ”wT/noT” means SUSY(withTop)/SUSY(noTop).

requirements SUSY(wT) SUSY(noT) ttInc WWj ZWj wT/noT x-sec(pb)NLO 52 52 830 269.91 51.5 -

Nev 1871 86523 139955 106796 53469 0.21 100pb−1 Nev 925 4275 83000 26991 5150 0.21 MET ≥ 200GeV 530 2467 395 97 28 0.21

nj ≥ 5 460 1427 250 31 10 0.32

nbj ≥ 1 300 385 143 1 1 0.77 A Convergent Fit 251 309 81 0 0 0.81 χ2probability > 0.05 63 34 25 0 0 1.81

nl ≥ 1 28 11 4 0 0 2.54

28.6 Conclusion

The capability of CMS to find low mass SUSY in events with a top quark in the final state was studied. A two constraints kinematic fit was utilized to improve the top quark extraction. It is shown that for point LM1 with an integrated luminosity of 30pb−1, a 5σ discovery is achievable provided the uncertainty is statistics dominated. The final signal over background is 12.

References

1. Stephen P. Martin, ‘A Supersymmery primer’,(hep-ph/9709356v3 7 Apr 1999). 2. http://twiki.cern.ch/twiki/bin/view/CMS/CSA07 3. Paktinat S, Pape L and Spiropulu M 2006, Search for SUSY in top ﬁnal states in the mSUGRA scenario at CMS, CMS NOTE 2006/102. 4. S.I. Bityukov, N.V.Krasnikov, ”On observability of signal over background”, NIM A 452: 518-524, 2000. 5. S.Paktinat Mehdiabadi , L. pape and M. Spiropulu , J.Phy. G:Nucl. Part . Phys , Search √ for low mass SUSY using hadronic top decays in pp collisions at s = 14 TeV with the CMS detector , 2007 , 34 , N13 N22. 6. J.D’Hondt et al.’Fitting of Event Topologies with External Kinematic Constraints in CMS’, CMS NOTE 2006/023

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School of Particles and Accelerators FIRST IPM MEETING Institute for Research in ON LHCPHYSICS Fundamental Sciences (IPM) VOL. 1, NO. 1 (p. 221) Isfahan, April 20-24, 2009

NS 29 g1 in the valon model

F. Taghavi-Shahria, F. Arashb, N. Mottaghib

aSchool of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran b Tafresh University,Tafresh,Iran

NS Abstract. We calculate the non-singlet spin structure function, g1 , of the nucleon in the valon representation. The valon is deﬁned as a valence quark plus its associated sea partons and gluons, emerging from dressing processes in QCD. The results of this calculations are in excellent agreement with all available experimental data for the entire measured range of x. The results have good agreement with all global ﬁts such as AAC, BB, GRSV, and DNS.

29.1 Polarized hadron structure function in the valon model

A central goal in the study of QCD is to understand the structure of hadrons in terms of their quark and gluon degrees of freedom. The most direct tool and sensitive test for probing the quark and gluon substructure of hadrons is the polarized Deep Inelastic Scattering (DIS)processes. In such experiments detailed information can be extracted on the shape and magnitude of the spin dependent par- 2 ton distributions, δqf(x, Q ). Any determination of parton distribution function in a nucleon in the framework of QCD always involves some model-dependent procedures. In valon model, it is assumed that a nucleon is composed of three dressed valence quarks,the valon. Each valon has its own internal structure which can be probed at high enough Q2. At low Q2, a valon behaves as a valence quark. The internal structure of a valon is calculated in the Next-to-Leading Order in 2 QCD. We have worked in MS scheme with ΛQCD = 0.22 GeV and Q0 = 0.283 GeV2. The details are given in [1] and [2]. In this framework, the helicity distributions of various parton in a hadron is given by:

X Z 1 2 dy x 2 δq i (x, Q ) = δG valon (y)δq i ( ,Q ) (29.1) h x y h valon y

h where δGvalon(y) is the helicity of the valon in the hosting hadron. It is related to unpolarized valon distribution by:

δGj(y) = δFj(y)Gj(y) (29.2)

where, Gj(y), are the unpolarized valon distributions and are determined by a phenomenological argument for a number of hadrons [3-5]. The functions δFj(y),

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222 F. Taghavi-Shahri, F. Arash, N. Javadi Mottaghi

x 2 where j refers to U and D type valons, are given in [1]. δqvalon( y ,Q ) is the polarized parton distribution in the valon. They are evaluated according to the DGLAP evolution equation subject to physically sensible initial conditions. Hav- ing speciﬁed the various components that contribute to the spin of a valon, we now turn to the polarized hadron structure, which is obtained by a convolution integral as follows: Z X 1 dy x gh(x, Q2) = δGh (y)gvalon( ,Q2) (29.3) 1 y valon 1 y valon x In the valon model the sea quark polarization is consistent with zero. This fact can be understood on the theoretical grounds. The valon structure is generated by perturbative dressing in QCD. In such processes with massless quarks, helicity is conserved and therefore, the hard gluons cannot induce sea quark polarization perturbatively. This result is in good agreement with recently experimental data from HERMES and with the newly released data from COMPASS [6,7]. The results for polarized parton distributions and polarized hadron structure functions are in very good agreements with all available experimental data and global ﬁts such as AAC, BB, GRSV and DNS [8,9,10,11](see the Fig. 29.1).

xg1p x g1d

0.08 COMPASS Q2>1 (Gev2) SLAC-E143 COMPASS Q2>0.7 (Gev2) SMC-low x SMC 0.07 HERMES HERMES AAC 0.03 AAC BB BB GRSV GRSV 0.06 MODEL MODEL

0.05 0.02

0.04

0.01 0.03

0.02 0 0.01

0 -0.01 10-4 10-3 10-2 10-1 100 10-3 10-2 10-1 100 x x

p 2 GeV 2 Fig. 29.1. Left:Polarized proton structure function, g1 at Q = 5( c ) .Right: Polarized d 2 GeV 2 deuteron structure function, g1 at Q = 3( c ) .

29.2 Non-Singlet spin structure function in the valon model

The non-singlet spin structure function is a convenient function both for QCD analysis (because of its simplicity) and future experimental test concerning the determination of the Bjorken sum rule:

Z 1 3 p n gA αs αs 2 αs 3 IBJ = (g1 − g1 )dx = (1 − − 3.583( ) − 4.4472( ) + ...) (29.4) 0 6 π π π i i i i i i

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NS 29 g1 in the valon model 223

NS xg1 Integrate[g1NS,{x,0.9}] 0.12 HERMES Q2=5 GeV2 SMC 0.11 HERMES calculation SMC(Low x -Low Q^2) 0.15 E143 MODEL 0.1 AAC BB 0.09 GRSV MODEL 0.08

0.07 0.1

0.06

0.05

0.04

0.03 0.05

0.02

0.01

0 0 10-4 10-3 10-2 10-1 100 0.2 0.4 0.6 0.8 1 x x

NS 2 GeV 2 Fig. 29.2. Left: xg1 at Q = 5 ( c ) that compared with the experimental data. Right: NS The integral of g1 over the range 0.02 < x < 0.9 measured by HERMES coll. as the 2 GeV 2 function of the low x limit of integration, xmin evaluated at Q = 10 ( c ) .The results from the model are compared with the experimental data from [6,12,13,14].

The non-singlet spin structure function is deﬁned as:

NS p n p d g1 ≡ g1 − g1 = 2[g1 − g1 /(1 − 1.5ωD)] (29.5) NS In Fig. 29.2(Left), the x dependence of xg1 in the valon model is shown in comparison with data from HERMES, E143, E155 and SMC. The results are in very good agreement with experimental data for the entire measured range of x. R 1 p n In Fig. 29.2(Right) The evolution of the Bjorken integral xmin(g1 − g1 )dx as a function of xmin is shown for the Model that compared with the recent HER- MES data [13]. Note that about 50 percent of the sum rule comes from x values below about 0.12 and that about 10-20 percent comes from values of x less than about 0.01. The results for the ﬁrst moment of non singlet spin structure function in the valon model in comparison with the experimental data are summarized in Table 28.1.

NS 2 2 Table 28.1. Numerical values for Γ1 at Q = 5GeV . Valon model 0.1380 HERMES 0.1479 ± 0.0055 ± 0.0142 ± 0.0055 E143 0.163 ± 0.01 ± 0.016 SMC 0.174 ± 0.024 ± 0.012

29.3 Conclusion

NS In this paper we calculated the non-singlet spin structure function, g1 , of the nucleon in the valon model. The results are in excellent agreement with all experimental data for the entire measured range of x. Then the evolution of the Bjorken

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integral as a function of xmin is calculated for the Model and compared with the recent HERMES data. The results for the ﬁrst moment of non singlet spin structure function in the valon model also have good agreement with the experimental data.

References

1. F. Arash and Fatemeh Taghavi-Shahri, JHEP 07 (2007) 071. 2. F. Arash, F Taghavi-Shahri, Phys. Lett B668 (2008) 193. 3. F. Arash, A. N. Khorramian, Phys. Rev. C 67 (2003) 045201. 4. F. Arash, Phys. Lett. B 557 (2003) 38. 5. F. Arash, Phys. Rev. D 679 (2004) 054024. 6. HERMES Collaboration, A. Airapetian et al;Phys.Rev.D75:012007,2007 7. COMPASS Collaboration, A. Korzenev, hep=ex/0704.3600; V. Yv. Alexakhin, et al; Phys. Lett B674 8 (2007). 8. Asymmetry Analysis Coll. (AAC), Y. Goto et al., Phys. Rev. D 62, (2000) 034017; ibid D 69, (2004) 054021. 9. J. Blumlein and H. Bottcher, Nucl. Phys. B 636, (2002)225. 10. M.Gluck, E. Reya, M. Stratmann, and W. Vogelsang, Phys. Rev. D 63, (2001) 094005. 11. D. de Florian, G. A. Navarro, R. Sasso, Phys. Rev. D 71 (2005) 094018. 12. SMC Collaboration,B. Adeva et al.Phys. Rev. D 58 112001 112001- 13. SMC Collaboration,B. Adeva et al. Phys. Rev. D 60, 072004 14. E143 Collaboration,K. Abe et al. Phys. Rev. L 75, 1,(1995)

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School of Particles and Accelerators FIRST IPM MEETING Institute for Research in ON LHCPHYSICS Fundamental Sciences (IPM) VOL. 1, NO. 1 (p. 225) Isfahan, April 20-24, 2009

30 The study of the Diffractive Parton Distribution Functions

S. Taheri Monfareda, A. Khorramiana,b, S. Atashbar Tehrania, F. Arbabifara, S. Tizchanga

aPhysics Department, Semnan University, Semnan, Iran bSchool of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran

Abstract. A detailed study about the Parton Distribution Functions based on diffractive deep inelastic scattering data measured at the DESY HERA experiments is performed. In this study it is assumed that the diffractive structure function is given by a sum of Pomeron and secondary Reggeon contributions. In order to obtain each contribution, The Pomeron/ Reggeon structure functions need to be multiplied by the corresponding ﬂux factor. Finally, the full diffractive structure function is obtained by adding the Pomeron and Reggeon contributions. The diffractive parton densities are made publicly available.

30.1 Introduction

Diffractive events are characterized by the fact that the incoming proton(s) emerge from the interaction intact, or are excited into a low mass state, with only a small energy loss. Diffractive processes, for proton energy losses up to a few percent, are mediated by an exchange with quantum numbers of the vacuum, the so- called Pomeron, IP[1], now understood in terms of partons from the proton. For larger energy losses, mesonic exchanges - Reggeons and pions - become important. The topology of diffractive events is characterized by a gap in the rapidity distribution of ﬁnal-state hadrons caused by the lack of color and the effective spin of the exchanged object[2].

30.2 Diffractive structure functions

The kinematics of γ∗p → Xp can be described by the invariants Q2 = −q2, t = (P − P 0)2, and by the square of the centre-of-mass energy in the photon-proton system, W2 = (P + q)2, where the four-momenta are deﬁned in Fig. 30.1. The variable β has the form of a Bjorken variable deﬁned with respect to the momentum P − P 0 lost by the initial proton instead of the initial proton momentum P. 2 The usual Bjorken variable xBj = Q /(2P ·q) is related to β and xIP as βxIP = xBj [3]. 2 Input parameters describing the DPDFs at a starting scale Q0 for QCD evolution are used to obtain the best description of the data after NLO DGLAP [3]

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226 S.Taheri Monfared, A. Khorramian, S. Atashbar, F. Arbabifar, S. Tizchang

Fig. 30.1. Schematic diagram of inclusive diffractive DIS, ep → eXp: xIP. Four-momenta are indicated in parentheses.

2 2 evolution to Q > Q0 and convolution of the DPDFs with coefﬁcient functions ( As summarized in Table 30.1)[4].

Table 30.1: The central values of the parameters extracted in the, ’H1 20006 DPDF FIT A’ and ’B’, and the corresponding experimental uncertainities. Fit Parameter Fit A Fit B

αIP(0) 1.118 ± 0.008 1.111 ± 0.007 −3 −3 nIR (1.7 ± 0.4) × 10 (1.4 ± 0.4) × 10

Aq 1.06 ±0.32 0.70 ± 0.11

Bq 2.30 ±0.36 1.50 ± 0.12

Cq 0.57± 0.15 0.45 ± 0.09

Ag 0.15 ± 0.03 0.37 ± 0.02

Cg −0.95 ± 0.20 0 (ﬁxed)

The DPDFs are modelled in terms of a light ﬂavor singlet distribution Σ(z), consisting of u, d and s quarks and anti-quarks with u = d = s = u¯ = d¯ = s¯ a gluon distribution g(z)[5]. Here, z is the longitudinal momentum fraction of the parton entering the hard sub-process with respect to the diffractive exchange, such that z = β for the lowest order quark-parton model process, whereas 0 < β < z for higher order processes[6]. The quark singlet and gluon distributions 2 are parameterized at Q0 using a similar approach to that commonly applied to hadronic parton densities[7], such that the most general form is [8]

2 B Ci zfi(z, Q0) = Aizi (1 − z) (30.1)

The parameters Cq and Cg thus have the freedom to take negative as well as positive values. The xIP dependence is parameterized using a ﬂux factor motivated by Regge theory, eBIP t f (x , t) = A · (30.2) IP/p IP IP 2α(t)−1 xIP 0 where the pomeron trajectory is assumed to be linear[9], αIP(t) = αIP(0) + αIPt, 0 and the parameters BIP and αIP and their uncertainties are obtained from ﬁts to

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30 The study of the Diffractive Parton Distribution Functions 227

H1 FPS data. To obtain a good description of the data, an additional sub-leading exchange (IR) is included, which contributes signiﬁcantly only at low β and large xIP. this contribution is assumed to factorize in the same way as the pomeron term, such that the evaluation of DPDFs becomes:

D 2 2 IR 2 fi (x, Q , xIP, t) = fIP/p(xIP, t) · fi(β, Q ) + nIR · fIR/P(xIP, t) · fi (β, Q ) (30.3)

The flux factor fIR/p takes the form of equation (30.2), normalized via a parameter AIR in the same manner as for the pomeron contribution and with fixed IR parameters from other H1 measurements. The parton densities fi are taken from a parametrization derived from fits to pion structure function data. For the quark singlet distribution, the data require the inclusion of all three parameters Aq, 2 B Ci Bqand Cq in equation zfi(z, Q0) = Aizi (1 − z) and the gluon density is para- 2 metrised at Q0 using only the Ag and Cg parameters. This parametrization and 2 2 the value of Q0 = 1.75GeV yield to ’H1 2006 DPDF Fit A’ . Referring to ’H1 2006 DPDF Fit B’,the gluon density is a simple constant at the starting scale for evolu- 2 2 2 tion, which is chosen to be Q0 = 2.5GeV . To calculate the Q evolution of the

0.25

0.20

0.15 ) 2 z,Q (

0.10

8.5 GeV

20 GeV

0.05

90 GeV

800 GeV

0.00

0.0 0.2 0.4 0.6 0.8

Fig. 30.2. zΣ(z, Q2) distribution function at different values of Q2, obtained from H1 data .

diffractive parton distributions, we need to Mellin transform these functions. The evolution of anomalous dimensions can be obtained by Mellin transformation of splitting functions. To obtain the x-dependence of parton distributions from the n-dependent exact analytical solutions in the Mellin-moment space, one has to perform a numerical integral in order to invert the Mellin-transformation[10]

Z ∞ k 2 1 iφ −c−weiφ iφ 2 f (x, Q ) = dwIm[e x Mk(n = c + we ,Q )]. (30.4) π 0

30.3 Conclusion

To determine the diffractive parton distribution functions, we apply the evolution 2 on available parameters at the starting scale Q0. The diffractive quark singlet and

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228 S.Taheri Monfared, A. Khorramian, S. Atashbar, F. Arbabifar, S. Tizchang

0.6

8.5 GeV

20 GeV 0.5

90 GeV

800 GeV

0.4 ) 2

0.3

z,Q g( z

0.2

0.1

0.0

0.0 0.2 0.4 0.6 0.8

Fig. 30.3. zg(z, Q2) distribution function at different values of Q2, obtained from H1 data .

gluon distribution functions from our attempt are shown in Fig. 30.2 and Fig. 30.3 at four different values of Q2 for the range 0.0043 < z < 0.8 corresponding approximately to that of the measurement. Our results are in good agreement with experimental H1 collaboration data shown in Fig. 30.4[4]. It is good to mention that we are going to ﬁt DESY experi- D mental data to reach unknown parameters and also F2 in our next step.

Fig. 30.4. H1 result for zΣ and zg as a function of z for different value of Q2 [4].

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30 The study of the Diffractive Parton Distribution Functions 229 References

1. V. Barone, Berlin, Germany: Springer (2002) 407 p 2. A. D. Martin, M. G. Ryskin and G. Watt, Phys. Lett. B 644, 131 (2007) [arXiv:hep- ph/0609273]. 3. G. Watt, arXiv:hep-ph/0511333. 4. A. Aktas et al. [H1 Collaboration], Eur. Phys. J. C 48, 715 (2006) [arXiv:hep- ex/0606004]. 5. A. Vogt, Comput. Phys. Commun. 170, 65 (2005) [arXiv:hep-ph/0408244]. 6. K. J. Golec-Biernat and A. Luszczak, Phys. Rev. D 76, 114014 (2007) [arXiv:0704.1608 [hep-ph]]. 7. D. W. Duke and J. F. Owens, Phys. Rev. D 30, 49 (1984). 8. A. D. Martin, M. G. Ryskin and G. Watt, Eur. Phys. J. C 44, 69 (2005) [arXiv:hep- ph/0504132]. 9. M. Kuroda and D. Schildknecht, Phys. Rev. D 67, 094008 (2003) [arXiv:hep- ph/0301156]. 10. A. N. Khorramian, A. Mirjalili and S. A. Tehrani, JHEP 0410, 062 (2004) [arXiv:hep- ph/0411390].

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School of Particles and Accelerators FIRST IPM MEETING Institute for Research in ON LHCPHYSICS Fundamental Sciences (IPM) VOL. 1, NO. 1 (p. 231) Isfahan, April 20-24, 2009

31 Electron and photon reconstruction in the CMS experiment at the LHC

P. Vanlaer

Universite´ Libre de Bruxelles, Interuniversity Institute for High Energies (IIHE-ULB) on behalf of the CMS Collaboration.

Abstract. The CMS electromagnetic calorimeter (ECAL) is described as well as its expected performance and recent ECAL commissioning results. Electron and photon reconstruction are then described, starting from the reconstruction of energy deposits in the ECAL by energy clustering algorithms, then proceeding with electron tracking. Electron and photon selection are described. The commissioning of electron and photon physics objects from the measurement of electroweak processes is also shown.

31.1 The CMS Electromagnetic Calorimeter ECAL

The CMS electromagnetic calorimeter ECAL and its performance are presented in Refs. [1,2]. The ECAL is divided in a barrel section (EB) and two endcaps (EE), as shown in Fig. 31.1. The excellent linearity between the energy deposited by electromagnetic showers and the measured electronics signals, as determined through calibration procedures, is expected to lead√ to an energy resolution given by a quadratic sum of terms:√ σ/E = 0.55% ⊕ 2.7%/ E ⊕ 0.155/E in EB for η = 0, and σ/E = 0.55% ⊕ 5.7%/ E ⊕ 0.205/E in EE for η = 2, with E in GeV [2]. At high energy, the constant term dominates, and the energy resolution is expected to be ' 0.6%.

31.1.1 ECAL geometry

3 The ECAL consists of 75848 PbWO4 crystals, with density ρ = 8.3 g/cm , radiation length X0 = 0.89 cm and Moliere radius rM = 2.19 cm. The crystals are positioned according to a quasi-projective geometry toward the nominal interaction point, with additional off-pointings intended at reducing the effects of cracks. The off-pointings are of 3◦ both in the azimuthal (φ) and the polar (θ) directions for the barrel, and of 3◦ in φ and between 2 to 8◦ in θ for the endcaps. The barrel covers the rapidity region |η| < 1.479 (θ = 25.6◦). It is divided in two halves, consisting of 18 supermodules, each of which covers 20◦ in φ. Each supermodule is divided in four modules, and each module is composed of glass- ﬁber alveola structures called sub-modules, housing 5 × 2 crystals in η × φ. The η × φ extension of the modules is of 4 × 4 trigger towers of 5 × 5 crystals (5 × 4 towers for the ﬁrst module). The gaps between modules are of ∼ 6 mm in both

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Fig. 31.1. Longitudinal view of one quarter of the ECAL [2].

η and φ. The 61200 EB crystals have truncated pyramidal shapes (17 types in total to ensure complete coverage) with (approximately) squared ∼ 2.2 × 2.2 cm2 front faces, which corresponds to widths in φ of ∼ 1◦ ' 0.0174 rad and in η of ∼ 0.0174, nearly constant over the whole EB length. The crystal lateral extensions thus correspond to about 1 rM. The crystal length in the EB is 230 mm, i.e. 25.8 X0. The centres of the crystal front faces are lying at a radius R = 1.29 m of the beam axis. The endcaps, situated at 3.21 m of the nominal interaction point, extend the angular coverage to |η| < 3.0 (θ = 5.7◦). Each is made of two D-shaped structures, where the crystals are distributed in a x − y grid. The 14648 EE crystals have a nearly parallelipipedic shape, with ∼ 2.9 × 2.9 cm2 front faces and length 220 mm, i.e. 24.7 X0. In front of most of the endcaps, a Pb–Si preshower covers 1.653 ≤ |η| ≤ 2.6 (i.e. radii 123 cm ≥ R ≥ 45 cm from the beam axis). Its thickness corresponds to 3 X0. The ECAL calorimeter is surrounding the tracker, and is inserted into the hadronic calorimeter HCAL. The material budget in front of the ECAL crystals, due to beam pipe, tracker, cables and supports, varies with η from a minimum of 0.4 X0 at η = 0 to a maximum of 1.7 X0 for |η| ' 1.4, with 1 X0 for |η| = 2.5 [1].

31.1.2 PbWO4 scintillating crystals

The characteristics of the PbWO4 crystals make them an appropriate choice for operation at LHC. The high density, short radiation length and small Moliere` radius result in a ﬁne granularity and a compact calorimeter. An electromagnetic shower of 100 GeV is essentially fully contained in length. The small Moliere` radius makes it such that a 5 × 5 crystal matrix in the barrel (resp. in the endcaps) contains 96.5% (resp. 97.5%) of the energy of an incident unconverted photon. The scintillation decay time of CMS crystals is of the same order of magnitude as the LHC bunch crossing time: about 80% of the light is emitted in 25 ns. The light output is relatively low: at 18oC about 4.5 photoelectrons per MeV

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31 Electron and photon reconstruction in the CMS experiment at the LHC 233

are collected in the photoamplifiers (APDs in the barrel and VPTs in the endcaps). The crystals emit blue-green scintillation light with a broad maximum at 420-430 nm. The light yield of the crystals varies with temperature (-2%/oC at 18oC) and so does the gain of the barrel APDs (-2.3%/oC) [4]. The crystal and photoamplifier temperature is thus required to be stabilized to 50 millidegrees in the barrel (0.1 degree in the endcaps) so that temperature fluctuations have a negligible contribution to the ECAL energy resolution. Temperature stability well within specifications was demonstrated in an extended one-month data taking period in cosmic rays in october-november 2008, during which the CMS magnetic field was kept at its nominal value of 3.8 Tesla (Cosmic Ray test At Four Tesla - CRAFT08) [4]. An important constraint is the radiation environment. The dose expected is 4 kGy at shower maximum in the ECAL barrel, 90 kGy at |η| = 2.6, 200 kGy at |η| = 3. The permanent damage to crystals was tested to be such that the scintillation light attenuation length remains longer than three times the crystal length. The irradiation also results in a transient, dose-rate dependent light attenuation. The dose rate expected at high LHC luminosity is 0.3 Gy/h at shower maximum in the barrel, 6.5 Gy/h at |η| = 2.6 and 15 Gy/h at |η| = 3. In the varying conditions of LHC running the result is a cyclic transparency behaviour between LHC collision runs and machine refills. The magnitude of the changes is dose-rate dependent, and is expected to range from 1 or 2 per cent at low luminosity in the barrel, to tens of per cent in the high η regions of the endcap at high luminosity. Under continuous irradiation the time to reach a constant light yield amounts to about 1 day [3]. To achieve design energy resolution the evolution of the crystal transparency must be monitored continuously. This monitoring is performed using laser pulses injected into the crystals via optical fibres. The response is normalized by the laser APD(t) pulse magnitude measured using silicon PN photodiodes. Thus R(t) = PN(t) is used as the measure of the crystal transparency. Because of the different optical paths and spectra of the injected laser pulses and the scintillation light, the changes in crystal transparency cause a change in response to the laser light which is not necessarily equal to the change in response to scintillation light. For attenuations < 10% the relationship between the changes can be expressed by a power law, S(t) R(t) α = S(t0) R(t0) where S(t) represents the response to scintillation light and α ' 1.6 is a characteristic of the production process and can be determined using data. This power law describes well the behaviour of all the crystals that have been evaluated in the test beam, and this formula is expected to be valid in the barrel for both low and high luminosity at LHC. The entire ECAL is scanned every 30 minutes. The stability of the laser monitoring system was tested in absence of irradiation during CRAFT08. In nominal data taking conditions, a stability better than the required 0.2% was measured for a period of 1 week [4].

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31.1.3 Photoampliﬁers

The barrel crystal scintillation light are readout by a pair of Avalanche PhotoDi- odes (APDs) operated at a gain of 50. Since the APD gain has a high dependence on the bias voltage (αV = 1/M.dM/dV ' 3%/V at gain 50), to keep this contribution to the resolution at the level of per mille, the APDs require a very stable power supply system: the stability of the voltage has to be of the order of few tens of mV. A stability of 2.1 mV RMS, and below 10 mV for all channels, was recorded during CRAFT08 [4]. In the endcaps, Vacuum PhotoTriodes (VPTs) are used and operated at a gain of 10. The spread in response among the VPTs is 25% (RMS). They are therefore sorted into six groups which are distributed on the endcaps with the highest sensitivities at the outer circumference grading to the lowest sensitivities at the inner circumference. This arrangement provides a roughly constant sensitivity to the transverse energy across the endcaps.

31.2 Energy reconstruction

About 96.5% of the shower of an incident unconverted photon is contained in a matrix of 5 × 5 crystals in η × φ in Module 1 of the ECAL barrel. This fraction is measured in test beams with electrons, in the absence of tracker material in front of the crystals and in the absence of magnetic ﬁeld. In the experiment, electrons will emit Bremsstrahlung photons, and an important fraction of the photons will convert. Their energy will be spread in φ because of the magnetic ﬁeld. Hit crystals belonging to the same shower are grouped together in clusters and their energy is summed (superclustering). For this sum to be a precise measurement of the electron or photon energy at the primary vertex, a number of calibrations and energy corrections have to be performed:

• the uniformization of the response of the different crystals to a ﬁxed incident energy, or crystal-to-crystal intercalibration; • the corrections applied to the supercluster energy, for the non-uniform energy loss in η due to the quasi-pointing geometry of the crystals in the ECAL barrel and due to tracker material, for the non-uniformity due to intermodule cracks, and the small difference in containment dependent on the position of the particle impact point within a crystal. In spite of the very good linearity of the ECAL response, small residual dependences on ET due to material effects and rear leakage at very high energy are expected, which also have to be corrected for; • the scale determination, i.e. the global constant factor by which the energies of the corrected superclusters have to be multiplied in order to yield an accurate estimation of the particle energy at production vertex. After deﬁning the crystal intercalibration and the cluster energy corrections as described in section 31.2.2 this remaining factor should be zero.

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31 Electron and photon reconstruction in the CMS experiment at the LHC 235

31.2.1 Superclustering Superclustering algorithms are designed to collect in (super-)clusters a fraction as large and as stable as possible of the shower energy, in particular by recover- ing energy spread in φ due to secondary Bremsstrahlung emission and photon conversions in the material in front of the ECAL. On the other hand, they should also avoid collecting in the same (super-)cluster energy deposits due to different particles, and to minimize the effects of noise fluctuations. The CMS standard superclustering algorithms are: the Hybrid algorithm in the barrel region and the Multi5x5 algorithm for the endcaps (Refs. [2,5]). Local maxima (“seeds”) in energy deposit above some threshold are identified, to which neighboring cells are joint as long as they contain an energy deposit significantly higher than the noise (80 MeV in EB, 300 MeV in EE). Electromag- netic “clusters” are thus formed, which in turn can be associated into “superclusters”. For the Hybrid algorithm, a list of “seed” crystals with transverse energy above 1 GeV is first constructed. Starting from a seed crystal, a cluster is defined as an ensemble of φ-contiguous “dominos” which have collected an energy larger than 100 MeV. Each domino consists of 5 crystals with the same φ value, which corresponds to a domino width of 0.087 in η. Valleys, where less than 100 MeV are collected in a domino, separate different clusters. The dominos are then clustered in φ, each distinct cluster of dominos being requested to have a seed domino with energy greater than 0.35 GeV. The φ roads are allowed to extend up to ±10 crystals around the seed, which corresponds to ±0.174 rad. For the Multi5x5 algorithm, the ET threshold on seed crystals is 180 MeV. Clusters are formed as 5 × 5 matrices of crystals centred on the seed crystals; in case of overlaps the overlapping crystals are associated to the cluster with the largest seed ET . Clusters with an ET greater than 1 GeV are then eligible as seed clusters for the superclustering. Those clusters, the seed clusters of which are within ±0.3 radians in φ and within ±0.07 units in η from the seed crystal of the seed cluster, are grouped together. These algorithms thus differ slightly in the maximum φ extension for Bremss- trahlung recovery (±10 crystals = 0.174 rad for the Hybrid algorithm versus ±0.3 rad for the Multi5x5 algorithm), and more significantly in the maximum lateral (η) extension of (super-)clusters. For both algorithms, an energy threshold of 4 GeV is requested for a supercluster.

31.2.2 Intercalibration and energy corrections

The e/γ energy is computed as the sum of the calibrated signal amplitudes measured in the channels included in the supercluster, corrected as follows: X Ee/γ = f5x5(η) × fbrem × f(η, ET ) × GciAi cluster

where the Ai are the amplitudes measured in each crystal in ADC counts, ci are the crystal intercalibration constants, G deﬁnes the crystal scale in MeV/ADC

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count and f5x5(η), fbrem and f(η, ET ) are supercluster energy correction functions defined further in the text. The crystal scale factor G is defined such that, for P unconverted photons in test beam configuration, the cluster GciAi factor in a 5 × 5 crystal matrix in barrel Module 1 is equal to the unconverted photon energy at vertex. The intercalibration procedures aim at determining the ci coefficients. The largest sources of variations are due to the light yield difference between the crystals, and to the VPT gain variations. These variations are reduced by calibration with radioactive sources in the laboratory down to an initial dispersion of 5% for 1 barrel crystals [6] and 7.4% for the endcaps [4]. Then, 4 of the barrel supermodules have been exposed to test beams and intercalibrated to a precision of 0.3%. All the other barrel supermodules have been tested with cosmic rays, the light yield of minimum ionizing muons with quasi-normal incidence in the crystals allowing to intercalibrate them to 1.4%-2.2% [6]. Endcap supercrystals could not be intercalibrated with cosmic rays due to the time constraints of the CMS detector integration. In-situ intercalibration with collision data will be performed in several steps:

• using the symmetry of the energy deposits in φ at each η value. Decomposing the ECAL acceptance into η rings, a precision of 1-3% can be achieved with a few days of collision data [2]. The ultimate precision is limited due to the non-uniformity of the tracker material in φ; • selecting π0, η → γγ events and constraining the di-photon invariant mass to the know masses of tbe resonances also allows rapid intercalibration to 1% precision [2].

The f5x5(η) function is correcting for the leakage of energy due to crystal staggering in the barrel, which increases with η. This correction was measured in test beams and reproduced accurately with Monte Carlo simulations. It ranges from no correction at |η| = 0 to 0.7% at |η| = 1.4 [6] and is applied to all superclusters[6]. The Bremsstrahlung correction is parametrized for several ET bins as a function of the measured cluster width in the φ direction, σφ. The cluster width in φ is an estimation of the amount of energy radiated in the tracker material. This correction is estimated from Monte Carlo simulations. It is expected not to depend much on the precise modelling of the amount of tracker material and its distribution, since it is parametrized as a function of an observable that is correlated with the resulting energy loss (smaller σφ meaning less material or material concentrated at higher R, hence smaller energy loss energy). A determination of the residual electron energy correction f(η, ET ) will be performed by constraining the invariant mass of Z → e+e− events to the known Z boson mass. Due to the convolution of the energy resolution with the Breit- Wigner lineshape of the Z boson, the precision of the determination of the f(η) correction function will be about 1%. This determination will be combined with the correction derived from an independent measurement, the E/p ratio of non- radiating electrons from W → eν decays. For photons, the small difference in energy scale compared to electrons, due to the later development of the EM shower,

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31 Electron and photon reconstruction in the CMS experiment at the LHC 237

will at ﬁrst be corrected using Monte Carlo simulations, then will be measured using ﬁnal-state radiation photons in Z → µ+µ−γ. An integrated luminosity of order of 1 fb−1 is required for this measurement to be performed. The energy resolution obtained with barrel supermodules in test beams is shown in Fig. 31.2 for 120 GeV electrons, before and after all relevant corrections have been applied.

Fig. 31.2. Energy resolution measured Fig. 31.3. Electron reconstruction efﬁ- with barrel supermodules in a test beam ciency vs. |η| for a uniform pT distribution with 120 GeV electrons [1]. between 5 and 50 GeV/c [2].

31.3 Electron reconstruction

Electron candidates are formed by associating an ECAL supercluster to a track reconstructed in the tracker. Two complementary approaches have been developed. In the first approach, the track search is seeded by the supercluster in that the initial track segments formed with two hits in the pixel detector layers and/or inner silicon strip detector layers are considered only if they match the supercluster in η and φ and in pT , accounting for the track curvature expected from the supercluster ET and the four Tesla magnetic field. Both charge hypotheses are considered, and the electron is assumed to originate from the measured beam spot. This approach is well-suited for high-pT electrons (pT > 5 − 10 GeV), where the supercluster energy and position estimations are reliable and kinks due to Bremsstrahlung do not impair track reconstruction much [7,2]. The electron reconstruction efficiency of this approach is shown in Fig. 31.3. In the second approach, short track segments with as little as 3 hits reconstructed with the standard tracking algorithm are loosely matched to ECAL deposits in η, φ and ET . To reduce the number of charged pions faking electrons, a pre-identification is performed using a boosted decision tree. The input variables are the ECAL matching variables, preshower information in the endcaps,

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the number of hits along the trajectory, the track ﬁt χ2 and an estimation of the Bremsstrahlung energy loss from the difference in the track momentum estimated at the vertex and at the ECAL surface. This approach is well suited for electrons with pT < 5 − 10 GeV. The electron track ﬁt has to account for the higher average energy loss compared to minimum ionizing particles and by the non-Gaussian nature of the Bre- msstrahlung energy losses. To account for the latter, a Gaussian-Sum Filter (GSF) has been developed [8] allowing good estimation of the track momentum both at the vertex and at the ECAL surface. The electron energy is estimated as the average of the supercluster energy and the track momentum weighted by their respective errors, as described in [7]. The supercluster energy contribution dominates for ET > 20 GeV.

31.4 Electron selection

Jets have a high probability of faking electron candidates by having an electromagnetic energy deposit coincident with a charged particle track. Electron selection aims at purifying the sample of electron candidates, and is conceptually factorized in two aspects: • identification, performed on the basis of the measurements associated to the electron candidate (the ECAL cluster, the HCAL energy behind the ECAL cluster and the trajectory measured in the tracker). Identification is essentially independent of the event topology; • isolation, aiming at selecting isolated primary electrons by requiring little event activity surrounding them. A set of four robust identification variables have been identified, that are not affected by initial detector miscalibrations and misalignment and can be used at the start of data taking: the differences between the energy-weighted position in (η, φ) of the supercluster and the (η, φ) of the GSF track at the innermost point ex- trapolated to the ECAL, the ECAL shower width in the η direction (the direction which is not affected by Bremsstrahlung) and the ratio of the energy measured in the HCAL beyond the ECAL shower to the supercluster energy. The isolation variables consist of sums of transverse components of energy deposits in ECAL and HCAL and track pT within conical regions of ∆R < 0.4. The regions are centred on the supercluster position for the calorimetric isolation variables, and on the track direction at the vertex for the track isolation. In all three cases the possible track or energy footprint of the electron is removed by excluding an inner cone, and in the case of the ECAL sum also a narrow strip in the φ direction. The cuts applied on these variables can be optimized in an analysis-dependent way so as to achieve the required signal-to-background ratio. Measurements of the Z → e+e− and W → eν cross-sections will provide excellent benchmark channels to study the performance of electron reconstruction and selection at the start of data taking. About 4000 Z → e+e− and 40000 W → eν events are expected after 10 pb−1 of data at 10 TeV. The expected spectrum of di-electron events in the

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31 Electron and photon reconstruction in the CMS experiment at the LHC 239

+ − Z → e e analysis and the expected 6ET spectrum in the W → eν analysis are shown in Figs. 31.4 and 31.5 [9]. In these analyses, the electron selection and pT cut have been tuned so as to minimize the total cross-section uncertainty (statistical and systematic). In particular a tight selection has been designed that reduces the uncertainty on the W → eν cross-section due to jet background. The total reconstruction and selection efﬁciency corresponding to the selections used for the Z → e+e− analysis is 90% per electron in the ECAL ﬁducial volume (respectively 75% for the W → eν analysis) [9].

) -1 2 -1 CMS Preliminary , Ldt = 10 pb CMS Preliminary , ∫Ldt = 10 pb 2500 ∫

103 di-jets γ */Z → e+e- Signal+Bkgd tt 2000 W+jets γ * → τ τ 102 /Z γ+jets 1500 Events / 1.0 GeV

W → eν Events / ( 2 GeV/c 10 1000 Signal+Bkgd di-jets γ+jets γ */Z → e+e- 500 W → τ ν 1 t t

0 40 60 80 100 120 140 0 20 40 60 80 100 2 M + - (GeV/c ) e e ET (GeV)

Fig. 31.4. Invariant mass distribution of Fig. 31.5. 6ET distribution in the W → eν the pair of selected highest-pT electrons in analysis [9]. the Z → e+e− analysis [9].

31.5 Photon reconstruction and selection

The main issue in photon energy reconstruction consists in paying special attention to unconverted photons. Optimal energy resolution is expected for these photons, and their contribution to the visibility of the H → γγ channel is expected to be the largest thanks to the good resolution of the di-photon mass peak [10]. The energy of those photons is measured best using the calibrated energy contained in a 5 × 5 crystal matrix around the seed crystal, corrected for the lateral leakage correction f5x5(η) and for module border effects but otherwise uncorrected. Unconverted photons are identiﬁed by means of the R9 variable, the ratio of the energy contained in a 3 × 3 crystal matrix to the supercluster energy, which is smaller for unconverted photons. Photon selection and the rejection of jet background relies on shower shape variables and isolation [11,12]. To ease photon commissioning at the start of data taking (see section 31.6) it is advantageous to make use of variables that are ex-

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pected to have similar distributions for electrons and photons, which can be done by carefully choosing the electron track and energy footprint removal regions.

31.6 Commissioning of electron and photon reconstruction with data

An essential tool to commission electron reconstruction is the tag-and-probe method [13]. This method relies upon γ/Z → e+e− decays to provide an unbiased, high-purity, electron sample with which to measure the efficiency of a particular cut or trigger. Using events passing a single electron trigger, events which contain a well reconstructed electron (the tag) are selected. A second electron, the probe, is selected with criteria leaving it unbiassed with respect to the efficiency under study. Purity is ensured by requiring that the invariant mass of the tag and probe electrons is consistent with the mZ. The efficiency is estimated as the fraction of probes passing the selection criteria under study. A pure, unbiassed sample of photons will only be available after ∼ 1 fb−1 of data from final-state radiation events Z → l+l−γ. The photon selection efficiency can be measured in early data using the tag-and-probe method on γ/Z → e+e− events and applying photon selection criteria to the probe electron. The remaining small differences between electrons and photons can be corrected using Monte Carlo simulations [12].

31.7 Conclusion

After extensive crystal intercalibration measurements in laboratory and test beams, the CMS electromagnetic calorimeter has been completed with the installation of the endcap Dees in summer 2008 and the installation of the preshower in spring 2009. Intercalibration of frac14 of the barrel supermodules was performed in test beams to a precision of 0.3%, while the remaining supermodules have been intercalibrated to about 1.5% in cosmic rays. With extended periods of data taking with cosmic rays and at full magnetic ﬁeld performed in 2008, the commissioning of the CMS detector and especially of the ECAL proceeds well. The precision of the crystal intercalibration performed in laboratory was checked from the dE/dx of cosmic rays and with beam dump events. Although the precision of these methods is limited to 1-2% in the barrel and about 10% in the endcaps, the intercalibration was found to be consistent with laboratory measurements and intercalibration in cosmic rays [4]. The temperature and bias voltage stability have been found to match the design requirements. First system tests of the monitoring of the crystal transparency using laser light pulsing delivered encouraging results. Developments of electron and photon reconstruction and selection algorithms proceed on the basis of simulated data. Commissioning of electron and photon physics objects will rely heavily on the measurement of electroweak processes such as Z → e+e− events and W → eν.

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31 Electron and photon reconstruction in the CMS experiment at the LHC 241 References

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