Thesis Submitted to Mcgill University in Partial Fulﬁlment of the Requirements for the Degree of Master of Science

A BABAR sensitivity study on the search for the invisible decay of J/ψ in B± → K∗± J/ψ

Racha Cheaib

Physics Department Master of Science

McGill University,Montreal

September 9, 2011 A thesis submitted to McGill University in partial fulﬁlment of the requirements for the degree of Master of Science.

c Racha Cheaib, 2011

Acknowledgements

I am grateful to the BABAR collaboration, physicists and engineers, for the quality and precision of the BABAR detector and BABAR dataset. I would like to thank my supervisor, Steven Robertson, for his continuous help through all stages of this analysis. I also want to thank Dana Lindemann, Wissam Moussa, and other colleagues in the physics department for their valuable input. Also, special thanks to the Leptonic Analysis Working Group for their help and contribution.

ii Abstract

We present a sensitivity study on the search for J/ψ νν in B± K∗± → → J/ψ using data from the BABAR experiment at the SLAC National Accelerator Laboratory. The decay is highly suppressed in the Standard Model and thus is a possible window for new physics such as supersymmetry and dark matter. Hadronic tag reconstruction is employed for the analysis, where one B is fully reconstructed using hadronic decay modes. The remaining tracks and clusters are attributed to the signal B on which the B± K∗± J/ψ cut-based signal → selection is applied. The associated K∗ is allowed to decay via two modes, Mode 1: K∗± K0 π± and Mode 2: K∗± K± π0. The approach is to → S → reconstruct a K∗± candidate, the only signature in a signal event, and calculate the recoiling mass. The data is left blinded in the signal region and only a range of the branching fraction limits is calculated to determine the sensitivity. The result for Mode 1 is an upper limit, at the 90% conﬁdence level, on ( J/ψ B νν) of 9.13 10−2 using the Barlow method and 11.10 10−2 using the → × × Feldmann-Cousins method. The upper limit for Mode 2, also at the 90% CL, is estimated to be 2.49 10−2 and 2.98 10−2 using Barlow and Feldmann- × × Cousins respectively. The branching fractions thus yield a sensitivity of order 10−2. Although the result is not an improvement on the current J/ψ νν → limits, this method can be extended to other cc quarkonium modes and could further yield a much better result with data from the newly approved SuperB experiment, the extension of BABAR to higher luminosities.

iii Abr´eg´e

Nous présentons une étude de sensibilitésur la recherche de J/ψ νν → dans B± J/ψ K∗± en utilisant les donnéesde l’expérimentation BABAR du → Centre de l’accélérateur linéaire de Stanford. La radioactivitéest hautement suppriméedans le modèle standard et offre donc de nouvelles opportunités physiques telles que la supersymétrie et la matière noire. Une reconstruction hadronique fut employéepour l’analyse, oùun B fut totalement reconstruit en utilisant les modes de transformations hadroniques. Les pistes et regroupe- ments restants furent attribuésau signal de B sur laquelle une sélection de signal coupéeàla base fut appliquée. Le K∗ associéest capable de se trans- former en deux modes, Mode 1: K∗± K0 π± et Mode 2: K∗± K± π0. → S → L’approche est de reconstruire un candidat K∗, la seule signature d’un signal, et de calculer la masse de recul. La donnéeest invisible dans la région du signal et seulement un intervalle des embranchements fractionnaires est cal- culépour déterminer la sensibilité. Le résultat pour Mode 1 est une limite supérieure, avec un intervalle de confiance de 90%, sur (J/ψ νν) de 9.13 B → 10−2 en utilisant la méthode de Barlow et de 11.10 10−2en utilisant celle × × de Feldmann-Cousins. Le résultat pour Mode 2, aussi avec un intervalle de confiance de 90%, est calculéà2.49 10−2 et 2.98 10−2 en utilisant Barlow et × × Feldmann-Cousin respectivement. Les fractions d’embranchements ont donc une sensibilitéde l’ordre de 10−2. Bien que ce n’est pas une amélioration des limites actuelles de J/ψ νν, cette méthode peut être étendue àd’autres → modes quarkonium cc et pourrait aboutir àde meilleurs résultats avec les don- néesde SuperB, une nouvelle expérimentation amélioréede BABAR offrant un niveau de luminositéplus supérieur.

iv Contents

1 Introduction 1

2 Theory 3

2.1 The Standard Model ...... 4 2.1.1 Leptons and Quarks ...... 4 2.1.2 Gauge bosons ...... 5 2.1.3 The Higgs Boson ...... 7 2.2 Beyond the Standard Model ...... 8 2.2.1 Dark Matter ...... 10 2.3 J/ψ νν: Signiﬁcance and Motivation ...... 11 → 2.3.1 Related Studies ...... 14

3 SLAC and the BABAR Detector 16

3.1 PEP-II and SLAC linac ...... 16

3.2 The BABAR Detector ...... 17 3.2.1 The Silicon Vertex Tracker ...... 19 3.2.2 The Drift Chamber ...... 21 3.2.3 Detector of Internally Reﬂected Cherenkov Light . . . . 22 3.2.4 The Electromagnetic Calorimeter ...... 24 3.2.5 Instrumented Flux Return ...... 26 3.2.6 Trigger System ...... 28

v 4 Analysis Tools 30

4.1 Hadronic Reconstruction Method ...... 30 4.2 Ntuple Production ...... 31 4.3 Event Reconstruction ...... 32

4.4 BABAR Dataset ...... 34 4.5 Monte Carlo Background ...... 35 4.6 Signal Monte Carlo ...... 37 4.7 J/ψ → `+`− in B± → K∗± J/ψ Monte Carlo ...... 37

5 Background Analysis 39

5.1 Background Events ...... 39 5.2 BackgroundCuts ...... 41

5.2.1 Btag Cuts...... 41

5.2.2 mES Cut ...... 43 5.2.3 Continuum Likelihood Cut ...... 44

5.3 mES Sideband Substitution ...... 48

6 Signal Selection 52

6.1 Particle Identiﬁcation ...... 52

∗± 0 ± 0 + − 6.2 Mode 1: K → KS π ;KS → π π ...... 54 6.2.1 Track Multiplicity and Particle ID cut ...... 55

6.2.2 Eextra and cos θP miss ...... 56

0 6.2.3 KS reconstruction ...... 58 6.2.4 K∗ reconstruction ...... 59 6.3 Mode 2: K∗± → K± π0 ...... 61

6.3.1 Track Multiplicity, Particle ID and cos ΘP miss Cut . . . . 61 6.3.2 π0 reconstruction ...... 62

∗ 6.3.3 Eextra cut and K Reconstruction ...... 63

vi 6.4 Signal Selection Cross Check ...... 64 6.4.1 J/ψ → `+`− ...... 65

0 ∗ 6.4.2 D → K l ν` Study ...... 69

7 Eﬃciencies 72

8 Uncertainties 76

8.1 Btag Yield...... 77 8.2 Continuum Likelihood Suppression ...... 79 8.3 Track Multiplicity Cut ...... 80 8.4 ParticleID...... 81

8.5 cos ΘP miss Cut ...... 82

8.6 Eextra Cut...... 83 8.7 π0 reconstruction and π0 Mass Cut ...... 86

0 8.8 KS reconstruction and Mass Cut ...... 88 8.8.1 Summary of Systematic Errors...... 89

9 ( J/ψ νν) 91 B → 9.1 Expected Background Estimate ...... 92 9.1.1 Combinatorial Background Estimate ...... 92 9.1.2 Peaking Background Estimate ...... 94 9.2 Results and Limits ...... 94

10 Conclusion 99

11 Appendecies v

11.1 Likelihood Selector ...... v 11.2 Decision Tree Selector ...... vi 11.3 Performance of chosen PID selectors ...... vii

vii Chapter 1

Introduction

Over the past few decades, the Standard Model has become a widely accepted description of essentially all the particles observed to date and their interactions. It has gained popularity in both the theoretical and experimental segments of particle physics, mainly due to its predictive power and precision measurements. However, many particle physicists still believe that this model is not the complete story and a more fundamental theory awaits discovery. The aim of this thesis is to push forward the ongoing hunt for physics beyond the Standard Model. By measuring the branching fraction of J/ψ νν in B± → → K∗± J/ψ , the model’s known particle interactions are put to test. This is true since the invisible decay of J/ψ has a highly suppressed branching fraction and occurs only via one annihilation channel. Because the Standard Model rate is below our current sensitivity, any signal, if found, is a clear hint of new physics.

The BABAR experiment at SLAC National Accelerator Laboratory completed its last run at the Υ (4S) resonance, in 2008, reaching an integrated luminosity of 429 fb−1. More than 470 million B meson pairs were produced allowing for a branching fraction measurement of J/ψ νν. The aim of this analysis is → to determine the sensitivity of the BABAR dataset to this branching fraction

1 using Monte Carlo simulation. A hadronic tag reconstruction method is employed, where one B is reconstructed exclusively via hadronic modes in the decay Υ (4S) BB. The remaining tracks and clusters are then used to form → a K∗ candidate and evidence of an invisible decaying J/ψ is sought by computing the invariant mass at the system recoiling against the K∗. Before discussing the details of our analysis approach, chapter 2 of this thesis focuses on the Standard Model and its possible extensions. An overview of the

BABAR detector and the PEP-II storage ring is provided in chapter 3. Chapter 4 lists the analysis tools used, including data and Monte Carlo samples as well as the hadronic Btag reconstruction method. The background associated with this analysis is discussed in chapter 5. The signal selection is explained in detail in chapter 6, and the resulting eﬃciencies are listed in chapter 7. The systematic uncertainties associated with the signal selection are discussed in chapter 8, and the branching fraction calculation is outlined in chapter 9. The ﬁnal results and conclusions are stated in chapter 10.

2 Chapter 2

Theory

The Standard Model has been classiﬁed as one of the greatest achievements of modern day particle physics. It has successfully passed very precise tests and provided an elegant theoretical framework for all known elementary particles and their interactions (via 3 of the 4 known fundamental forces). The discovery of the top quark, tau neutrino, as well as the W ± and the Z0 bosons have proven the viability of this theory and its ability to explain observable phenomena. Nonetheless, the Standard Model could not answer questions about the baryonic asymmetry in the universe, the presence of dark matter, or the observation of neutrino oscillations and their nonzero mass. These suggest that this model is far from being complete and a more comprehensive theory is in order. Before discussing the motivation behind this analysis, an overview of the Stan- dard Model and its particle content is presented. Furthermore, a brief introduction of the most relevant extensions to the Standard Model is also included.

3 2.1 The Standard Model

The Standard Model is a model based on quantum field theory and the gauge symmetry SU(3)C SU(2)L U(1)Y . In any quantum field theory, the La- × × grangian defines the dynamics of the theory, while reflecting the internal symmetries of the system. The Standard Model Lagrangian can be divided into two components: SM = QCD + Electroweak. Here, the first part, quantum L L L chromodynamics, corresponds to the strong force and the symmetry group

SU(3)C . The second part represents the weak and electromagnetic forces and their associated symmetry group SU(2)L U(1)Y . The latter two forces are × said to be uniﬁed into the electroweak force, since the U(1)Y appears in the

SM as a subgroup of SU(2)L U(1)Y . × Each kind of particle in the Standard Model is described in terms of a dynamical field, while the forces are represented by gauge fields which act on the dynamical fields [1]. These are discussed in greater detail below.

2.1.1 Leptons and Quarks

The basic constituent of the Standard Model is a spin 1/2 fermion which obeys Fermi-Dirac statistics and the Pauli exclusion principle. There are 12 1 such fermions grouped into two categories, 6 quarks and 6 leptons, according to the forces with which they interact. The leptons are: the electron, e−, the muon, µ−, and the tau, τ −, with an electromagnetic (EM) charge of Q=-1 and their corresponding neutrinos: νe, νµ, and ντ , with an EM charge Q=0. On the other hand, the six ﬂavours of quarks are : u, d, c, s, b and t and carry a fractional charge of either Q= 2 or Q= 1 . The leptons and quarks are also grouped 3 − 3 into 3 generations with identical properties except for mass. Each member

1The sum does not include antiparticles which yield a total of 24 fermions in the SM.

4 of a generation has a greater mass than the previous one, and due to baryon number conservation, the ﬁrst generation charged particles are stable. Table 2.1 lists the particle content of the Standard Model and their associated charge.

Charge Generation 1 Generation 2 Generation 3 0 νe νµ ντ Leptons 1 e− µ− τ − 2 + 3 u c t Quarks 1 d s b − 3 Table 2.1: The quarks and leptons of the Standard Model.

Charged leptons interact via the weak and electromagnetic forces, whereas the neutrinos only interact via the weak force. In addition to EM charge, quarks also carry colour charge and hence interact via the strong interaction, along with the electromagnetic and weak interactions. Colour charge is a conserved quantum number, playing a role similar to that of the electric charge in electromagnetic interactions. Furthermore, while any lepton can be isolated singularly, quarks bind to one another in pairs or triplets.[2] This is due to a phenomenon called colour conﬁnement, where only colour neutral composite particles are allowed to exist. Thus, there are two possible types of hadrons: mesons, composed of quark and anti-quark pairs, or baryons, made up of three quarks or three antiquarks. The hadrons relevant to this analysis are listed in Table 2.2, along with their mass and quark content.

2.1.2 Gauge bosons

In the Standard Model, gauge bosons mediate interactions amongst the leptons and quarks. The number of gauge ﬁelds is equal to the number of generators of a speciﬁc symmetry group, and therefore there are 8+3+1 gauge bosons. These correspond to the eight gluons, gα = 1 ... 8 of SU(3)C , the three weak bosons,

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Flavour changing weak interactions only occur for left-handed particles or right-handed antiparticles. Furthermore, it was experimentally observed, in K± decays, that the weak force is CP violating, which implies that a particle

6 will not react the same way if interchanged with its antiparticle and its parity swapped. Initially, CP-violation in the weak sector could have been the answer to the baryonic asymmetry of the universe and how the universe is dominated by matter. However, it has been shown to be insuﬃcient to account for such a large discrepancy. On the other hand, the strong force does not appear to violate CP- a puzzling fact known as the strong CP problem. The Standard Model’s inability to account for the matter-antimatter imbalance and the absence of CP-violation in the strong sector is another driving force for a new model in particle physics.[1]

2.1.3 The Higgs Boson

The fact that the W ± and Z0 gauge bosons are not massless implies that

SU(2)L U(1)Y is not a symmetry of the vacuum. To become massive, the elec- × troweak symmetry associated with these gauge bosons must be spontaneously broken at an energy scale of 300 GeV. This is known as the Higgs Mechanism ≈ and occurs in the form: SU(3)C SU(2)L U(1)L SU(3)C U(1)(EM). The × × → × introduction of a new field, the Higgs field, with a non-zero expectation value induces the symmetry breaking and further predicts the presence of a new scalar, electrically neutral particle known as the Higgs Boson. The mass of all Standard Model fermions is shown to be an outcome of their interaction with the Higgs field[1]. However, even though there is much evidence of electroweak symmetry breaking, the Higgs boson has not been found yet. Table 2.3 lists all the bosons of the Standard Model and the forces which they mediate.2

2 + 0 0 The limit on the Higgs boson mass is obtained from the study of e e− H Z at the four LEP experiments: ALEPH[5], DELPHI[6], L3[7], and OPAL[8] →

7 Gauge Boson Mass ( GeV/c2) Spin Force γ < 1 10−27 1 electromagnetic × W ± 80.4 1 weak Z0 91.2 1 weak gluons 0 1 strong Scalar Boson Higgs > 114.4 at 95% C.L. 0 -

Table 2.3: List of Standard Model particles and their associated forces.[3]

2.2 Beyond the Standard Model

Even though all experimental observations in particle physics are consistent with the Standard Model, many questions remain unanswered. Over the years, theorists have developed various new models which account for these linger- ing issues and unexplained phenomena. However, many such models predict new physics observations at an energy scale which is way beyond our current experimental limits. Below, two extensions of the Standard Model, for which experimental veriﬁcation is possible in the near future, are discussed. Fur- thermore, an introduction to Dark Matter and how it relates to new physics searches is also presented.

SuperSymmetry and the Minimal Supersymmetric Standard Model

In the Standard Model, fermionic and bosonic ﬁelds separately obey anti- commutation and commutation relations respectively. Supersymmetry, known as SUSY, extends these commutator relations to include ones which directly relate a fermion to a boson. A supersymmetry transformation thus turns a fermionic state into a bosonic state and vice versa. The irreducible representa- tion of the supersymmetry algebra is a supermultiplet, containing both fermion and boson states.[9]

8 Particle Symbol Spin Superparticle Symbol Spin Quark q 1/2 Squark q˜ 0 Electron e 1/2 Selectron e˜ 0 Muon µ 1/2 Smuon µ˜ 0 Tauon τ − 1/2 Stauon τ˜− 0 W ± W 1 Wino W˜ 1/2 Z0 Z0 1 Zino Z˜ 1/2 Photon γ 1 Photino γ˜ 1/2 Gluon g 1 Gluino g˜ 1/2 Higgs H 0 Higgsino H˜ 1/2

Table 2.4: Particles of the Minimal Super Symmetric Model.[2]

The Minimal Supersymmetric Standard Model, MSSM, is an instance of supersymmetry where every known elementary particle is assigned a supersymmetric partner. In this model, the only additional particles are the superpartners of those in the Standard model. Thus, every spin 1/2 lepton or quark has a spin-0 superpartner, and every spin-1 boson has a spin 1/2 superpartner, as shown in Table 2.4. Even though associating a superpartner to each Standard Model particle is fairly straightforward, more than one Higgs superpartner is required, since the presence of only one Higgsino would lead to a gauge anomaly and thus an inconsistent theory. Evidence of MSSM can be found by producing these superparticles in the laboratory. However, the fact that such particles have not been detected already implies that they are much more massive than their Standard Model partners. Thus, supersymmetry is not an exact symmetry and is broken by introducing soft supersymmetry breaking operators into the MSSM lagrangian. R-parity is also introduced into the MSSM in order to explain the stability of the proton and its long lifetime. This symmetry acts on the MSSM ﬁelds in order to forbid all the renormalizable couplings of the theory that do not conserve lepton or baryon number.[2]

9 Left-Right Symmetry

Another extension of the Standard Model is the introduction of a new symmetry, called the “left-right” symmetry (LRS). Doing so, the violation of parity by the weak force is corrected. Furthermore, with this new symmetry, high energy W ±’ and Z0’ are introduced and couple with the right handed quarks and leptons. The group extension can be written as follows:

SU(3)C SU(2)L U(1)Y SU(3)C SU(2)L SU(2)R U(1)B−L (2.1) × × → × × × where B-L corresponds to the baryon number minus the lepton number. The left-right symmetry can be spontaneously broken at a certain energy, restoring the Standard Model.[10]

2.2.1 Dark Matter

The study of particle physics and the constituents of matter has wide implica- tions in the ﬁeld of cosmology. This is true since only modern day and future collider experiments could ever mimic the conditions of the early universe. Measurements of the mass of galaxies or clusters of galaxies and the mass of visible matter reveal a discrepancy, which could be corrected by introducing what is known as dark matter. Dark matter is non-luminous, gravitation- ally interacting matter that cannot be detected by electromagnetic radiation. Its presence can also be implied by measurements of galactic rotation curves, which were shown to be uniform even at large distances from the galactic bulge. According to Newtonian gravity, this should not be the case unless more than 50% of the mass of galaxies is contained in the relatively dark galactic halo. Other evidence for the presence of dark matter includes the dispersion of veloc- ities of galactic clusters, measurements of the Cosmic Microwave Background,

10 and the observation of X-ray emissions from the intra cluster medium.[11] There are many questions about the constituents of this dark matter. The most accepted theory at present is that dark matter consists of non-baryonic matter in the form of “weakly interacting massive particles” or WIMPS. Cur- rently, there are no known candidates for WIMPS and therefore new particles must be postulated. One possibility is the lightest superpartner in the MSSM, the neutralino, which is stable and interacts only via the weak interaction. The exact mass of this candidate is not known-only an upper bound of >40 GeV.3

2.3 J/ψ νν: Signiﬁcance and Motivation → Within the Standard Model, the invisible decay of J/ψ occurs only through one annihilation channel into three types of neutrino-antineutrino pairs, via a neutral Z boson shown in Fig 2.2. The associated branching fraction is (J/ψ νν) = 2.5 10−8 and the decay width is given by: B → ×

2 4 Γ(J/ψ νν) 27G MJ/ψ 8 2 −7 → = (1 sin θW ) = 4.54 10 (2.2) Γ(J/ψ e+e−) 256π2α2 − 3 × → where MJ/ψ is the mass of J/ψ , G and α are the Fermi and ﬁne structure constants respectively, and θW is the weak mixing angle[12]. The branching fraction of this decay mode is considered theoretically clean and thus provides a golden opportunity for new physics searches. Extensions to the Standard Model can enhance or suppress the value given above. For instance, in the case of spontaneously broken SUSY, J/ψ can decay into invisible goldstinos,g ˜, in addition to the neutrino channel. This would

3This is one upper limit on the lightest neutralino measured at OPAL. Other limits exist and range between >32.5 and >46 GeV.[3]

11 c ν

c ν

Figure 2.2: The invisible decay of J/ψ in the Standard Model.

occur via a virtual Z in the s-channel and the exchange of c -squarks in the t-channel, as shown in Fig 2.3. The corresponding rates for these decays are shown in equations (2.3) and (2.4) respectively[12]:

¯ 2 8 4 2 Γ(J/ψ g˜g˜) 9G MJ/ψ v cos 2β 8 2 → = (1 sin θW ) (2.3) Γ(J/ψ e+e−) 4096π2α2F 8 − 3 →

2 10 Γ(J/ψ g˜g˜¯) 9MJ/ψ mc → = (2.4) Γ(J/ψ e+e−) 32π2α2m˜ 4F 8 → c where mc(m ˜c) is the mass of the c-quark (squark), F is the SUSY-breaking

2 2 2 2 scale, v = v +v (174 GeV) and tan β = v2/v1.[12] Because the rates above 1 2 ≈ are inversely proportional to the SUSY-breaking scale, they are considered extremely small and thus far beyond our current experimental capabilities. Another contribution to Γ(J/ψ invis) is the presence of an additional → annihilation channel provided by an extra neutral Z’ gauge boson, which is typically introduced in left-right symmetric models. The extra Z’ boson con- tributes to the J/ψ width as follows[12]:

2 4 Γ(J/ψ νν) 27G MJ/ψ 8 2 2 2 → = (1 sin θW ) ∆ (2.5) Γ(J/ψ e+e−) 256π2α2 − 3 →

12 c g˜

c g˜

c g˜ c g˜

Figure 2.3: The invisible decay of J/ψ to a pair of goldstinos in SUSY: s-channel (left), t-channel (right).

4 2 2 sin θW MZ where ∆ = 1 (1 ) 2 (2.6) − − cos 2θW MZ0

As can be readily seen, the extra Z’ boson would cause a decrease in the invisible J/ψ decay width. In addition to possible extensions to the Standard Model, Γ(J/ψ invis) → can be increased considerably through dark matter couplings. This can only take place if the dark matter candidate is light with a mass range in the MeV scale. Even though most models suggest that the leading dark matter candi-

2 date is the lightest supersymmetric particle with a mass of Mχ > 10 GeV/c , it is by no means proven that this candidate cannot be less massive[13]. In fact, there exist several attractive models that can accommodate a light Dark Matter candidate and thus a light Higgs. The problem of having these as light candidates is related, since a light Dark Matter particle χ requires a new light particle U with MU 2Mχ to serve as the mediator in the s-channel ≈ annihilations of χ. Requiring a light mediator particle to account for the large annihilation cross section is the main reason nearly all the models which do not support light Dark Matter cannot do so.[13] Therefore, the limiting factor is the presence of this mediator and not the light Dark Matter candidate it-

13 self. One possible solution for this would be that the mediator particle U is a pseudoscalar Higgs, which would have a lighter mass due to the introduction of new symmetries. In this case, a light dark matter candidate is possible and can be detected in the invisible decays of any quarkonia state. Besides the theoretical arguments, there exists experimental hints that the Dark Matter candidate is potentially light. Recent observations of a 511 keV gamma ray line from the galactic bulge have been reported by the SPI spec- trometer at INTEGRAL (International Gamma Ray Astrophysics Lab). The corresponding positron ﬂux can be interpreted as resulting from the annihilation of light dark matter into electron positron pairs[14]. For this to be true, the dark matter candidate should be lighter than 100 MeV and its presence is predicted to considerably increase the invisible branching fraction of J/ψ [13] : (J/ψ χχ) 2.5 10−5 (2.7) B → ≈ ×

The prediction above is based on the assumption that the pair annihilation cross section of dark matter into SM quarks σ(χχ qq) is the same for → the time reversed reaction σ(qq χχ), where the former is estimated using → cosmological arguments.[13] In this analysis, the invisible branching fraction of J/ψ is examined in the rare decay B± K∗± J/ψ where K∗ decays via two possible modes: →

Mode 1: K∗± K0 π±, K0 π+ π− • → S S →

Mode 2: K∗± K± π0 • →

2.3.1 Related Studies

Invisible decays of heavy quarkonia, such as J/ψ , have recently become of interest to many collider experiments. The potential discovery of new physics or

14 a light dark matter candidate has driven the search for the invisible decay of Υ (1S) [15] [16], η , η0 [17], and most recently J/ψ [18]. Table 2.5 lists the different experiments involved and their corresponding results. Other quarkonium states, such as φ(ss), have not yet been studied by a specific experiment. Fur- thermore, even though the invisible decay of J/ψ has already been examined by BES, the decay mode considered here is totally different. The former measured the invisible branching fraction of J/ψ in ψ(2S) π+ π− J/ψ , whereas → here the search for J/ψ νν is done with J/ψ recoiling against the K∗ system → in B± K∗± J/ψ . This is the first attempt of this kind and it will be extended → to other resonances, such as Ψ(3770).

Colla- qq Decay Mode Results (90% CL) boration BES J/ψ ψ(2S) π+ π− J/ψ B(J/ψ →νν) = 1.2 10−2 → B(J/ψ →µ+µ−) × BELLE Υ (1S) Υ (3S) Υ (1S) π+ π− (Υ (1S) νν) < 2.5 10−3% → B B(η→ν→ν) × −3 BES η J/ψ φ η B(J/ψ →γγ) = 1.65 10 → 0 × BES η0 J/ψ φ η0 B(η →νν) = 6.69 10−2 → B(J/ψ →γγ) × CLEO Υ (1S) Υ (2S) Υ (1S) π+ π− (Υ (1S) νν) < 0.39% → B → Table 2.5: List of similar invisible searches.

15 Chapter 3

SLAC and the BABAR Detector

The BABAR experiment was designed to study CP violation effects in the decay of B mesons. The goal of the experiment also extended to making precision measurements of charm and bottom meson decays, as well as τ lepton decays. Furthermore, the high luminosity of the PEP-II storage ring also motivated searches for physics beyond the Standard Model. The experiment has finalized its data collection in April 2008 and 470.97 106 BB events have been recorded, × allowing for physics analyses of great interest. Below is a description of the different components of the BABAR experiment: accelerator and detector.

3.1 PEP-II and SLAC linac

The BABAR experiment collides an electron and positron beam using the SLAC linac and the PEP-II storage rings, shown in Fig 3.1. The SLAC linac acceler- ates the electron and positron beams to the required energies and then injects them into the PEP-II storage ring. The electron and positron beams then col- lide in the storage ring at an energy of 9.0 GeV and 3.1 GeV respectively. The energy diﬀerence between both beams is why the PEP-II ring is an asymmetric collider. It is designed to operate at a luminosity of 3 1033 cm2 s−1 and a ×

16 centre of mass energy around 10.58 GeV. This corresponds to the mass of the Υ (4S) resonance, which decays almost exclusively into B0B0 or B+B− pairs. The daughter B mesons are produced approximately at rest and decay almost instantly. The asymmetry in the beam energies allows each B to travel a small distance before it decays and thus full reconstruction of its decay vertex is possible. This way the decay time of each meson can be determined allowing for accurate measurements of time-dependent CP violation.[19]

Figure 3.1: A schematic diagram of the SLAC linac and the PEP-II storage ring.

3.2 The BABAR Detector

The BABAR detector is built asymmetrically around the PEP-II interaction region. It is displaced 0.37 m relative to the beam-beam interaction point, in order to maximize the detector’s acceptance in the boosted Υ (4S) frame. With the very small branching fraction of B mesons into CP eigenstates ( 10−4), ≈ a high level of precision is required from the detector. Thus, a set of challeng- ing requirements must be placed to ensure such a high performance. These include a very good reconstruction eﬃciency for tracks (p>60 MeV/c) and photons (E>20 MeV), excellent vertex resolution (< 60µm) as well as energy

17 and angular resolution, efficient and accurate e, µ identification, a sufficient kaon-pion separation (> 3σ), and a light composition to minimize scattering of charged particles.

The inner components of the BABAR detector are: silicon vertex tracker (SVT), drift chamber (DCH), detector of internally reflected Cherenkov light (DIRC), and the electromagnetic calorimeter (EMC). These are surrounded by a superconducting solenoid , which is designed for a magnetic field of magnitude 1.5 T. In addition, an instrumented flux return (IFR) surrounds the magnet and allows for the detection of muons and neutral hadrons. A schematic diagram of the longitudinal cross section of the detector is shown in Fig 3.2. The detector’s end view is displayed in Fig 3.3.[19] 2

Detector C L Instrumented Flux Return (IFR)) 0 Scale 4m I.P. Barrel Superconducting BABAR Coordinate System Coil y 1015 1749 x Electromagnetic Cryogenic 1149 4050 1149 Calorimeter (EMC) z Chimney 370 Drift Chamber (DCH) Cherenkov Detector Silicon Vertex (DIRC) Tracker (SVT)

IFR Magnetic Shield 1225 Endcap for DIRC Forward 3045 End Plug Bucking Coil 1375 Support Tube 810 e– e+

Q4 Q2

Q1 3500 B1

Floor 3-2001 8583A50

Figure 1. BABAR detector longitudinal section.

Figure 3.2:excellent The energyB andA angularBAR resolutiondetector: for B longitudinalflavor-tagging, and for the reconstruction cross section. • the detection of photons from π0and η0 de- of exclusive states; modes such as B0 0 + → cays, and from radiative decays in the range K±π∓ or B π π−,aswellasincharm from 20 MeV to 4 GeV; meson and τ decays;→ aflexible,redundant,andselectivetrigger very good vertex resolution, both transverse • • and parallel to the beam direction; system; low-noise electronics and a reliable, high efficient electron and muon identification, • bandwidth data-acquisition and control sys- • with low misidentification probablities for tem; hadrons. This feature is crucial for tagging the B flavor, for the reconstruction of char- detailed monitoring and automated calibra- monium states, and is also important for • tion; the study of decays involving leptons; an online computing and network system efficient and accurate identification of • that can control, process, and store the ex- • hadrons over a wide range of momenta for pected high volume of data; and

18 Figure 3.3: The end view of the BABAR detector.3

0Scale 4m IFR Barrel BABAR Coordinate System y Cutaway Superconducting Section x Coil z DIRC

EMC DCH

SVT IFR Cylindrical RPCs Corner Plates

Earthquake Tie-down Gap Filler Plates

3500 Earthquake Isolator

Floor 3-2001 8583A51

Figure 2. BABAR detector end view.

detector components that can tolerate sig- and operation of the detector. Finally, a detailed • nificant radiation doses and operate reliably presentation of the design, construction, and per- under high-background conditions. formance of all BABAR detector systems is pro- 3.2.1 The Silicon Vertex Trackervided. To reach the desired sensitivity for the most in- 8 teresting measurements, data sets of order 10 B 2. Detector Overview mesons will be needed. For the peak cross section at the Υ (4S)ofabout1.1nb,thiswillrequirean The BABAR detector was designed and built by 1 integrated luminosity of order 100 fb− or three alargeinternationalteamofscientistsanden- The silicon vertexyears trackerof reliable and highly ispositioned efficient operation of closestgineers. Details to ofthe its original interaction design are docu- region, within adetectorwithstate-of-theartcapabilities. mented in the Technical Design Report [3], issued In the following, a brief overview of the princi- in 1995. the BABAR supportpal components tube- of the a detector, cylindrical the trigger, the structureFigure 1 shows a with longitudinal a section 20 through cm radius designed data-acquisition, and the online computing and the detector center, and Figure 2 shows an end control system is given. This overview is followed view with the principal dimensions. The detector by brief descriptions of the PEP-II interaction re- surrounds the PEP-II interaction region. To max- to support the beamgion, the beam pipe. characteristics, The and of the main impact purposeimize the geometric of acceptance theSVT for the boosted is to measure the of the beam generated background on the design Υ (4S)decays,thewholedetectorisoffset rela- position and angle of charged tracks, thus allowing for precise reconstruction of their trajectories and decay vertices. Its mean resolution for a B decay vertex should be 80 µm to avoid any significant impact on the CP asymmetry ≈ measurements. Furthermore, because some B daughters have low pt, the SVT must provide stand alone tracking for particles with a transverse momentum less than 120 MeV/c. The SVT is composed of 5 cylindrical layers of double-sided silicon strip detectors, which are assembled in modules with readout at each end. To achieve the desired precision, the three inner layers must have a spatial resolution of 10-15 µm for perpendicular tracks, while the resolution of the outer two layers must be 40 µm. The former are located as close as 3.2 cm away from the inter- ≈ action point and are required for impact parameter measurements. The latter are located up to 14.0 cm away and are crucial for pattern recognition and low

19 pt tracking, as well as linking SVT and drift chamber tracks. A schematic of the SVT longitudinal section is shown in Fig 3.4.[19] 25

580 mm Space Frame

Bkwd. support cone 520 mrad Fwd. support350 mrad cone e- Front end e + electronics

Beam Pipe

Figure 17. Schematic view of SVT: longitudinal section. The roman numerals label the six different types Figureof sensors. 3.4: Longitudinal view of the SVT, where the roman numerals stand for the different types of silicon detectors. layers are straight, while the modules of layers 4 To satisfy the different geometrical require- and 5 are arch-shaped (Figures 17 and 18). ments of the five SVT layers, five different sen- This arch design was chosen to minimize the sor shapes are required to assemble the planar amount of silicon required to cover the solid angle, sections of the layers. The smallest detectors whileCharged increasing tracks the crossing traversing angle for the particles silicon stripsare 43 deposit42 mm2 ( energy,z φ), andthus the providing largest are near the edges of acceptance. A photograph of 68 53× mm2.Twoidenticaltrapezoidalsensors× informationan outer layer arch about module their is shown position in Figure and 19. momenta.are× added The (one strips each at have the forward two different and back- The modules are divided electrically into two half- ward ends) to form the arch modules. The half- modules, which are read out at the ends. modules are given mechanical stiffness by means orientations, the φ measuring strips orientedof two parallel carbon fiber/kevlar to the beam ribs, which axis are and visible the Beam Pipe 27.8mm radius in Figure 19. The φ strips of sensors in the same z measuring strips which are directed transverselyhalf-module to are the electrically beam connected axis. These with wire are Layer 5a bonds to form a single readout strip. This results placed orthogonal to one anotherLayer on5b eachin side a total of stripthe length sensor. up to Additionally, 140 mm (240 mm) the in the inner (outer) layers. Layer 4b The signals from the z strips are brought to the modules in the first 3 layers of the SVT arereadout straight electronics whereas using those fanout circuits in the consist- outer Layer 4a ing of conducting traces on a thin (50 µm) insu- 2 layers are arch-shaped, as shown in Fig 3.5.lating The Upilex arch [33] shape substrate. is used For the to innermost reduce three layers, each z strip is connected to its own the amount of silicon required to cover thepreamplifier solid angle channel, while while inmaximizing layers 4 and 5 the the Layer 3 number of z strips on a half-module exceeds the Layer 2 number of electronics channels available, requir- crossing angle for particles near the edge ofing acceptance. that two z strips Moreover, on different the sensors modules be elec- Layer 1 trically connected (ganged) to a single electronics are divided into two halves electronically, withchannel. the Theφ lengthsensors of a connectedz strip is about by 50 wire mm (no ganging) or 100 mm (two strips connected). bonds to form a single readout strip. On theThe other ganging hand, introduces the anz ambiguitystrips in on layers the z Figure 18. Schematic view of SVT: tranverse sec- coordinate measurement, which must be resolved 1tion. to 3 are connected to their own preamplifierby the channels pattern recognition each, while algorithms. in layers The to- 4 and 5 every two z strips are connected to a single electronics channel. Overall, there are a total of 150,000 read-out channels in the SVT. ∼

20 25

580 mm Space Frame

Bkwd. support cone 520 mrad Fwd. support350 mrad cone e- Front end e + electronics

Beam Pipe

Figure 17. Schematic view of SVT: longitudinal section. The roman numerals label the six diﬀerent types of sensors.

layers are straight, while the modules of layers 4 To satisfy the different geometrical require- and 5 are arch-shaped (Figures 17 and 18). ments of the five SVT layers, five different sen- This arch design was chosen to minimize the sor shapes are required to assemble the planar amount of silicon required to cover the solid angle, sections of the layers. The smallest detectors while increasing the crossing angle for particles are 43 42 mm2 (z φ), and the largest are near the edges of acceptance. A photograph of 68 53× mm2.Twoidenticaltrapezoidalsensors× an outer layer arch module is shown in Figure 19. are× added (one each at the forward and back- The modules are divided electrically into two half- ward ends) to form the arch modules. The half- modules, which are read out at the ends. modules are given mechanical stiffness by means of two carbon fiber/kevlar ribs, which are visible Beam Pipe 27.8mm radius in Figure 19. The φ strips of sensors in the same half-module are electrically connected with wire Layer 5a bonds to form a single readout strip. This results Layer 5b in a total strip length up to 140 mm (240 mm) in the inner (outer) layers. Layer 4b The signals from the z strips are brought to the readout electronics using fanout circuits consist- Layer 4a ing of conducting traces on a thin (50 µm) insulating Upilex [33] substrate. For the innermost three layers, each z strip is connected to its own preamplifier channel, while in layers 4 and 5 the Layer 3 number of z strips on a half-module exceeds the Layer 2 number of electronics channels available, requiring that two z strips on different sensors be elec- Layer 1 trically connected (ganged) to a single electronics channel. The length of a z strip is about 50 mm (no ganging) or 100 mm (two strips connected). The ganging introduces an ambiguity on the z Figure 18. Schematic view of SVT: tranverse sec- coordinate measurement, which must be resolved by the pattern recognition algorithms. The to- Figure 3.5: The differenttion. layers of the silicon vertex tracker.

3.2.2 The Drift Chamber

The main goal of the drift chamber (DCH) is to provide high precision measurements of track momenta and their angles. It complements the measurements of the SVT and provides particle identification by determining the ionization loss, dE/dx, of charged particles. For π/K separation up to 700 MeV/c2, the required resolution for dE/dx measurements should be 7%. Furthermore, ∼ 0 tracks outside the volume of the SVT, such as KS ’s, rely solely on the drift chamber for the reconstruction of their decay and interaction vertices. There- fore, the DCH must be able to measure their longitudinal position with a resolution of 1 mm. Also, in order to reduce multiple scattering, material in ∼ front of and inside the volume of the DCH should be minimized. This is why a helium gas mixture (80% helium and 20% isobutane) along with low mass aluminum wires are used. The main component of a drift chamber is a gas-filled volume containing field wires, used to maintain an electric field, and sense wires, used to detect ionization electrons. Charged tracks passing through the DCH will ionize the gas, producing free electrons that will drift towards the detection wires. In

BABAR, the drift chamber is a cylindrical structure surrounding the silicon ver-

21 tex tracker, with its centre oﬀset by 370 mm from the interaction point. It is made up of 40 layers of small hexagonal cells, which allow for 40 position and dE/dx measurements for tracks with a pt greater than 180 MeV/c. Fur- thermore, wires are placed in 24 of the 40 layers at small angles to the z-axis to provide longitudinal position information. The DCH has a relatively small radius (0.8 m), but it is about 3 m long. Its inner cylindrical wall is kept thin to allow for track matching with the SVT and to reduce the background from photon interactions. The rear end plate is almost twice the thickness and all the read-out electronics are mounted on it. Fig 3.6 shows a schematic diagram of the drift chamber’s longitudinal cross-section.[19] 36

630 1015 1749 68

Elec– tronics 809

485 27.4 1358 Be 17.2 236 e– 464 IP e+ 469

1-2001 8583A13

Figure 28. Longitudinal section of the DCH with principal dimensions; the chamber center is oﬀset by 370 mm fromFigure the interaction 3.6: The point longitudinal(IP). cross section of the DCH.

also eliminates the need for a massive, heavily end, this thickness is reduced to 12 mm beyond shielded cable plant. aradiusof46.9cmtominimizethematerialin Alongitudinalcrosssectionanddimensionsof front of the calorimeter endcap. For this thick- the DCH are shown in Figure 28. The DCH is ness, the estimated safety margin on the plastic bounded radially by the support tube at its in- yield point for endplate material (6061T651 alu- 3.2.3ner radius Detector and the DIRC at of its outer Internally radius. The Reflectedminum) is not more Cherenkov than a factor of two. Light The device is asymmetrically located with respect to maximum total deflection of the endplates under the IP. The forward length of 1749mm is chosen loading is small, about 2 mm or 28% of the 7 mm so that particles emitted at polar angles of 17.2◦ wire elongation under tension. During installa- Thetraverse DIRC, at least detector half of the of layers internally of the chamber reflectedtion of Cherenkov the wires, this small light, deflection is designed was taken to before exiting through the front endplate. In the into account by over-tensioning the wires. providebackwardπ/K direction,separation the length of of 10154 mmσ within means the momentumThe inner and outer range cylinder 500 cylindrical MeV/c wallsto 4.5 that particles with polar angles∼ down to 152.6◦ are load bearing to reduce the maximum stress traverse at least half of the layers. This choice en- and deflections of the endplates. The stepped GeV/csures. It suffi servescient coverage as a for particle forward-going identification tracks, forward system endplate with created a fast a complication signal response during and thus avoids significant degradation of the in- the assembly, because the thinner forward end- and avariant tolerance mass resolution, to high while backgrounds. at the same time Theplate DIRC would deflect consists more ofthan 4.9 the mthicker long back- bars, maintaining a good safety margin on the electri- ward endplate. The outside rim of the forward cal stability of the chamber. The DCH extends endplate had to be pre-loaded, i.e., displaced by madebeyond of synthetic the endplate fused by 485 mm silica at the with backward a rectangular2.17 mm in cross the forward section direction, of to 1.7 maintain4.3 the cm. end to accommodate the readout electronics, ca- inside and outside rims of the rear endplate× at the bles, and an rf shield. It extends beyond the for- same longitudinal position after the load of the Silicaward is chosenendplate by because 68mm to provide of its space large for wire index ofwires refraction, was transfered low from attenuationthe stringing fixture length, to feed-throughs and an rf shield. the outer cylinder. resistance to ionizing radiation, and its lowPrior chromatic to installation dispersion on the inner cylinder, within the the 6.2.2. Structural Components two endplates were inspected on a coordinate- Details of the DCH mechanical design are pre- measuring machine. All sense wire holes, as well sented in Figure 29. The endplates, which carry 22 as 5% of the field and clearing field wire holes, an axial load of 31,800 kN, are made from alu- were measured to determine their absolute loca- minum plates of 24mm thickness. At the forward tions. The achieved accuracy of the hole place- DIRC’s wavelength acceptance. The bars are arranged into 12 hermetically sealed containers called bar boxes. Each bar box contains 12 bars, and thus there are a total of 144 bars in the DIRC. A fused silica wedge is also glued to the end of each bar for readout. The bar boxes are supported by a thin, double-walled, aluminum tube, the Central Support tube. In addition, a steel cylinder, called the Strong Support tube, is located inside the ends of the IFR and used to provide mechanical support for the entire DIRC. Fig 3.7 displays a diagram of the DIRC and its support structure.[19]

Figure 49. Exploded view of the DIRC mechani- Figure 52. Transverse section of the nominal Figure 3.7: An overviewcal support of the structure. DIRC, The its steel main magnetic components shield andDIRC support bar box imbedded struc- in the CST. All dimen- is not shown. sions are given in mm. ture. fused silica, thus minimizing the total internal reflection at silica-water interface. Furthermore, its chromaticity index is a close match to that of fused silica, effectively eliminating dispersion at Cherenkov light is produced by charged particles traversingthe silica-water the silica interface. bars. The steel gusset supports the standoff box. A steel shield, supple- These photons will be transmitted, by total internal reflection,mented to by one a bucking or both coil,surroundsthestandoff box to reduce the field in the PMT region to below 1 Gauss [28]. ends of the bar, depending on the particle’s incident angle. AThe mirror PMTs is at placedthe rear of the standoff box lie on a surface that is approximately toroidal. Each at the front end of each bar to reflect incident photons to theof the backward 12 PMT sectors end, contains 896 PMTs (ETL model 9125 [61,62]) with 29 mm-diameter, in a closely packed array inside the water volume. A where a detection apparatusFigure 50. Schematics is setup. of thePhotons DIRC bar arriving box as- atdouble the backward o-ring water end seal is made between the sembly. PMTs and the wall of the standoff box. The are reflected at large angles to the bar axis due to the presencePMTs are of installed the silica from the inside of the standoff Tube (CST), attached to the SST via an alu- box and connected via a feed-through to a base wedge and emerge intominum a transition water-filled flange. expansion The CST is regiona thin, knownmounted as outside. the stand- The hexagonal light catcher double-walled, cylindrical shell, using aircraft- cone is mounted in front of the photocathode of type construction with stressed aluminum skins each PMT, which results in an effective active sur- off box. The stand-offand boxbulkheads is composed having riveted of or glued a stainless-steel joints. The face cone area and light cylinder collection fraction of about 90%. CST also provides the support for the DCH. The geometry of the DIRC is shown in Figures 51 along with 12 sectors ofThe photomultiplier standoff box is made tubes of stainless (PMT’s). steel, Eachand 52.of these sectors consisting of a cone, cylinder, and 12 sectors of The DIRC occupies 80 mm of radial space in PMTs. It contains about 6,000 liters of purified the central detector volume including supports water. Water is used to fill this region because and construction tolerances, with a total of about it is inexpensive and has23 an average index of re- 17% radiation length thickness at normal inci- fraction (n 1.346) reasonably close to that of dence. The radiator bars subtend a solid angle ≈ corresponding to about 94% of the azimuth and consists of 896 PMT’s which lie on an almost toroidal surface. The reflected photons are detected by these densely packed PMT’s, located a distance of 1.2 m from the bar end. The expected Cherenkov light pattern is a cone section, with the opening angle being the Cherenkov production angle. It is reconstructed from the position and time of arrival of the photons at the PMTs. Using this Cherenkov angle, the velocity of a charged track can be determined. Combining this with the momentum measurements of the tracking system, the mass of a particle can be calculated revealing its identity. The signal- carrying components of the DIRC and their associated geometry are shown in Fig 3.8.[19] 52

PMT + Base 10,752 PMT's asymmetry, particles are produced preferentially forward in the detector. To minimize interfer-

Standoff ence with other detector systems in the forward Purified Water Light Catcher Box region, the DIRC photon detector is placed at the

17.25 mm Thickness backward end. (35.00 mm Width) Bar Box The principal components of the DIRC are Track shown schematically in Figure 49. The bars PMT Surface Trajectory Wedge are placed into 12 hermetically sealed containers, Mirror called bar boxes,madeofverythinaluminum- Bar Window hexcel panels. Each bar box, shown in Figure 50,

4.9 m 1.17 m contains 12 bars, for a total of 144 bars. Within 4 x 1.225m Bars abarboxthe12barsareopticallyisolatedbya { glued end-to-end { 8-2000 150µm air gap between neighboring bars, en- 8524A6 forced∼ by custom shims made from aluminum foil. The bars are 17 mm-thick, 35 mm-wide, and 4.9 Figure 3.8: Signal propagationFigure 48. Schematics in the of the DIRC: DIRC fusedsilica silica bar andm-long. stand-off Each bar box. is assembled from four 1.225 m radiator bar and imaging region. Not shown is a pieces that are glued end-to-end; this length is the 6mradangleonthebottomsurfaceofthewedge longest high-quality bar currently obtainable [58, (see text). 60]. The bars are supported at 600 mm intervals by angle is the Cherenkov production angle modi- small nylon buttons for optical isolation from the fied by refraction at the exit from the fused silica bar box. Each bar has a fused silica wedge glued 3.2.4 The Electromagneticwindow. Calorimeter to it at the readout end. The wedge, made of the The DIRC is intrinsically a three-dimensional same material as the bar, is 91 mm-long with very imaging device, using the position and arrival nearly the same width as the bars (33 mm) and a time of the PMT signals. Photons generated in trapezoidal profile (27 mm-high at bar end, and The purpose of the electromagneticabararefocusedontothephototubedetection calorimeter is to measure79 mm the at theenergy light exit and end). The bottom of the surface via a “pinhole” defined by the exit aper- wedge (see Figure 48) has a slight ( 6mrad)up- ∼ position of electromagneticture of the showers bar. In order generated to associate by the charged photon particlesward slope or to photons. minimize the displacement of the signals with a track traversing a bar, the vector downward reflected image due to the finite bar pointing from the center of the bar end to the thickness. The twelve wedges in a bar box are It covers an energy rangecenter from of each 20 PMT MeV is taken to as 9 a measure GeV, thus of the allowingglued to the a common detection 10 mm-thick fused silica win- photon propagation angles αx, αy,andαz.Since dow, that provides the interface and seal to the of low energy π0’s andtheη track’s and position high and energy angles are electrons known from and the photons.purified water The in formerthe standoff box. tracking system, the three α angles can be used The mechanical support of the DIRC, shown to determine the two Cherenkov angles θc and φc. in Figure 49, is cantilevered from the steel of are abundant in rare decaysIn addition, of theB arrivaland timeD mesons, of the signal whereas provides thethe latter IFR. The contributeStrong Support Tube (SST) is a an independent measurement of the propagation steel cylinder located inside the end doors of the to the flavour taggingof of theB photon,mesons and can in be semi-leptonic related to the propaga- decays andIFR and measurements provides the basic support for the entire tion angles α.Thisover-constraintontheangles DIRC. In turn, the SST is supported by a steel and the signal timing are particularly useful in support gusset that fixes it to the barrel magnet of QED processes. Todealing allow with ambiguities for such in studies, the signal association an energysteel. resolution It also minimizes of 1 the magnetic flux gap (see Section 8.6.1) and high background rates. caused by the DIRC∼ bars extending through the flux return, and supports the axial load of the in- 8.3. Mechanical Design24 ner magnetic plug surrounding the beam in this and Physical Description region. The DIRC bars are arranged in a 12-sided The bar boxes are supported in the active re- polygonal barrel. Because of the beam energy gion by an aluminum tube, the Central Support to 2 % is required along with an angular resolution of a few mrad. Such a resolution requires stable operating conditions along with frequent calibration of the electronics and energy response.

2359

1555 2295 External Support

1375 1127 1801 26.8˚ 920

38.2˚ 558 15.8˚ 22.7˚

Interaction Point 1-2001 1979 8572A03 Figure 61. A longitudinal cross section of the EMC (only the top half is shown) indicating the arrangement of the 56 crystal rings. The detector is axially symmetric around the z-axis. All dimensions are given in Figuremm. 3.9: Longitudinal cross section of the electromagnetic calorimeter.

Table 12 9.2.2. Crystal Fabrication and Assembly Layout of the EMC, composed of 56 axially sym- The crystals were grown in boules from a melt metric rings, each consisting of CsI crystals of of CsI salt doped with 0.1% thallium [73]. They Theidentical EMC dimensions. consists of an array of thalliumwere cut from doped the boules, cesium machined iodide(CsI(Tl)) into tapered trapezoids (Figure 62) to a tolerance of 150 µm, θ Interval Length # Crystals and then polished [74]. The transverse± dimen- crystals,(radians) arranged (X into)Rings/Ring modules. Thallium-doped CsI was chosen because of 0 sions of the crystals for each of the 56 rings vary to Barrel achieve the required hermetic coverage. The typi- 2 its high2.456 light1.214 yield 16.0 (50,000 27γ/ MeV),120 smallcal area Molière of the front radius face is 4.7 (3.84.7cm cm),whilethe and other − back face area is typically 6.1 ×6.0cm2.Thecrys- 1.213 0.902 16.5 7 120 × properties0.901 − which0.655 17.0 allow for7 excellent 120 energytals act not and only as angular a total-absorption resolution, scintillating as well 0.654 − 0.473 17.5 7 120 medium, but also as a light guide to collect light − at the photodiodes that are mounted on the rear as shower containmentEndcap within a compactsurface. design. At the polished The crystalEMC surface consists light is of two 0.469 0.398 17.5 3 120 internally reflected, and a small fraction is trans- 0.397 − 0.327 17.5 3 100 mitted. The transmitted light is recovered in part sections:0.326 a− 0 barrel.301 17.5 and a 1 forward 80 end-cap,by wrapping thus the covering crystal with twoa polar layers of diangleffuse from 0.300 − 0.277 16.5 1 80 white reflector [75,76], each 165 µmthick.The ◦ − ◦ uniformity of light yield along the wrapped crys- 15.8 to 141.8 and the full azimuthal angle.tal was measured There byare recording 5,760 the signal crystals from a in the highly collimated radioactive source at 20 points The SVT support structure and electronics, as along the length of the crystal. The light yield barrelwell structure, as the B1 dipole shadowarranged the inner in three 48 rings distinct rings whereas the end-cap carries was required to be uniform to within 2% in the of the endcap, resulting in up to 3.0X for the 0 front half of the crystal; the limit increased± lin- innermost ring. The principal purpose of the two early up to a maximum of 5% at the rear face. 820 crystalsinnermost rings in is to8 enhance such shower rings. containment A longitudinal cross section of the EMC and Adjustments were made on± individual crystals to for particles close to the acceptance limit. the layout of these rings is shown in Figmeet 3.9. these Furthermore,criteria by selectively roughingthe crystals or pol- have a tapered trapezoidal structure, with their length increasing in the forward direction in order to prevent leakage from increasingly high energy particles. They are inserted into trapezoidal modules, which are bonded to an aluminum strong back mounted to the external support. Supporting the modules from the back helps reduce the amount of material in front of and at the centre of

25 the calorimeter. Each crystal is readout individually, using a pair of silicon PIN diodes. These are in turn connected to a preampliﬁer each. In addition, access ports for digitizing electronics crates are placed on each annular edge of the aluminum support cylinder along with their cooling channels. Fig 3.10 displays the barrel structure of the EMC and the arrangement of the modules and readout electronics. 66

Detail of Module Detail of Mini–Crate

Bulkhead Mounting Features Fan Out Board

Cableway

Cooling Channels ADBs IOB Aluminum Cu Heat Sink Carbon Strongback Fiber Tubes

0.9 m Electronic 0.48 m Aluminum Mini–Crates 4 m RF Shield Aluminum Support Cylinder 3-2001 8572A06 Figure 63. The EMC barrel support structure, with details on the modules and electronics crates (not to scale). Figure 3.10: The EMC barrel structure, the inserted modules, and the readout electronics. thus assures that the forces on the crystal sur- Each module was installed into the 2.5 cm-thick, faces never exceed its own weight. Each module 4m-longaluminumsupportcylinder,andsubse- is surrounded by an additional layer of 300 µm quently aligned. On each of the thick annular CFC to provide additional strength. The mod- end-flanges this cylinder contains access ports for ules are bonded to an aluminum strong-back that digitizing electronics crates with associated cool- is mounted on the external support. This scheme ing channels, as well as mounting features and minimizes inter-crystal materials while exerting alignment dowels for the forward endcap. minimal force on the crystal surfaces; this pre- The endcap is constructed from 20 identical vents deformations and surface degradation that CFC modules (each with 41 crystals), individu- could compromise performance. By supporting ally aligned and bolted to one of two semi-circular the modules at the back, the material in front of support structures. The endcap is split vertically 3.2.5 Instrumentedthe crystals is kept to a minimum. Flux Returninto two halves to facilitate access to the central The barrel section is divided into 280 sepa- detector components. rate modules, each holding 21 crystals (7 3in The entire calorimeter is surrounded by a dou- θ φ). After the insertion of the crystals,× the ble Faraday shield composed of two 1 mm-thick aluminum× readout frames, which also stiffen the aluminum sheets so that the diodes and pream- The Instrumentedmodule, areFlux attached Return, with thermally-conducting IFR, is designedplifiers are further to shielded detect from external muons noise. and neutral epoxy to each of the CFC compartments. The en- This cage also serves as the environmental bar- tire 100 kg-module0 is then bolted and again ther- rier, allowing the slightly hygroscopic crystals to hadrons, such asmallyK epoxiedand to an aluminum neutrons, strong-back. while The providingreside in a dry, temperature flux return controlled nitrogen for the magnetic strong-backL contains alignment features as well atmosphere. as channels that couple into the cooling system. solenoid. To allow for accurate studies of semi-leptonic and rare decays of B and D mesons, the IFR is required to be efficient with a large angular coverage. It should also provide high background rejection for muons with a momentum less than 1 GeV/c. A schematic diagram of the IFR structure is shown in Fig 3.11.

The magnet ﬂux return steel in the barrel and the two end-caps is segmented into layers and function as muon ﬁlters and hadron absorbers. There

26 76

Figure 73. Overview of the IFR: Barrel sectors and forward (FW) and backward (BW) end doors; the Figure 3.11:shape Diagram of the RPC modules of the and different their dimensions sections are indicated. of the IFR (barrel and end doors) and the shapethe modules of its are matched modules. to the steel dimensions cal readout strips. with very little dead space. More than 25 differ- The readout strips are separated from the ent shapes and sizes were built. Because the size ground aluminum plane by a 4 mm-thick foam of a module is limited by the maximum size of sheet and form strip lines of 33 Ω impedance. The the material available, i.e., 320 130 cm2 for the strips are connected to the readout electronics at bakelite sheets, two or three RPC× modules are one end and terminated with a 2 kΩ resistor at joined to form a gap-size chamber. The modules the other. Even and odd numbered strips are are 18 suchof layers, each chamber increasing are connected to the in gas thickness system connected from to di 2fferent cm front-end for cardsthe (FECs), inner so 9 layers to in series, while the high voltage is supplied sepa- that a failure of a card does not result in a to- rately to each module. tal loss of signal, since a particle crossing the gap 10 cm for theIn the outermost barrel sectors, the gaps ones. between theThe steel gapstypically between generates signals these in two absorbers or more adja- are filled plates extend 375 cm in the z direction and vary cent strips. in width from 180 cm to 320 cm. Three modules The cylindrical RPC is divided into four sec- with single gapare needed resistive to cover the whole plate area chambersof the gap, as (RPC’s),tions, each covering which a quarter detect of the circumfer- streamers from shown in Figure 73. Each barrel module has 32 ence. Each of these sections has four sets of two strips running perpendicular to the beam axis to single gap RPCs with orthogonal readout strips, measure the z coordinate and 96 strips in the or- the inner with helical u–v strips that run paral- ionizing particlesthogonal direction via extending capacitive over three modules readoutlel strips. to the diagonals There of the module, are and 19 the outerRPC layers in to measure φ. with strips parallel to φ and z.Withineachsec- Each of the four half end doors is divided into tion, the strips of the four sets of RPCs in a given the barrel, 18three in sections the by steelend-caps, spacers that are and needed two additionalreadout plane are connected cylindrical to form long RPC’s strips inserted for mechanical strength. Each of these sections is extending over the whole chamber. Details of the covered by two RPC modules that are joined to segmentation and dimensions can be found in Ta- between theform EMC a larger chamber and with the horizontal magnet and verti- cryostatble 13. to detect particles leaving the calorimeter. RPC’s are simple, cost-effective, and can be constructed to cover different shapes with minimal dead space. Fig 3.12 displays the cross section of a planar RPC and its voltage connections. It is composed of two bakelite sheets, 2mm thick, separated by a 2 mm gap that is filled with the gas mixture. The external surfaces of the sheets are coated with graphite and connected to 8 kV potential. Cylindrical RPC’s are based on the same concept as the pla- ∼ nar ones, but differ in detail. Furthermore, due to efficiency losses and rapid aging, the Barrel RPC’s were replaced by Limited Streamer Tubes (LST’s) during the summer of 2006. The latter are composed of silver plated wires which collect the free charge in a CO2 based gas mixture. Free electrons resulting from the interaction of charged particles with the gas mixture drift toward the graphite sheets for readout. In general, muons pen-

27 etrate more layers than neutral hadrons. Therefore, if hits in multiple IFR layers are present and can be linked to a track in the SVT and DCH, then the track in question is a muon. Otherwise, the particle is a neutral hadron

interacting with the steel of the magnetic flux return. 75 background rejection for muons down to mo- Aluminum menta below 1 GeV/c.Forneutralhadrons,high X Strips Foam efficiency and good angular resolution are most H.V. Insulator important. Because this system is very large and Graphite difficult to access, high reliability and extensive Bakelite 2 mm monitoring of the detector performance and the Gas 2 mm Bakelite 2 mm associated electronics plus the voltage distribu- Graphite tion are required. Insulator Foam Y Strips Spacers 10.2. Overview and RPC Concept Aluminum The IFR uses the steel flux return of the mag- 8-2000 8564A4 net as a muon filter and hadron absorber. Sin- gle gap resistive plate chambers (RPCs) [96] with two-coordinate readout have been chosen as de- Figure 74. Cross section of a planar RPC with the tectors. Figure 3.12: Crossschematics section of the of high a planar voltage (HV) Resistive connection. Plate Chamber. The RPCs are installed in the gaps of the finely segmented steel (see Section 4) of the barrel and edge by a 7 mm wide frame. The gap width is the end doors of the flux return, as illustrated in kept uniform by polycarbonate spacers (0.8cm2) Figure 73. The steel segmentation has been cho- that are glued to the bakelite, spaced at dis- sen on the basis of Monte Carlo studies of muon tances of about 10cm. The bulk resistivity of penetration and charged and neutral hadron in- the bakelite sheets has been especially tuned to teractions. The steel is segmented3.2.6 into Trigger 18 plates, System1011–1012 Ω cm. The external surfaces are coated increasing in thickness from 2 cm for the inner with graphite to achieve a surface resistivity of nine plates to 10 cm for the outermost plates. The 100 kΩ/square. These two graphite surfaces are∼ nominal gap between theA steel trigger plates system is 3.5 cm is implementedconnected to high in order voltage to( 8kV)andground, select the events of interest result- in the inner layers of the barrel and 3.2 cm else- and protected by an insulating∼ mylar film. The where. There are 19 RPC layers in the barrel+ − bakelite surfaces facing the gap are treated with and 18 in the endcaps. Ining addition, from two the layerse e of collisions.linseed oil. At Thethe RPCs designated are operated luminosity, in limited a background rate of cylindrical RPCs are installed between the EMC streamer mode and the signals are read out ca- and the magnet cryostat to20 detect kHz particles each exit- is expectedpacitively, for oneon both or sides more of tracksthe gap, inby externalthe DCH (pt > 120 MeV/c) ing the EMC. ∼ electrodes made of aluminum strips on a mylar RPCs detect streamersor from at ionizing least particlesone EMC clustersubstrate. (E > 100 MeV). The trigger system must keep via capacitive readout strips. They offer several The cylindrical RPCs have resistive electrodes advantages: simple, low cost construction and the made of a special plastic composed of a conduct- possibility of covering oddthe shapes total with event minimal rate belowing polymer 120 Hz. and ABSFurthermore, plastic. The gap it shouldthickness provide an efficiency dead space. Further benefits are large signals and and the spacers are identical to the planar RPCs. fast response allowing forexceeding simple and robust 99% front- for BBNoevents linseed andoil or 95% any other for surface continuum treatments (qq) events, while con- end electronics and good time resolution, typi- have been applied. The very thin and flexible cally 1–2 ns. The position resolution depends on tributing a maximumelectrodes of 1% dead are laminated time. to fiberglass boards and the segmentation of the readout; a value of a few foam to form a rigid structure. The copper read- mm is achievable. out strips are attached to the fiberglass boards. The construction of theThe planar trigger and cylindrical system consists of two levels, Level 1 in hardware (L1) and Level RPCs differ in detail, but they are based on the 10.3. RPC Design and Construction same concept. A cross section of an RPC is shown The IFR detectors cover a total active area of schematically in Figure 74.3 in software (L3). Theabout L1 2,000 trigger m2.Thereareatotalof806RPC uses tracks in the DCH, above a preset pt, The planar RPCs consist of two bakelite (phe- modules, 57 in each of the six barrel sectors, 108 nolic polymer) sheets, 2 mm-thickand IFR and as separated well as showersin each inof the the four EMC half end to doors, determine and 32 in its the decision. The data is by a gap of 2mm. The gap is enclosed at the two cylindrical layers. The size and the shape of processed by three specialized hardware processors: the drift chamber trigger (DCT), the electromagnetic calorimeter trigger (ECT), and the instrumented flux return trigger (IFT). The DCT and ECT each satisfy the full trigger re-

28 quirements independently, thus providing a high level of redundancy. The IFT is used for µ+µ− and cosmic ray triggering and its output is compared with that of the DCT and ECT. The L3 trigger receives the L1 output and performs stage 2 rate reductions for the main physics events. It also identiﬁes categories of special events needed for calibration, luminosity determination, as well as online monitoring tasks. Its ﬁlter acceptance is 90 Hz for physics events, while the remaining 30 ∼ ∼ Hz contain the events of special categories.

29 Chapter 4

Analysis Tools

The hadronic reconstruction method is explained in this chapter. Details of the event reconstruction and the associated software packages are also outlined. Furthermore, information about the Monte Carlo samples and the

BABAR dataset, used for this analysis, is presented.

4.1 Hadronic Reconstruction Method

Hadronic reconstruction is employed for this analysis in order to signiﬁcantly reduce continuum background and allow for a highly pure signal extraction. In this exclusive method, one B meson, Btag, is reconstructed fully via hadronic decay modes. The remaining clusters and tracks in an event are then assigned to the other B meson, Bsig, on which the signal analysis is performed. This way a considerable amount of the continuum background is eliminated which allows for the potential observation of a signal candidate with suﬃciently low background levels. In addition, the method also provides a useful Bsig rest frame. The four momentum of Btag, and therefore Bsig, is fully determined by the hadronic reconstruction. Furthermore, because Btag is fully reconstructed, any missing energy in an event can be directly attributed to Bsig which is an

30 ideal situation for invisible searches. However, since only a small fraction of B mesons can be correctly reconstructed hadronically, this method results in a low signal eﬃciency and thus a statistically limited result.

4.2 Ntuple Production

Software in BABAR is organized in releases, each with hundreds of packages used to perform a speciﬁc task. The goal is to select, from the data and Monte Carlo simulation, events that are of interest to physics research. The R24c physics release is used for this analysis. Furthermore, events are chosen using the BSemiExcl skim, which is a skimming code that selects candidate events with tracks that can be attributed exclusively to a reconstructed Btag, and are analyzed using the following packages:

BRecoilTools V00-03-08 •

BRecoilUser HEAD •

BetaPid V00-15-02 •

workdir V00-04-21 •

These packages are conﬁgured for analyses with a reconstructed B± or B0. Ntuples are then produced here at McGill university containing all the relevant information on the Bsig daughter tracks and clusters. However, events with more than 9 tracks and 12 clusters on the Bsig side are excluded due to storage constraints. Furthermore, information about the Btag reconstruction is also stored in these ntuples, mainly the charge, energy substituted mass, ∆E, the truth information, and purity values. The R24 ntuples also include information about the D seed and X particles (deﬁned in the next section)

31 forming the Btag.[21]

4.3 Event Reconstruction

Because B-mesons decay predominantly into ﬁnal states which include charmed mesons, the BSemiExcl skim employs a D∗0 or a D∗± seed along with a combination of pions and kaons to reconstruct a Btag candidate. The decay chains included in the D reconstruction are:

D∗0 D0 π0, D0 γ • →

D∗± D0 π± • →

D0 K± π∓, K± π∓ π0, K± π∓ π+ π−, K0 π+ π− • → S

D± K0 π±,K0 π± π0, K0 π± π+ π−, K± π+ π−, K± π+ π− π0 • → S S S

Using any of the above decay modes, a D candidate is formed and then combined with the remaining pions and kaons in the event according to the

± ± 0 0 decay chain B D + X. Here, X = n1π + n2K + n3K + n4π and → S n1, n2, n3, n4 are restricted according to the following [21]:

n1 + n2 + n3 + n4 5 • ≤

n1 + n2 5 • ≤

1 <= n1 5 • ≤

n2 2 • ≤

n3, n4 2 • ≤

32 Furthermore, the combination of pions and kaons that make up X is chosen such that the energy substituted mass, mES, of Btag is within the appropriate

B-meson mass range. mES is calculated as follows:

q 2 2 mES = E p (4.1) beam − Btag where Ebeam is the beam CM energy and −→p is the CM 3-momentum of Btag.

To survive the BSemiExcl skim, mES should range between 5.20 and 5.30

2 GeV/c . Furthermore, the CM energy of Btag should be within range of the calibrated CM beam energy. ∆E deﬁned as ∆E = EB Ebeam should | tag − | therefore lie between -0.20 and +0.20 GeV. If so, an event passes the BSemiExcl skim with a properly reconstructed Btag candidate; otherwise, it is discarded. The BSemiExcl skim can result in multiple B candidates per event. Therefore, to further increase the purity of the Btag sample, the McGill skim is applied and only includes events that satisfy the “Best B” criteria. According to the “Best B” criteria, the D mass is used to select a single B candidate in events which have multiple Btag candidates. Furthermore, the cut on ∆E varies according to the decay mode of the Btag. Thus, for every D+X combination used in the

Btag reconstruction, a diﬀerent range of ∆E values is allowed and thus a better D seed is selected. Fig 4.1 shows the diﬀerent cuts on ∆E introduced by the McGill skim. Events that pass this selection are then stored in the ntuples for analysis.

33 ×103 tautau 1800 uds ccbar 1600 B0B0bar BpBm Data 1400

1200 Number of Events

1000

800

600

400

200

0 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 delta E (GeV)

Figure 4.1: The allowed ranges of ∆E depending on the Btag decay mode, introduced by the McGill skim.

4.4 BABAR Dataset

This analysis uses on-peak BABAR data, taken at the Υ (4S) resonance with a total integrated luminosity of 429.06 fb−1. The data sample is divided into 6 runs, each run corresponding to a diﬀerent set of detector conditions. The luminosity and B-counting values for each run are summarized in Table 4.1.

Run Data Set Luminosity B-counting # ( pb−1) ( 106) × 1 Lumi-BSemiExcl-Run1-OnPeak-R24c 20597.096 22.557 0.138 ± 2 Lumi-BSemiExcl-Run2-OnPeak-R24c 62075.982 68.439 0.413 ± 3 Lumi-BSemiExcl-Run3-OnPeak-R24c 32669.310 35.751 0.217 ± 4 Lumi-BSemiExcl-Run4-OnPeak-R24c 100809.151 111.430 0.671 ± 5 Lumi-BSemiExcl-Run5-OnPeak-R24c 133886.691 147.620 0.888 ± 6 Lumi-BSemiExcl-Run6-OnPeak-R24c 79021.759 85.173 0.513 ± Table 4.1: Luminosity and B-counting values for the BABAR dataset. The listed uncertainties include both the systematic and statistical error involved in determining the number of BB events.

34 4.5 Monte Carlo Background

Generic background Monte Carlo is used to check the validity of the signal selection in this invisible search. It is also essential in providing a reasonable estimate of the results expected from the BABAR dataset, which is blinded in the signal region. The Monte Carlo samples are divided into five different categories: B+B−, B0B0, cc, uds, and τ +τ −1. Each category is split into 6 runs, corresponding to the different detector conditions present during data collection. The number of generated and skimmed events for each run of each Monte Carlo type is listed in Table 4.2, where the corresponding errors are statistical only.

1The diﬀerent MC types will be further discussed in Chapter 5.

35 Run Generated Skimmed Skim Eﬃciency Cross-Section Normalization # Events Events ( %) ( nb) weight B+B− Monte Carlo SP-1235 1 34878000 2653635 7.608 0.0048 0.5476 0.323368 ± 2 104761000 7834295 7.478 0.0028 0.5513 0.326645 ± 3 56035000 4314119 7.699 0.0039 0.5472 0.319008 ± 4 166784000 12826637 7.691 0.0022 0.5527 0.334054 ± 5 214488000 16165968 7.537 0.0019 0.5513 0.344123 ± 6 130336000 10082381 7.736 0.0025 0.5389 0.32667 ± B0B0 Monte Carlo SP-1237 1 34941000 2353851 6.737 0.0045 0.5476 0.322785 ± 2 103308000 6833737 6.615 0.0026 0.5513 0.331239 ± 3 57888000 3961504 6.843 0.0036 0.5472 0.308797 ± 4 169801000 11525561 6.788 0.0021 0.5527 0.328118 ± 5 215177000 14220041 6.609 0.0018 0.5513 0.343021 ± 6 135104000 9123609 6.753 0.0023 0.5389 0.315213 ± cc Monte Carlo SP-1005 1 55254000 3345866 6.055 0.0034 1.3 0.484602 ± 2 164146000 9886074 6.023 0.0020 1.3 0.491628 ± 3 88321000 5408009 6.123 0.0027 1.3 0.480861 ± 4 267308000 16614784 6.216 0.0016 1.3 0.490266 ± 5 343667000 21201330 6.169 0.0014 1.3 0.506457 ± 6 208664000 13460064 6.451 0.0018 1.3 0.492314 ± uds Monte Carlo SP-998 1 159138000 5957690 3.744 0.0016 2.09 0.270507 ± 2 451172000 16920777 3.750 0.0009 2.09 0.28756 ± 3 275869000 10490416 3.803 0.0012 2.09 0.247505 ± 4 421599000 16409952 3.892 0.0010 2.09 0.499743 ± 5 553604000 21539120 3.891 0.0009 2.09 0.505457 ± 6 327032000 13416411 4.102 0.0011 2.09 0.505013 ± τ +τ − Monte Carlo SP-3429 1 48501000 8805 0.018 0.002 0.94 0.399193 ± 2 15583900 29942 1.921 0.011 0.94 0.374434 ± 3 59268000 11361 0.019 0.0001 0.94 0.51814 ± 4 180077000 37215 0.021 0.0001 0.94 0.526223 ± 5 237094000 51473 0.022 0.0001 0.94 0.530817 ± 6 139552000 33702 0.024 0.0001 0.94 0.532278 ± Table 4.2: Generic Background Monte Carlo Information. The uncertainty on the skim eﬃciency is statistical only.

36 4.6 Signal Monte Carlo

In addition to generic background Monte Carlo, a signal Monte Carlo sample (SP-9709) was generated using EvtGen and used in this invisible search. The signal sample accounts for both K∗± decay chains, each at a diﬀerent rate, with J/ψ decaying invisibly. Furthermore, the K∗ helicity amplitudes are considered and are taken from a previous BABARanalysis.[20] Table 4.3 lists the number of generated events for this signal sample along with the simulated rate of each K∗ decay mode.

Mode # Generated Decay Decay Rate Events Chain (%) ∗± 0 ± 9709 2956000 K KS π 59.20 K∗± → K± π0 40.62 K0 →π+ π− 100 S → Table 4.3: Signal Monte Carlo information.

4.7 J/ψ → `+`− in B± → K∗± J/ψ Monte

Carlo

As will be further discussed, it is important to cross check the signal selection for a speciﬁc mode with similar decay chains. Thus, a control sample (SP- 10029) where the J/ψ does not decay into a pair of neutrinos is generated and used. Here, the J/ψ decays into `+`−, where (l = µ, e), whereas the K∗ decay chains are not changed. The rate of each leptonic J/ψ decay is speciﬁed in Table 4.4. The K∗ decay rates are the same as for the signal Monte Carlo (SP-9709).

37 Mode # Generated Decay Decay Events Chain Rate (%) 10029 2138000 J/ψ e+e− 50 J/ψ → µ+µ− 50 → Table 4.4: J/ψ `+`− control sample information. →

38 Chapter 5

Background Analysis

It is important to understand the diﬀerent background types available for this analysis, and how they are scaled to match with data. Also, before applying the signal cuts, it is necessary to reduce the amount of background events abundant in the ntuples. Furthermore, because the Monte Carlo does not simulate the data exactly, the calculated eﬃciencies and number of surviving events have an associated systematic error. To reduce this error, a mES sideband substitution is used and will be discussed in detail below.

5.1 Background Events

In general, background events can be divided into 3 categories:

Peaking BB events: events where there is a properly reconstructed Btag • coming from the Υ (4S) decay into a BB pair; however, Bsig does not decay via the appropriate signal mode.

Non Peaking BB events: Υ (4S) BB events, where a Btag candidate • → is poorly reconstructed and thus lies in the combinatorial region of the

mES distribution.

39 Continuum events: e+e− qq events where q=u,d,s,c , or e+e− `+`− • → → events where l is any lepton. The e+e− pair annihilate into a pair of quarks or leptons instead of a Υ (4S) resonance. Such events include a combination of tracks and clusters which can be mistakenly joined to

form a Btag candidate.

Peaking and non-peaking BB events are modelled using B+B− and B0B0 Monte Carlo samples. cc, uds, and τ +τ − Monte Carlo represent continuum events. Here, cc events are considered separately because they can produce correctly reconstructed D-meson candidates. Furthermore, only τ +τ − Monte Carlo samples are used to model e+e− `+`− events. This is mainly due → to the relatively long tau life time and its ability to decay hadronically [22]. Even so, the contribution of τ +τ − background is very small and many times not visible in the displayed analysis plots, as will be seen later. The remaining e+e− `+`− events are usually removed by the BSemiExcl skim. →

Each background type is assigned a weight to match the data luminosity of each run. These weights are calculated as follows:

Ldata Nevents weight = where LMC = (5.1) LMC σMC

where Ldata and LMC are the data and Monte Carlo luminosities respectively,

Nevents is the number of generated events per run per Monte Carlo type and

σMC is the cross-section of the decays modelled in each Monte Carlo sample.

The cross-section and weight of each Monte Carlo sample for each run is listed in Table 4.2. The cross-sections of the continuum Monte Carlo are obtained from the BABAR physics book [23]. The B+B− and B0B0 cross sections

40 are calculated using the B-counting method, where, assuming an equal number of generated charged and neutral BB events, the B-count of each run is divided in half and the cross-section is then found using:

B σ = count (5.2) 2 Ldata ×

In all the ﬁgures of this document, each Monte Carlo background sample is scaled by the appropriate weight to match the data luminosity.

5.2 Background Cuts

A series of cuts is used to separate between background and signal events.

Initially, it is necessary to select events with a properly reconstructed Btag and thus get rid of most of the continuum background. For this reason, the following cuts are applied1:

There is exactly one reconstructed Btag. •

The charge of Btag is 1. • ±

The mES (energy substituted mass) of Btag is within the correct B-meson • mass range.

Continuum-Likelihood Cut: the event-shape variables :R2All,thrust mag- • nitude, cos ΘB, thrustz, and cos ΘT are consistent with a B-meson decay | | rather than a continuum event decay.

5.2.1 Btag Cuts

It is necessary to require the presence of exactly one properly reconstructed

Btag in an event. This is true since there is a small number of events produced 1The listed cuts will be referred to as the “background cuts” from this point forth.

41 using the McGill skim that have zero reconstructed Btag’s. Furthermore, the requirement on the charge of Btag is also essential to help reduce the number of background events where there is a properly reconstructed Btag, but it is neutral and therefore cannot decay via the appropriate signal mode. A question arises here of of whether or not the assumed charge of the Btag is true, since one

± can reconstruct an event where a track (such as π ) which is a Btag daughter is mistakenly assigned to the signal side. This way an event is tagged as B0B0

+ − instead of B B . If such an event where to be reconstructed, than the Btag will not peak in the proper mES region, which is, at the reconstruction level, a 100 MeV window. Fig 5.1 shows the mES distribution of all Monte Carlo

2 events in the region 5.20 < mES < 5.30 GeV/c for events that are required to

0 0 have one neutral Btag. As can be readily seen, only B B events peak in that

+ − region. The same is true for B B events when one charged Btag is required as shown in Fig 5.2. The peak observed in the mES distribution of Fig 5.2 is then isolated using a tighter cut, which follows that on the Btag charge. Doing so further ensures that mis-reconstructed events do not pass the selection.

70000 tautau uds ccbar 60000 BpBm B0B0bar

50000

40000

30000

20000

10000

0 5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3

Figure 5.1: mES distribution for Monte Carlo background after requiring one neutral Btag.

42 5.2.2 mES Cut

As shown in (4.1), the mES of Btag is calculated using the beam energy in the center-of-mass frame. The energy of Btag is not used to remove resolution uncertainties associated with its measurement. If an event is properly reconstructed, then mES should peak exactly at the B-meson nominal mass, 5.279

2 GeV/c . Figure 5.1 a) and b) show the mES distribution for signal and background events respectively, after applying the ﬁrst two cuts mentioned above. As can be seen, signal events have a clear peak in the region about the nominal B mass. Background events also have a peak in the right B-meson mass region; however, it is accompanied by an Argus-shaped2 tail in the sideband region dominated by continuum background.The data mES distribution is also shown as points with error bars in Fig 5.2. In this analysis, the nominal B-meson

2 mass range is chosen to be (5.270 < mES < 5.290) GeV/c .

b) a) ×103 tautau 350 uds 1200 ccbar B0B0bar 300 BpBm Data 1000 250 Number of Events 800 Number of Events 200

600 150

400 100

200 50

0 0 5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3 5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3 mES (GeV/c^2) mES (GeV/c^2)

Figure 5.2: a) Signal mES distribution b) Monte Carlo background and Data mES distribution.

2An Argus distribution is the probability distribution of a particle’s invariant mass in x 2 q x b[1 ( ) ] a continuum event and is presented as ax 1 ( )2e − Ebeam , where a and b are − Ebeam constants determined from the data. [24]

43 5.2.3 Continuum Likelihood Cut

When Υ (4S) decays into a BB pair, the particles produced are almost at rest mainly due to their large rest mass. Therefore, the direction of the decay products in such events is usually uniform. On the contrary, the qq pair produced in a continuum event are characterized with high momentum and therefore produce jets which lie closer to the beam line. Because the two types of events have such varying topologies, a number of event-shape variables can be used to diﬀerentiate between them. Here, a multivariate likelihood approach is employed dependant on the ﬁve following variables: R2All, thrust magnitude, cos ΘB, thrustz, and cos ΘT .

R2All is deﬁned as the ratio of the 2nd to 0th Fox-Wolfram3 moments • using all charged and neutral particles in an event. It is used to quantify the “jettiness” of a speciﬁc decay and ranges between 0 and 1, 0 being an isotropic event and 1 a jet-like event.[21] As you can see in Fig 5.3, BB events, along with signal events, have an R2All value closer to zero and therefore are less jet-like.

The thrust axis of an event is the axis which maximizes the longitudinal • momenta for a set of tracks or decay products. The magnitude of the thrust is thus higher for continuum events when compared to BB and signal events, as shown in Fig 5.4.

cos ΘT is deﬁned as the absolute value of the cosine of the angle between •| | the thrust axes of Bsig and Btag in the center-of-mass frame. Continuum events will have the thrust axis of the qq pair back to back and therefore

3 P pi pj Fox-Wolfram moment is deﬁned as Hl = | ||2 | Pl(cos θij), where pi is momentum i,j Evis of particle i,j , Evis is the total visible energy of the event, and θi.j is the angle between particle i and j. [25]

44 ×103 140 tautau uds ccbar 350 B0B0bar 120 BpBm Data Signal 300 100 250 Number of Events 80 200

60 150

40 100

20 50

0 0 0 0.2 0.4 0.6 0.8 1 R2All

Figure 5.3: R2All values for signal and background Monte Carlo along with data events.

×103 tautau 1200 uds ccbar 400 B0B0bar BpBm Data 1000 350 Signal

300 800 Number of Events 250 600 200

150 400

100 200 50

0 0 0.5 0.6 0.7 0.8 0.9 1 1.1 Thrust Magnitude (GeV)

Figure 5.4: Thrust Magnitude distribution for signal,background and data events.

the value of cos ΘT will be strongly peaked at 1. On the other hand, | | BB events have a relatively ﬂat distribution speciﬁcally since there is no

correlation between the directions of the Bsig and Btag decay products. Fig 5.5 clearly depicts this diﬀerence in topology.

In addition, another variable used in this continuum likelihood cut is • thrustz. It is deﬁned as the magnitude of the z-component of the thrust axis- the component along the beam line. Again, continuum events produce qq jets with high momentum. These jets are more likely to travel at small angles to the beam axis and thus have a higher thrustz value as

45 ×103 350 tautau uds ccbar B0B0bar 300 BpBm 120 Data Signal 250 100

200 80

150 60

100 40

50 20

0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Figure 5.5: cos ΘT distribution for signal,background and data events.

compared to BB events whose decay products are more likely to travel within the central region of the detector. See Fig 5.6.

tautau uds 60000 ccbar 60000 B0B0bar BpBm Data Signal 50000 50000

Number of Events 40000 40000

30000 30000

20000 20000

10000 10000

0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Thrustz (GeV)

Figure 5.6: Magnitude of thrustz for signal,background and data events.

Finally, cos ΘB is the cosine of the angle between the CM momentum of • Btag and the beam axis. BB events generally have this value peaking at

around 0, because the Btag decay products are again more likely to be directed towards the central region of the detector. As can be seen in Fig 5.7, continuum events do not display this behaviour.

The variables mentioned above are extremely useful in separating BB and continuum events. Therefore, for each event, the value of each variable is found; and based on that value, an event is assigned a probability of being

46 tautau 160 uds ccbar 50000 B0B0bar 140 BpBm Data Signal 120 40000

Number of Events 100

30000 80

60 20000

10000 20

0 0 •1 •0.8 •0.6 •0.4 •0.2 0 0.2 0.4 0.6 0.8 1 cosThetaB

Figure 5.7: cos ΘB distribution for signal,background and data events.

continuum (Pc) and a probability of being BB (PBB). Then, accounting for all ﬁve variables, a cumulative BB probability and continuum probability is calculated. The ratio: PBB/(PBB + Pc) is computed for each event. Fig 5.8 shows the distribution of this ratio for data, signal, and background events. Continuum events peak at values closer to zero, whereas signal and BB events are dominant in the region closer to 1. To get rid of a large amount of continuum background without harming the signal eﬃciency, a cut at r=0.3 is applied.

×103 tautau uds 120 ccbar 600 B0B0bar BpBm Data 100 Signal 500

Number of Events 80 400

60 300

40 200

20 100

0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Continuum Likelihood Ratio

Figure 5.8: Continuum Likelihood Ratio.

47 5.3 mES Sideband Substitution

To achieve the desired accuracy in an analysis, the Monte Carlo background, normalized to the data luminosity, should be in good agreement with the data. However, as shown in 5.2, there is a discrepancy between data and Monte Carlo.

Therefore, to correct for this, a mES sideband substitution is applied. To do so, the mES distribution is divided into two regions: signal (5.27 < mES <

2 2 5.29) GeV/c and sideband (5.21 < mES < 5.26) GeV/c . Furthermore, the Monte Carlo background is divided into two types:

Combinatorial background: cc, τ +τ −, uds, B0B0 and mis-reconstructed • B+B−

Peaking background: correctly reconstructed B+B− •

The goal of this approach is to substitute the combinatorial background in the mES signal region with sideband data. This way any systematic error associated with the combinatorial contribution of the MC background is eliminated and the sideband data distribution is used instead. The peaking B+B− distribution is then corrected to match with the peaking data, in order to achieve maximum agreement between data and Monte Carlo. Fig 5.9 shows a plot of track multiplicity, the total number of tracks in an event, in the range:

2 5.27 < mES < 5.29 GeV/c . As an example, a sideband substitution will be applied on this variable to achieve a better agreement between data and Monte Carlo.

First, the combinatorial background contribution in the mES signal region should be determined. The assumption made here is that the combinatorial background has the same composition in both the signal and sideband regions. Therefore, for each of cc,τ +τ −, uds and B0B0, the ratio of events in the signal

48 ×103

MC Background

1000 Data

800 Number of Events

600

400

200

0 0 1 2 3 4 5 6 7 8 9 10 Number of Tracks per Event

Figure 5.9: Track multiplicity before mES sideband substitution. region to events in the sideband region is calculated:

Nsignal RMC = ; (5.3) Nsideband where Nsignal and Nsideband are the number of events in the signal and sideband mES regions respectively. This ratio quantiﬁes the contribution of each Monte Carlo type to the signal region. The non-peaking component of B+B− is determined based on the B0B0 distribution; i.e. it is assumed that both Monte Carlo samples have a similar non-peaking distribution in the signal region. This assumption results from

+ − 0 0 the fact that the mES distributions of B B and B B have a similar proﬁle in the sideband region, as can be readily seen in Fig 5.2. A weighted ratio, given in (5.4), is then calculated, providing an estimate of the continuum background contribution in the signal region. The sideband data is therefore scaled to this ratio and then used to substitute the non-peaking background contribution.

R = f + − R + − + fuds Ruds + fcc Rcc + (f 0 0 + f + − ) R 0 0 (5.4) τ τ × τ τ × × B B B B × B B where f is the fraction of each background type to the total Monte Carlo in the sideband region and R is the ratio calculated in (5.3).

49 At this point, any discrepancy between data and Monte Carlo is mainly due to the peaking B+B− background. To account for this, the peaking contribution of B+B− Monte Carlo should ﬁrst be calculated. Therefore, it is again assumed that the non-peaking B+B− distribution has the same combinatorial shape as B0B0. The fraction of peaking B+B− is then found as follows:

Nsignal (RB0B0 Nsideband) fpeaking = − × (5.5) Nsignal

where Nsignal and Nsideband are the number of events in the signal and side-

+ − 0 0 band mES distribution of B B . RB0B0 is the B B ratio calculated according to (5.3).

×103 data BpBm 100

80 Number of Events

0 5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3 Peaking mes component (GeV/c^2)

+ − Figure 5.10: Data and B B mES peaking distribution.

As shown in (5.5), the peaking component of B+B− is determined by scaling the B0B0 distribution to the B+B− sideband, and then subtracting it from the B+B− distribution in the signal region. When this component is added to the scaled sideband data, the resulting distribution does not fully agree with the actual data in the signal region. To examine this eﬀect, Fig 5.10

+ − displays the peaking component of B B and data for the full mES distribution. The peaking data component is calculated by subtracting the continuum MC

50 background in the signal region from the data distribution in the signal region. The B0B0 MC distribution is then scaled to match with the data distribution in the sideband region and then subtracted from data in the signal region. As can be seen, the peaking Monte Carlo component overestimates the peaking data and is slightly shifted to the right. The ﬁnal step in this sideband substitution is to correct this discrepancy. To do so, the peaking B+B− distribution is scaled according to:

N CorrectionF actor = Data (5.6) NB+B− where NData and NB+B− are the number of peaking events in the signal mES region for the data and B+B− samples.

×103

Signal Region Data 1000

MC background

800 Number of Events

600

400

200

0 0 1 2 3 4 5 6 7 8 9 10 Number of Tracks per Event

Figure 5.11: Track multiplicity after mES sideband substitution.

The result of the mES sideband substitution for track multiplicity is shown in Fig 5.11 with a ratio of 0.2264 0.0001 and a correction factor of 0.9612 ± 0.002, where the uncertainty here is statistical only. The data and Monte ± Carlo are clearly in better agreement. This substitution will be used later in the analysis to get a proper estimate of the systematic uncertainties and expected background levels associated with the signal selection.

51 Chapter 6

Signal Selection

The background cuts listed in the previous chapter considerably reduce the amount of continuum and B0B0 background. However, there is still a large number of events that have a properly reconstructed charged Btag, but the signal B does not decay via the appropriate signal mode. Therefore, a number of cuts is applied to select only those events where J/ψ decays invisibly and a

∗± 0 ± ± 0 K decays either to KS π (Mode 1) or K π (Mode 2). The approach here is to fully reconstruct a K∗ candidate and ensure that there is nothing else in the event. This way if the invariant mass recoiling against the K∗±, calculated

∗ by subtracting the K 4-momentum from that of Bsig, is consistent with the J/ψ mass, then a signal event has been found.

6.1 Particle Identiﬁcation

To select for a specific K∗ decay mode, particle identification is implemented as an essential part of this analysis, using PID selectors 1. A PID selector is a developed code that employs information recorded by the detector in order to distinguish a specific particle type. Four PID selectors are used in this analysis

1See Appendix 1.

52 to determine whether a track is a kaon, electron, muon, proton or pion:

SBtrkPIDisBDTTKaon (Tight K± PID selector) •

SBtrkPIDisLHTElec (Tight e± PID selector) •

SBtrkPIDisBDTLMuon (Tight µ± PID selector) •

SBtrkPIDisLHTProton (Tight p± PID selector) • Bagger Decision Tree selectors are used to identify kaon and muon candidates, chosen at the tight and loose level respectively. Furthermore, tight likelihood selectors are chosen for selecting electron and proton candidates. The former is based on an SPR (StatPatternRecognition) algorithm[26] and uses momentum, position and charge measurements to classify tracks. Fur- thermore, it uses variables such as: the number of hits and interaction lengths in the IFR, the deposited energy in the EMC, and the dE/dx and number of hits in the DCH to form a muon PID criteria. The latter calculates a likelihood for each particle hypothesis using information from the SVT, the DCH and the DIRC. It compares for instance the measured dE/dx in the SVT with the expected one if the particle in question were a charged kaon. Each track in an event is checked by the selectors listed above in the order given. Therefore, first a track is checked to see whether or not it passes the tight kaon selector. If that is the case, the track is considered a kaon and no further particle identification is applied. Otherwise, it is checked by the tight electron and then the tight muon selectors. If it passes the former, it is assigned as an electron and therefore the muon and proton identification is skipped. However, if it fails the kaon and electron PID selectors and passes the tight muon BDT selector, it is considered a muon. Finally, if a track fails the kaon, electron and muon selector and passes a proton selector, it is assigned as a proton. If it fails all four selectors, it is considered a pion. At

53 the end this process, each track is then assigned the mass corresponding to its resulting particle ID. To do so, the energy of the track is changed, with the momentum 3-vector ﬁxed, such that the resulting mass is at the appropriate value. Fig 6.1 shows the output of this particle identiﬁcation order for signal MC, background MC and data events.

a) Results for Kaon PID b) Results for Electron PID 6 ×103 ×10 tautau tautau 9000 uds uds ccbar ccbar B0B0bar 12 B0B0bar 8000 BpBm BpBm Data Data 7000 10

Number of Events 6000 Number of Events 8

5000

4000 6

3000 4

2000 2 1000

0 0 0 1 2 3 4 5 0 1 2 3 4 5 Number of PID Kaons per event Number of PID electrons per event c) Results for Muon PID d) Results for Pion PID 6 ×10 ×103 tautau tautau uds uds 12 ccbar ccbar B0B0bar 2500 B0B0bar BpBm BpBm Data Data 10 2000 Number of Events Number of Events 8

1500 6

1000 4

500 2

0 0 0 1 2 3 4 5 0 1 2 3 4 5 6 7 8 9 10 Number of PID muons per event Number of PID pions per event

Figure 6.1: Results of particle identiﬁcation for a)Kaons b)Electrons c) Muons and d)Pions.

∗± 0 ± 0 + − 6.2 Mode 1: K → KS π ;KS → π π

The following cuts are applied, in addition to the background cuts2, to properly reconstruct a K∗ candidate assumed to decay via Mode 1:

There are exactly three charged tracks in an event, excluding the tracks • associated with the Btag reconstruction.

The three tracks must satisfy the pion ID requirement as described in • the previous section.

2 Recall that the background cuts are the Btag cuts (requiring exactly one charged B per event with a mES ranging between 5.27 and 5.29 GeV) and the continum likelihood cut.

54 The total energy of all clusters wih E > 50 MeV must be less than 500 • MeV.

0.78 < cos ΘP miss < 0.88, where ΘP miss is deﬁned as the angle between •− the beam line and the missing momentum vector of Bsig in the CM frame.

The three tracks must include at least one oppositely charged pair, from • 0 0 which the KS candidate, with a mass closest to the KS nominal mass, is chosen.

0 The K candidate chosen must lie within the mass range: 0.467 < MK0 < • S S 0.527 GeV/c2.

The remaining track, which is not included in the K0 reconstruction, • S must have a charge opposite to that of Btag.

Combining the third track and the reconstructed K0 must yield a K∗ • S 2 candidate with a mass within the range: 0.82 < MK∗ < 0.98 GeV/c .

The mass recoiling against the reconstructed K∗ should range between • 2 2 3.0 < Mrecoil < 3.2 GeV/c , consistent with the J/ψ mass ( 3.1 GeV/c ). ≈

6.2.1 Track Multiplicity and Particle ID cut

As previously mentioned, the only visible signature in a signal event should be a properly reconstructed K∗. Therefore, for this mode, there must be exactly

0 + 3 charged tracks in a signal event, corresponding to the two KS daughters (π and π−) and the K∗ daughter (π±). To ensure that these tracks are actually charged pions, a pion particle ID requirement is applied; i.e., the three tracks should fail the four selectors listed in the previous section and therefore pass as candidate pions. Before imposing any requirement on the charge of these

55 tracks, a couple of cuts are introduced to ensure that there are no additional clusters and tracks in the event.

6.2.2 Eextra and cos θP miss

To get rid of events where J/ψ does not decay invisibly and to further reduce continuum background, two cuts are applied: the ﬁrst on the energy of the extra clusters in an event and the next on the missing momentum of Bsig. Fig

6.2 displays the distribution of Eextra, the total energy of all clusters whose individual energy is greater than 50 MeV, for signal and background after applying the background cuts and the track multiplicity and particle ID cuts. The distribution peaks around zero for signal events, whereas background events have Eextra peaking roughly around 2.0 GeV. As can be readily seen, a cut at 0.5 GeV considerably reduces background. Furthermore, even though this cut may aﬀect the signal eﬃciency, signal Monte Carlo events with Eextra greater than 500 MeV may include high energy clusters attributed to a background decay mode and therefore must be removed.

tautau 1 uds ccbar 0.9 1200 B0B0bar BpBm Data 0.8 Signal 1000 0.7 Number of Events 800 0.6 0.5 600 0.4

400 0.3

0.2 200 0.1

0 0 0 1 2 3 4 5 6 Extra Energy (GeV)

Figure 6.2: Eextra distribution after applying background, track multiplicity and particle ID cuts.

The track multiplicity and Eextra cuts combined ensure that the remaining events do not include any extra tracks or high energy clusters. However, the

56 absence of a J/ψ signature may not necessarily imply an invisible decay if the decay products pass outside the detector’s ﬁducial acceptance. To get rid of events where that is the case, a cut on the direction of Bsig missing momentum is applied using:

pZmiss cos ΘP miss = (6.1) −→p where −→p is the missing momentum vector of Bsig in the CM frame. It is calculated by subtracting the 4-momentum of all of the tracks and clusters in an event (including those on the Btag side) from the beam energy.

Fig 6.3 shows the signal and background distribution of cos ΘP miss after applying the background, track multiplicity and particle ID cuts. Signal events display a smooth peak around zero, while background events peak at 1. If the J/ψ decay products were to travel outside the detector’s ﬁducial ± acceptance, then the value of cos ΘP miss would be 1. Therefore a cut of ± 0.78 < cos ΘP miss < 0.88 is applied to ensure that this is not the case. −

tautau 1 8000 uds ccbar 0.9 B0B0bar BpBm 7000 Data 0.8 Signal 6000 0.7 Number of Events 5000 0.6

0.5 4000 0.4 3000 0.3 2000 0.2

1000 0.1

0 0 •1 •0.8 •0.6 •0.4 •0.2 0 0.2 0.4 0.6 0.8 1 Cosine of missing momentum angle

Figure 6.3: cos ΘP miss after applying background, track multiplicity and particle ID cuts.

57 0 6.2.3 KS reconstruction

0 The next step is to properly reconstruct a KS candidate. First, all events considered must have at least one oppositely charged pair of pions. Clearly,

0 with the three charged pions available, this would lead to two possible KS candidates, shown in Fig 6.4.

450 tautau uds ccbar 400 B0B0bar BpBm Data 350 Signal

300 Number of Events 250

200

150

100

0 0 0.5 1 1.5 2 2.5 3 Ks Mass (GeV/c^2)

0 Figure 6.4: Mass of candidate KS reconstructed by combining a pair of oppositely charged pions: signal Monte Carlo.

0 To decide which one of the two pion combinations is a better KS candidate, a mass criteria is used and the combination with a mass closest to 0.497

2 0 GeV/c , corresponding to the KS nominal mass, is chosen. The mass criteria, when checked with Monte Carlo, has 5.9% error rate, which is considered ≈ satisfactory for a sensitivity study. Fig 6.5 displays the mass distribution of

0 the chosen KS candidate for signal and background Monte Carlo. As can be readily seen, the distribution has a long tail extending beyond 1.0 GeV/c2. The tail corresponds to events where the chosen track combination still does

0 not form a properly reconstructed KS . To get rid of these, a mass cut of

2 0.467 < M 0 < 0.527 GeV/c is applied. If the selected track combination KS 0 survives this cut, then it is concluded that a KS candidate has been found and is therefore assigned a mass of 0.497 GeV/c2. As with the mass of the identiﬁed tracks, this is done by keeping the momentum 3 vector of the chosen

58 0 track combination constant and changing the value of the KS ’s energy such that it has the appropriate mass.

tautau uds ccbar 300 B0B0bar BpBm Data Signal 250 Number of Events 200

150

100

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Ks Mass (GeV/c^2)

0 Figure 6.5: Mass of chosen KS candidate.

6.2.4 K∗ reconstruction

To complete the K∗± reconstruction, the remaining pion in the event must be joined with the K0 candidate according to the Mode 1 decay chain: K∗± S → 0 ± ∗ KS π . To ensure that this pion is truly a K daughter, the requirement that it should have a charge opposite to that of Btag is imposed. This requirement results from the fact that if the pion is a K∗ daughter, it should have the same

∗ charge as the K and Bsig and therefore a charge opposite to Btag. Fig 6.6 shows the mass distribution of the reconstructed K∗± candidates for signal and background events after the above cut.

0 2 ∗ As in the case of KS , a mass cut of 0.82 < MK < 0.98 GeV/c must be applied on the distribution of K∗±. If a K∗± candidate survives this mass cut, it is assigned a mass of 0.8916 GeV/c2 corresponding to the nominal K∗ mass.

Thus, a K∗ candidate has been completely reconstructed and the mass recoiling against it can be easily calculated. The K∗ 4-vector is subtracted

59 tautau uds ccbar B0B0bar 50 BpBm Data Signal

40 Number of Events

0 0.6 0.8 1 1.2 1.4 1.6 1.8 2 K* Mass (GeV/c^2)

Figure 6.6: Mass of reconstructed K∗ candidate according to mode 1 decay chain.

tautau 100 uds ccbar B0B0bar BpBm Data 80 Signal Number of Events 60

0 1 1.5 2 2.5 3 3.5 4 4.5 5 Recoil Mass (GeV/c^2)

∗ ∗ 0 ± Figure 6.7: Mass recoiling against K where K decays into KS π .

from that of Bsig and the result is shown in Fig 6.7. Note that the data

2 distribution is blinded in the J/ψ mass region, 3.0 < MJ/ψ < 3.2 GeV/c , as well as several other cc quarkonia (ηc,χc1,ψ(2S),ψ(3770)), 3.41 < M < 3.80 GeV/c2. The ﬁnal step in this selection process is to cut on the mass recoiling against K∗. A signal event is found if this mass ranges within the J/ψ signal

2 region: 3.0 < MJ/ψ < 3.2 GeV/c .

60 6.3 Mode 2: K∗± → K± π0

In addition to the background cuts, the following cuts are applied to select signal events for this mode:

There is exactly one charged track in the event (excluding the tracks • associated with the Btag reconstruction).

The charged track must satisfy a kaon particle ID requirement as de- • scribed in section 6.1.

The charge of the kaon must be opposite to that of Btag. •

0.78 < cos ΘP miss < 0.88 . •−

Each of the clusters forming the π0 candidate should have an energy • greater than 100 MeV.

The reconstructed π0 candidate must have an invariant mass between • 0.124 and 0.154 GeV/c2.

The total energy of all clusters with energy>50 MeV, excluding the π0 • daughters, should be less than 500 MeV.

The mass of the K∗ candidate, formed from the kaon and pion combina- • 2 tion, should lie within the range 0.82 < MK∗ < 0.98 GeV/c .

The mass recoiling against K∗ should be between 3.0 and 3.2 GeV/c2. •

6.3.1 Track Multiplicity, Particle ID and cos ΘP miss Cut

Requiring the presence of only one track is necessary to exclude events that have more than just the K∗ candidate. This track must satisfy the kaon particle ID requirements described in section 6.1. Furthermore, as for mode 1

61 signal selection, a cut on the charge of the kaon is imposed to ensure that it is

∗ truly a K daughter, i.e. the kaon must have a charge opposite to that of Btag. This way it is deﬁnitely not mistaken for a kaon resulting from the decay of

± D in the reconstruction of Btag. After applying the above cuts, it is necessary to check that the J/ψ decay products did not pass outside of the detector’s acceptance. Therefore, a cut on cos ΘP miss:( 0.78 < cos ΘP miss < 0.88) is − applied.

6.3.2 π0 reconstruction

The next step is to reconstruct a π0 candidate and join it with the charged kaon to form a K∗. To do so, the cluster with the highest energy in the event is chosen. If this cluster has an energy less than 100 MeV, the event is discarded. Otherwise, it is joined with all other signal side clusters with E> 100 MeV in the event to form a set of π0 candidates. The 100 MeV energy cut is introduced here to reduce combinatorics from low energy clusters which are usually dominated by detector noise. The cluster combination with the mass closest to the nominal π0 mass, 0.139 GeV/c2, is then chosen. Fig 6.8 shows the mass distribution of the selected π0 candidates for signal and background events. As can be readily seen, a mass cut is required to get rid of the long tail of

0 0 2 mis-reconstructed π ’s. Thus, a tight cut of (0.124 < Mπ < 0.154) GeV/c , corresponding to approximately 2σ is introduced. The cluster combination ± that survives this cut is then assigned a mass of π0. To do so, the energy value of the clusters’ 4-vector is ﬁxed in this case and the momentum 3-vector is varied such that the cluster combination has a mass of 0.139 GeV/c2.

62 700 tautau uds ccbar B0B0bar 600 BpBm Data Signal 500 Number of Events 400

300

200

100

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Pion Mass (GeV/c^2)

Figure 6.8: Mass of reconstructed π0’s.

6.3.3 Eextra cut and K∗ Reconstruction

Before combining the K± and π0 to form a K∗, a cut on the extra energy in the event is applied to further reduce the contribution of background. Fig

6.9 displays the distribution of Eextra, excluding the energy of the two clusters forming the selected π0, and after imposing the above cuts. A cut at 0.5 GeV eliminates a considerable amount of background events, while retaining most of the signal events.

240 tautau uds 220 ccbar B0B0bar BpBm 200 Data Signal 180 160 Number of Events 140 120 100 80 60 40 20 0 0 0.5 1 1.5 2 2.5 3 3.5 4 Extra Energy (GeV)

0 Figure 6.9: Eextra minus the energy of the two π clusters.

After applying the above cuts, the K± and the reconstructed π0 are joined to form a K∗ candidate. At this stage, it is again necessary to apply a cut on

∗ 2 the K mass: (0.82 < MK∗ < 0.98) GeV/c and then calculate the recoiling

63 mass. As with Mode 1 decay, a reconstructed K∗ surviving this cut is assigned a mass of 0.89 GeV/c2. The results of the K∗ reconstruction and the recoiling mass are shown in Fig 6.10 and 6.11 respectively. The data is blinded in the

2 cc mass regions. Finally, a cut of (3.0 < Mrecoil < 3.2) GeV/c is applied on the recoiling mass distribution to further reduce the number of surviving background events and to increase the purity of the signal selection.

80 tautau uds ccbar B0B0bar 70 BpBm Data Signal 60

Number of Events 50

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 K* Mass (GeV/c^2)

Figure 6.10: K∗ mass reconstructed according to mode 2 decay chain.

tautau uds 90 ccbar B0B0bar BpBm 80 Data Signal 70

Number of Events 60

0 1 1.5 2 2.5 3 3.5 4 4.5 5 Recoil Mass (GeV/c^2)

Figure 6.11: Recoil mass distribution where K∗ decays into K± π0.

6.4 Signal Selection Cross Check

Before estimating the systematic error and calculating the associated branching fraction for both Mode 1 and Mode 2 decay, it is important to verify the

64 validity of the signal selection. Because both signal modes require a single K∗± candidate and nothing else in the event, one can simply validate the K∗± reconstruction by examining decay modes which include a K∗± candidate along with other B decay products. One obvious possibility is B± K∗± → J/ψ where J/ψ does not decay invisibly, but rather into a pair of oppositely charged leptons: J/ψ `+`− where l =µ or e. Furthermore, an alternative → 0 ∗± approach to this validation is considering the decay D K l ν`, where the → D0 is a B± daughter particle and the K∗± decays via either Mode 1 or Mode 2.

6.4.1 J/ψ → `+`−

As previously mentioned, a control sample is used for this cross check. The goal is to select for B+B− K∗± J/ψ , J/ψ `+`− events in this control → → sample, and then in data, using the K∗± reconstruction method employed in the Mode 1 and Mode 2 signal selection. With a few extra cuts on the J/ψ decay products, a peak at 3.1 GeV/c2 in the mass recoiling against the K∗± should be seen. Otherwise, the K∗± reconstruction method is not validated and an alternative approach to the signal selection should be considered. To validate Mode 1 K∗± reconstruction, the following cuts, along with the background cuts, are applied:

There must be exactly 5 tracks in the event (excluding the tracks asso- • ciated with Btag).

Three tracks must satisfy the pion ID requirement, whereas two tracks • must pass either the electron or the muon PID selectors.

The two tracks passing a lepton ID must be oppositely charged. •

The three pions must form a K∗ candidate as discussed in section 6.2. • 65 Furthermore, the cuts used to check Mode 2 K∗ reconstruction are:

There must be exactly 3 tracks in the event (excluding the tracks asso- • ciated with Btag).

One track must pass the kaon ID requirement, while the two should pass • the electron or muon PID selector.

The two tracks, tagged as leptons, must be oppositely charged. •

The remaining kaon should be joined with a reconstructed π0 candidate • to form a K∗ as previously mentioned in section 6.3 .

The cuts on the extra energy and missing momentum are excluded from the K∗± reconstruction, as these cuts were placed to ensure that there is nothing other than the K∗± candidate in the event. Mode 1 results are shown in Fig

0 6.12 and 6.13 for l = e and l = µ respectively. As can be seen, the KS and K∗± mass distributions peak in the appropriate regions for both the control sample and data. However, the mass recoiling against the K∗± peaks at the J/ψ nominal mass only for the control sample. The same is true for Fig 6.12 d) and 6.13 d) where the mass of the e+e− and µ+µ− sum is shown. As for Mode 2 leptonic cross check, the results are shown in Fig 6.14 and 6.15 for l = e and l = µ respectively. The π0 and K∗± peaks are again clearly visible in the control sample and data. However, the recoil mass distribution, along with the mass distribution of the lepton sum, peak at 3.1 GeV/c2 for the control sample only. The absence of a peak in data can be understood as either an indication of a potential error in the K∗± reconstruction or of low statistics. To verify the source of this discrepancy, an estimate of the number of events expected

66 a) Mass of Ks candidate b) Mass of K* candidate

160 tautau 50 tautau uds uds ccbar ccbar B0B0bar B0B0bar 140 BpBm BpBm Data Data Signal 40 Signal 120

Number of Events 100 Number of Events 30 80

60 20

40 10 20

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 Ks Mass (GeV/c^2) K* Mass ( GeV/c^2) c) Mass recoiling against K* d) Mass of electron sum

tautau tautau 30 uds 45 uds ccbar ccbar B0B0bar B0B0bar BpBm 40 BpBm Data Data 25 Signal Signal 35

20 30 Number of Events Number of Events

25 15 20

10 15

10 5 5

0 0 1.5 2 2.5 3 3.5 4 4.5 0 0.5 1 1.5 2 2.5 3 3.5 4 Recoil Mass (GeV/c^2) Electron Sum Mass ( GeV/c^2)

Figure 6.12: Results of J/ψ e+e− in B± K∗± J/ψ . → →

a) Mass of Ks candidate b) Mass of K* candidate

200 tautau tautau uds 80 uds ccbar ccbar 180 B0B0bar B0B0bar BpBm 70 BpBm 160 Data Data Signal Signal 60 140

Number of Events 120 Number of Events 50

100 40 80 30 60 20 40

20 10

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 Ks Mass (GeV/c^2) K* Mass (GeV/c^2) c) Mass recoiling against K* d) Mass of muon sum

tautau tautau 22 uds 70 uds ccbar ccbar 20 B0B0bar B0B0bar BpBm 60 BpBm Data Data 18 Signal Signal 16 50

Number of Events 14 Number of Events 40 12

10 30 8 6 20 4 10 2 0 0 1.5 2 2.5 3 3.5 4 4.5 0 0.5 1 1.5 2 2.5 3 3.5 4 Recoil Mass (GeV/c^2) Muon sum mass ( GeV/c^2)

Figure 6.13: Results of J/ψ µ+µ− in B± K∗± J/ψ . → → in the generic background Monte Carlo is in order here. This is done using:

N = σ (6.2) L × × B ×

−1 where is the BABAR luminosity (429 fb ), σ here is taken to be the cross- L

67 a)Mass of neutral pion candidate b) Mass of K* candidate

50 tautau tautau uds 50 uds ccbar ccbar B0B0bar B0B0bar BpBm BpBm 40 Data Data Signal 40 Signal

Number of Events 30 Number of Events 30

20 20

10 10

0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.5 1 1.5 2 2.5 3 3.5 Neutral Pion Mass (GeV/c^2) K* Mass (GeV/c^2) c)Mass recoiling against K* d) Mass of electron sum

tautau tautau uds uds ccbar ccbar 16 B0B0bar 30 B0B0bar BpBm BpBm Data Data 14 Signal Signal 25 12 Number of Events Number of Events 20 10

8 15

6 10 4 5 2

0 0 1.5 2 2.5 3 3.5 4 4.5 0 0.5 1 1.5 2 2.5 3 3.5 4 Recoil Mass (GeV/c^2) Electron Sum Mass (GeV/c^2)

Figure 6.14: Results of J/ψ e+e− in B± K± J/ψ . → →

a)Mass of neutral pion candidate b) Mass of K* candidate

tautau tautau 140 uds uds ccbar 35 ccbar B0B0bar B0B0bar 120 BpBm BpBm Data Data Signal 30 Signal 100 25 Number of Events Number of Events 80 20

60 15

40 10

20 5

0 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0.5 1 1.5 2 2.5 3 3.5 Neutral Pion Mass (GeV/c^2) K* Mass (GeV/c^2) c)Mass recoiling against K* d) Mass of muon sum

tautau 50 tautau uds uds ccbar ccbar B0B0bar B0B0bar 10 BpBm BpBm Data Data Signal 40 Signal 8

Number of Events Number of Events 30 6

20 4

10 2

0 0 1.5 2 2.5 3 3.5 4 4.5 0 0.5 1 1.5 2 2.5 3 3.5 4 Recoil Mass (GeV/c^2) Muon sum mass (GeV/c^2)

Figure 6.15: Results of J/ψ µ+µ− in B± K± J/ψ . → → section of the B+B− Monte Carlo (0.55 nb), and and are the branching B fraction and the signal eﬃciency of the decay mode in question respectively. Table 6.1 lists the branching fractions involved in this cross check. The signal eﬃciencies of each of the leptonic J/ψ decays, calculated using the J/ψ → `+`− control sample, are also provided in table 6.2. The branching fraction

68 associated with this decay is easily calculated by multiplying the + − ∗ BB B →K J/ψ −5 by + − , yielding a result of (8.5 10 ). Furthermore, a look at BJ/ψ →` ` ≈ × the values of table 6.2, an approximate signal eﬃciency of 0.01 % can be deduced. Therefore, the expected number of events in the generic Monte Carlo background for these leptonic J/ψ decays is of the order 1. This explains the absence of a peak in the data and thus another cross check is required to validate the signal selection.

Mode Branching Fraction B± K∗± J/ψ (1.43 0.08) 10−3 → ± × J/ψ `+`− (5.94 0.06)% → ± J/ψ µ+µ− (5.93 0.06)% → ± K∗± K π± or π0 100% → ≈ Table 6.1: List of the B±,J/ψ , and K∗± braching fractions associated with J/ψ `+`− cross check. →

Mode Number of Events Eﬃciency (%) K∗± K0 π±, J/ψ e+e− 186 (8.70 0.64) 10−3 → S → ± × K∗± K0 π±, J/ψ µ+µ− 162 (7.58 0.60) 10−3 → S → ± × K∗± K± π0, J/ψ e+e− 138 (6.45 0.55) 10−3 → → ± × K∗± K± π0, J/ψ µ+µ− 101 (4.72 0.47) 10−3 → → ± × Table 6.2: Eﬃciency for each of the leptonic J/ψ decay modes.

0 ∗ 6.4.2 D → K l ν` Study

Because the results of the J/ψ `+`− cross check are limited by low statistics, → the K∗± reconstruction method is tested on yet another decay chain: D0 → ∗ 0 K l ν`. Here, Bsig decays into D plus any other combination of tracks and clusters. To isolate such events in the background Monte Carlo, a set of additional cuts is applied, along with those necessary for the K∗± reconstruction. Furthermore, no dedicated MC sample was generated for this sanity check,

69 0 ∗ because the mode D K l ν` is modelled in the generic background Monte → Carlo. A small peak in the K∗ mass region is expected if the following cuts are applied:

Same cuts for mode 1 and mode 2 K∗± selection, excluding the track • multiplicity, Eextra and cos ΘP miss cuts.

At least one extra lepton in the event. •

Lepton must have a charge opposite to that of K∗±. •

Lepton and K∗± joined must have a mass less than 2.0 GeV/c2, i.e. less • than the D0 nominal mass (1.864 GeV/c2).

As for the previous cross check, K∗± is reconstructed the same way as in the actual signal selection. However, there is no restriction on the number of tracks in the event. The presence of three pions and one kaon is required for mode 1 and mode 2 K∗± decays respectively along with at least one extra lepton.

The cuts on Eextra and cos ΘP miss are not applied because the exact decay products of Bsig are not speciﬁed. To improve the selection, a cut on the charge of the extra lepton is placed instead. Furthermore, the invariant mass of the lepton and K∗ combination must be less than that of a D0. If not, the event is discarded. Because of the presence of the extra neutrino in this decay chain, a D0 peak cannot be fully reconstructed. The results of this cross check are shown in Fig 6.16 and 6.17 for Mode 1 and Mode 2 K∗± selections respectively. For both modes, a peak at about 0.89 GeV/c2 is visible in B+B− Monte Carlo, along

0 0 ∗± with a peak at the KS and π nominal mass as well. This implies that the K reconstruction used for this analysis is a reliable approach and thus is yielding

0 0 proper results. The same is true for the π and KS reconstruction methods.

70 a)Mass of Ks candidate b)Mass of K* candidate

tautau 160 tautau uds uds 7000 ccbar ccbar B0B0bar 140 B0B0bar BpBm BpBm 6000 Data Data 120

5000 Number of Events Number of Events 100

4000 80

3000 60

2000 40

1000 20

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Ks Mass (GeV/c^2) K* Mass (GeV/c^2)

0 ∗± 0 ∗ ∗± Figure 6.16: Mass of reconstructed a)KS and b) K in D K l ν`, K K0 π±. → → S

a)Mass of neutral pion b)Mass of K* candidate ×103 tautau 600 tautau 120 uds uds ccbar ccbar B0B0bar B0B0bar BpBm 500 BpBm 100 Data Data

400 Number of Events 80 Number of Events

60 300

40 200

20 100

0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 1.5 2 2.5 3 Pion Mass (GeV/c^2) K* Mass (GeV/c^2)

0 ∗± 0 ∗ ∗± Figure 6.17: Mass of reconstructed a)π and b) K in D K l ν`, K K± π0. → →

71 Chapter 7

Eﬃciencies

The total and partial eﬃciencies 1, as well as the number of signal Monte Carlo events, are listed in table 7.1, 7.2 and 7.3 after each of the background, mode 1 and mode 2 signal cuts respectively. The eﬃciency is calculated here as:

N = cut (7.1) Ntotal

where Ncut is the number of events surviving a specific set of cuts and Ntotal is the number of generated events (listed in Table 4.3 for signal Monte Carlo). Because the signal Monte Carlo sample consists of 59.20% Mode 1 events and 40.62% Mode 2 events, the total number of generated events is scaled by the associated fraction of each mode to determine the efficiency. Doing so, the final signal efficiency for Mode 1 is 0.039 % and that for Mode 2 is 0.037 %. However, in the case of Mode 1, the calculated value still does not take into

0 + account the fact that KS , in the signal Monte Carlo, decays exclusively into π π−.A K0 decays into a π+ π− pair with a fraction of (69.20 0.05)% and a S ± π0 π0 pair with a fraction of (30.69 0.05) % [3]. In addition, a K∗± decaying ± 1Partial eﬃciency is the eﬃciency of the next cut in a series of cuts relative to the previous one. It is given by: Ni+1 , where N and N are the number of events surviving cut (i+1) Ni i+1 i and cut(i) respectively.

72 0 ± 0 0 into K π decays into 50% KS and 50% KL and thus this effect must also be accounted for in the efficiency calculation. To do so, the calculated signal efficiency must be scaled by the associated fractions:(69.20 0.05)% and 50%. ± The result is a signal efficiency of (0.0136 0.0005)%2 for B± K∗± J/ψ , ± → K∗± K0 π±. → Cut Number of Total Efficiency Partial Efficiency Events ( 10−1%) (%) × Btag reconstruction 18535 6.27 0.05 (6.27 0.05) ± 10±−1 × One Recoil B Cut 13434 4.55 0.04 72.5 0.82 ± ± mES Cut 9463 3.20 0.03 70.4 0.95 ± ± Charged Btag Cut 9108 3.08 0.03 96.2 1.41 ± ± Continuum Likelihood 7834 2.65 0.03 86.0 1.33 Cut ± ±

Table 7.1: Number of events as well as total and partial eﬃciency values after background cuts for Signal Monte Carlo. The uncertainties are statistical only.

Cut Description Number of Total Partial Events Efficiency ( 10−2%) Efficiency(%) × Track multiplicity cut 2061 11.80 0.26 26.3 0.7 (3 tracks only) ± ± Pion particle ID cut 1598 9.13 0.23 77.5 2.6 ± ± Eextra cut 1330 7.60 0.21 83.2 3.1 ± ± cos ΘP miss cut 1286 7.35 0.21 96.7 3.8 ± ± K0 reconstruction 1267 7.24 0.20 98.5 3.9 S ± ± K0 mass cut 935 5.34 0.18 73.8 3.2 S ± ± K∗ reconstruction 921 5.26 0.17 98.5 4.6 ± ± K∗ mass cut 747 4.27 0.16 81.1 4.0 ± ± J/ψ mass cut 678 3.93 0.15 95.6 5.0 ± ± Table 7.2: Efficiency values and number of events after each selection cut for Mode 1 decay in Signal Monte Carlo. The uncertainties are statistical only.

Table 7.4 and 7.5 list the number of signal and background Monte Carlo events in the J/ψ signal and sideband region after the ﬁnal selection cuts for Mode 1 and Mode 2 respectively. As previously mentioned, the “signal” region

2The uncertainty listed is statistical only.

73 Cut Description Number of Total Partial Events Efficiency ( 10−2%) Efficiency(%) × Track multiplicity cut 3507 29.21 0.49 44.8 0.9 (one track only) ± ± Kaon particle ID 2545 21.20 0.42 72.6 1.9 ± ± Kaon charge cut 2544 21.19 0.42 99.9 2.8 ± ± cos ΘP miss cut 2446 20.37 0.41 96.1 2.7 ± ± π0 reconstruction 1662 13.84 0.34 67.9 2.2 ± ± π0 mass cut 797 6.64 0.24 48.0 2.1 ± ± Eextra cut 741 6.17 0.23 93.0 4.7 ± ± K∗ mass cut 565 4.71 0.20 76.2 4.3 ± ± J/ψ mass cut 493 3.71 0.17 91.5 5.6 ± ± Table 7.3: Efficiency values and number of events after each selection cut for Mode 2 decay in Signal Monte Carlo. The uncertainties are statistical only. is chosen to range from 3.00 to 3.20 GeV/c2 and from 3.41 to 3.80 GeV/c2, where the latter corresponds to other cc quarkonia. The “sideband” region consists of the entire mass range, excluding the signal region. The values for data are only included in the sideband region. As can be seen, data and Monte Carlo agree within error in almost the entire sideband region for both decay modes. Such an agreement leads to the conclusion that the Monte Carlo, within error, provides a reasonable estimate of the data in this analysis.

Mass Region Signal Events Background Events Data Events GeV/c2 MRecoil 3.00 10.0 3.2 10.4 2.0 7.0 2.6 ≤ ± ± ± 3.00 < MRecoil < 3.20 678.0 26.0 5.3 1.5 – ± ± 3.20 MRecoil 3.41 20.0 4.5 4.0 1.1 2.0 1.4 ≤ ≤ ± ± ± 3.41 < MRecoil < 3.80 16.0 2.4 8.0 2.8 – ± ± MRecoil 3.80 2.0 1.4 58.1 4.8 70.0 8.4 ≥ ± ± ± Table 7.4: Final Numbers after full Mode 1 signal selection.The uncertainties are statistical only.

74 Mass Region Signal Events MC Background Events Data Events GeV/c2 MRecoil 3.00 17.0 4.1 4.2 1.2 8.0 2.8 ≤ ± ± ± 3.00 < MRecoil < 3.20 493 22.2 2.0 0.9 – ± ± 3.20 MRecoil 3.41 42.0 6.5 2.7 0.9 2.0 1.4 ≤ ≤ ± ± ± 3.41 < MRecoil < 3.80 2.0 1.4 4.0 1.1 – ± ± MRecoil 3.80 0.0 0.0 13.1 2.2 15.0 3.9 ≥ ± ± ± Table 7.5: Final Numbers after full Mode 2 signal selection.The uncertainties are statistical only.

75 Chapter 8

Uncertainties

The accuracy of the results in this blinded analysis are highly dependant on Monte Carlo simulations. Therefore, it is necessary to investigate the overall agreement between data and Monte Carlo throughout the signal selection and account for all discrepancies. Furthermore, applying a cut on a certain variable in the signal selection can introduce a systematic error on the signal eﬃciency. It is thus necessary to examine the signal selection cuts closely, as well as the variables on which a cut is applied. Fig 8.1 a) and b) displays the value of the correction factor, calculated using equation (5.6), at each stage in the selection process for Mode 1 and Mode 2 respectively. The variable chosen here is Eextra, and therefore the cut on this variable is not included. A potential source of systematic error is any cut or variable used in the signal selection whose correction factor is largely shifted from 1 or from the previous step in the analysis process. This is true since a shift in the value of the correction factor implies that the data and Monte Carlo disagreement increased after applying the associated cut. Therefore, the variable on which the cut is made must be examined outside the signal region, to determine whether or not a systematic error is involved.The ﬁnal mass cuts on the K∗± and J/ψ mass are excluded

76 Mode 1 Signal Selection Mode 2 Signal Selection

2 1 1.5 0 1 •1 0.5 •2

0 •3

•0.5 •4

•1 •5

•6 Btag CutsContinuumTrack Likelihood #=3Pion PIDEextra CutCosThetaKs Cut ReconstructionKs Mass K*Cut ReconctrsuctionK* Mass JsiCut Mass Cut Btag CutsContinuumTrack Likelihood #=1Kaon PIDKaon ChargeCosTheta CutPi0 Cut ReconstructionPi0 Mass EextraCut CutK* Mass JsiCut Mass Cut

Figure 8.1: Correction Factor for a)Mode 1 and b)Mode 2 decay.

Source Value

Btag Yield (96.12 0.24) % ± Continuum Likelihood Suppression —- Track Multiplicity cut Mode 1: 0.42 % Mode 2: 0.24 % Particle ID Mode 1:10 .0 % Mode 2 :1.50 % cos ΘP miss 2.50 % Eextra Cut 5.98 % 0 KS reconstruction 0.562% π0 reconstruction 0.216% 0 KS mass cut 0.04% π0 mass cut 0.19%

Table 8.1: List of possible systematic errors and their value. due to low statistics and the blinding of data in the ﬁnal stage. Table 8.1 lists the possible sources of systematic errors associated with for Mode 1 and Mode 2 decay and their associated value.

8.1 Btag Yield

Determining the systematic uncertainty associated with the Btag yield entails providing a measure of the level of data and Monte Carlo agreement after the hadronic B reconstruction. Because this analysis is exclusive to the case where

+ − the Btag is charged, this involves determining the number of events in B B

77 Monte Carlo with a properly reconstructed Btag. Fig 8.2 a)-d) show the mES distribution after each sequential selection cut, excluding the mES cut. There is a discrepancy between data and Monte Carlo; the B+B− distribution must be corrected to match that of data. To do so, the peaking mES component of both data and Monte Carlo must be isolated and a correction factor must be calculated in the same way as in the mES sideband substitution, in section 5.3. Fig 8.2 e)-h) show the comparison between the data and B+B− Monte Carlo peaking components. As you can see, the disagreement between data and Monte Carlo decreases with the cut flow. Furthermore, after removing most of the continuum background, the B+B− Monte Carlo overestimates the actual data. To correct for this, the data yield is divided by the B+B− yield is calculate, as in equation (5.6), and a systematic uncertainty equal to the full size of the observed difference is assigned. Of course, the value of the uncertainty will vary depending on the stage of the background cut flow in which it it is calculated. For this analysis, the systematic uncertainty on the

Btag yield is assigned after applying the continuum likelihood cut. This way any systematic uncertainty associated with combinatorial or poorly modelled backgrounds is already accounted for.

78 a)mES no cuts e)mES no cuts ×103 tautau uds 70000 ccbar 500 B0B0bar BpBm 60000 Data

50000 400 data Number of Events Number of Events 40000 BpBm 300 30000

200 20000

10000 100

0 0 5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3 5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3 mES mES (GeV/c^2) b)mES after cut on Btag number: RBn==1 f)mES after cut on Btag number: RBn==1 ×103 tautau uds 70000 ccbar 500 B0B0bar BpBm 60000 Data

50000 400 data Number of Events Number of EVents 40000 BpBm 300 30000

200 20000

10000 100

0 0 5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3 5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3 mES (GeV/c^2) mES (GeV/c^2) c)mES after Btag charge cut g)mES after Btag charge cut ×103 ×103 tautau 350 uds ccbar 120 B0B0bar 300 BpBm Data 100

250 data

Number of Events Number of Events 80

200 BpBm 60 150 40 100 20 50 0 0 5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3 5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3 mES (GeV/c^2) mES (GeV/c^2) d)mES after continuum likelihood suppression h)mES after continuum likelihood suppression ×103 ×103 tautau 220 uds ccbar 200 B0B0bar 100 BpBm 180 Data 160 80 data

Number of Events 140 Number of Events 120 60 BpBm 100 40 80 60 20 40

20 0 0 5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3 5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3 mES (GeV/c^2) mES(GeV/c^2)

Figure 8.2: mES distribution after:a)no cuts b)Btag multiplicity cut c)Btag charge cut d)contnuum likelihood cut. e)-h) Comparison between peaking data and peaking B+B− after each of the cuts.

8.2 Continuum Likelihood Suppression

The systematic uncertainty associated with the continuum likelihood suppression is considered to be accounted for when determining that of the Btag yield. By scaling the B+B− distribution after applying the continuum likelihood cut, the renormalized Monte Carlo has already been corrected for potential discrepancies between data and Monte Carlo for the ﬁve event shape variables.

79 8.3 Track Multiplicity Cut

Before calculating the systematic uncertainty of the remaining variables in the

+ − signal selection, the B B Monte Carlo is scaled by the Btag correction factor.

This way the error associated with the Btag yield is not accounted for more than once. A plot of the track multiplicity, after applying the background cuts and correcting for the Btag uncertainty, is shown in Fig 8.3 a). The agreement between data and Monte Carlo is highly satisfactory, especially for low track multiplicity events. To enhance this agreement, a sideband substitution is applied, shown in Fig 8.3 b). The signal selection is restricted to events with either one or three tracks and therefore it is only necessary to determine the systematic error when that is the case. To do so, the tau-31 method 1, developed by the BABAR tracking AWG, is used[27] . This method utilizes τ pair events to evaluate the tracking eﬃciency systematics and is applicable here due to the low multiplicity of our signal events. According to this method, a 0.24 % systematic error must be associated with each track. Therefore, the tracking uncertainty for Mode 1 decay is 0.73% and Mode 2 decay 0.24%.

×103 ×103 600 MC Background Signal Region Data 500 500 Data MC background

400 400 Number of Events Number of Events

300 300

200 200

100 100

0 0 0 2 4 6 8 10 12 0 2 4 6 8 10 12 Number of Tracks per Event Number of Tracks per Event

Figure 8.3: Track multiplicity distribution:a)before and b)after sideband substitution.

1See Appendix 2 for details.

80 8.4 Particle ID

The output of the PID selectors used in this analysis is shown in Fig 6.1. As you can see, the discrepancy between data and Monte Carlo is very similar to that for the track multiplicity variable. Because the systematic uncertainty for track multiplicity has already been determined, it follows that the error associated with the number of identified tracks (either as pions, kaon, muons or electrons) is accounted for. The remaining data-MC difference is related to having an event with a pion misidentified as a kaon for example. If such events survive the signal selection, they are not expected to peak in the recoil mass distribution. Thus, the uncertainty to be determined here is not related to the data-MC yield, but to the signal efficiency. To determine the systematic error, the difference between a PID selector’s performance in data and MC is determined as a function of particle momentum.2 Thus, in the case of kaon PID, the momentum range of the kaon used in a signal event K∗ reconstruction is determined to be between 0.5 to 2 GeV. A look at Fig 11.2 in Appendix 1 shows that in this range, the discrepancy between data and MC is at large 1.5%, and thus this value of the systematic uncertainty is conservatively associated with kaon PID. Determining the pion PID systematic is not as straightforward, since a particle is only identified as a pion if it fails all of the four selectors used in this analysis. Thus, the PID performance plots of interest here are the pion fake rates of the four selectors. However, not all the selectors will have a significant contribution to the pion systematic. As can be seen in the Fig 11.6, 11.8, 11.9 of Appendix 1, the kaon, proton, and electron PID selectors display a good data-MC agreement for the pion fake rate. In fact, the only significant contribution will be that of the muon selector. As shown in Fig 11.7, the dis-

2See Appendix 1 for the performance plots of each PID selector used in this analysis.

81 Cosine of missing momentum angle ×103 tautau 100 uds ccbar B0B0bar BpBm 80 Data Number of Events 60

0 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 cosTheta

Figure 8.4: cos ΘP miss after background cuts and Btag correction.

crepancy between data and Monte in the momentum region of interest, 0 to 2 GeV, ranges between 0 and 22%. The systematic uncertainty assigned in this case is then the average value of the observed discrepancy:10%.

8.5 cos ΘP miss Cut

Fig 8.4 displays the distribution of cos ΘP miss after applying the background cuts and correcting for the Btag uncertainty. As can be seen, the agreement between data and Monte Carlo is very good in the range 0.78 < cos ΘP miss < − 0.88. However, in the outer region, the discrepancy increases reaching a high of 7% at the maximum value of +1. To determine the systematic error for this ∼ variable, the percent diﬀerence between data and Monte Carlo is calculated on a bin by bin basis and then averaged out over the full distribution. The result is a conservative 2.5% uncertainty on the cosine of the missing momentum angle.

82 45000 45000 MC Background Signal Region Data

40000 40000 Data MC background

35000 35000

30000

Number of Events 30000 Number of Events

25000 25000

20000 20000

15000 15000

10000 10000

5000 5000

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 1 2 3 4 5 Extra Energy (GeV) Extra Energy (GeV)

Figure 8.5: Eextra distribution: a)after background cuts and Btag correction b)after sideband substitution.

8.6 Eextra Cut

For Eextra, the data-MC disagreement improves after applying a sideband substitution, as shown in Fig 8.5a) and b). Thus, the main uncertainty here is on the signal eﬃciency, not on the data-MC yield.

The systematic on the signal efficiency entails determining the difference in the data and Monte Carlo efficiencies after applying the Eextra cut. This differs from estimating the data and Monte Carlo disagreement in the actual

Eextra distribution. To calculate this error, the Eextra cut must be applied on a class of events that mimics that of the signal region but is not identical to it. To achieve this, Bsig is reconstructed for each of the events with a proper

Btag such that the only daughter particles on the signal side are tracks. This is done by applying the following cuts along with the background cuts listed in section 5.2:

∆E of Btag should range between 0.2 < ∆E < 0.2 GeV. • −

cos ΘB = 1 . • 6 ±

There are exactly 3 or 5 tracks in the event. •

83 The sum of the charges of all signal side tracks is opposite to the Btag • charge.

The ∆E and cos ΘB cuts are placed to ensure that the selected events have a properly reconstructed Btag. Furthermore, the cut on the track multiplicity is placed because only events with an odd number of tracks can yield a charged B. Events with 1 track are excluded of course, along with those with a number of tracks 7 because of their increased complexity. Thus, only events with 3 ≥ or 5 tracks can be used for this study.

To reconstruct Bsig, ﬁrst all the tracks in a single event are added together. The mES distribution is then calculated using (4.1), along with the ∆E distribution. The result is shown in Fig 8.6 a) and b) for 3 track events and Fig 8.6 c) and d) for 5 track events. Now, to exclude events where Bsig decays into clusters,

2 a mES and ∆E cut are applied on the track sum: (5.27 < mES < 5.29) GeV/c and ( 0.2 < ∆E < 0.2) GeV. If an event passes the above cuts, then a proper − B has been reconstructed. This B decays only into tracks and therefore the value of the extra energy should ideally be zero. However, as can be readily seen in Fig 8.7 a) and b), the Eextra distribution has a non zero component.

The next step is to apply the Eextra cut used in the signal selection on this nonzero component and calculate the difference in partial efficiency between data and Monte Carlo. Table 8.2 lists the result of applying a cut of E<0.5 GeV on data and Monte Carlo for 3 and 5 track events. The difference between the partial efficiency is calculated for each case and the average of both, 5.98%, is considered the Eextra systematic on the signal efficiency.

84 a) b)

tautau tautau uds uds 160 ccbar 14000 ccbar B0B0bar B0B0bar BpBm BpBm 140 Data 12000 Data

120 10000 Number of Events 100 8000 80 6000 60

4000 40

20 2000

0 0 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 0 1 2 3 4 5 Delta E (GeV) c) d)

tautau 22000 tautau uds uds 700 ccbar 20000 ccbar B0B0bar B0B0bar BpBm 18000 BpBm 600 Data Data 16000 500

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400 12000

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200 6000

4000 100 2000

0 0 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 −1 0 1 2 3 4 mES (GeV/c^2) Delta E (GeV)

Figure 8.6: Reconstructed Bsig: a-c)mES distribution of 3 and 5 track sum b-d)∆E distribution of 3 and 5 track sum.

a) b)

tautau 200 tautau uds uds 50 ccbar ccbar B0B0bar 180 B0B0bar BpBm BpBm Data 160 Data 40 140 Number of Events Number of Events 120 30 100

80 20 60

10 40 20

0 0 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 Extra Energy (GeV) Extra Energy (GeV)

Figure 8.7: Eextra distribution of reconstructed Bsig after mES and ∆E cut:a)3 track events b) 5 track events.

Number of Events Number of Events Partial before Cut after Cut Eﬃciency(%) Events with 3 Tracks Data 383.0 256.0 66.84 MC 413.8 304.07 73.48 Events with Five Tracks Data 1608.0 992.0 61.7 MC 1892.7 1268.6 67.02

Table 8.2: The partial eﬃciencies after applying the Eextra cut on the distribution for reconstructed Bsig.

85 8.7 π0 reconstruction and π0 Mass Cut

To determine the error associated with this method, the π0 reconstruction is ﬁrst removed from the context of the signal selection. The reconstruction is then applied alone, in order to examine the data and Monte Carlo agreement of its output. Even though the signal selection cuts are discarded for this part of the analysis, the background cuts3 are kept and applied on the data and Monte Carlo ntuples before reconstructing the π0’s. This way events with a mis-reconstructed Btag or combinatorial background events are not included in calculating the systematic uncertainty. Fig 8.8 a) shows the mass of the reconstructed γγ combinations after applying the background cuts only. As with other variables in this analysis, the Monte Carlo overestimates the actual data. Fig 8.8 b) displays the mass of the chosen π0 candidate. Recall that for each event a single π0 candidate is selected based on how close its mass is to the nominal π0 mass. As can be readily seen, the agreement between data and Monte Carlo is much increased after removing the mis-reconstructed π0’s and decreasing the number of candidates to only one per event. This agreement is further enhanced by applying a mES sideband substitution as shown in Fig 8.9. The value of the data-MC scale factor calculated using (5.6) is 99.784%. Thus, the uncertainty on the data-MC yield due to the π0 reconstruction is 1-0.99784= 0.216%.

To examine the impact of the mass cut on the data-MC agreement, it is applied to the distribution of Fig 8.9. The resulting partial efficiencies are listed in Table 8.3. The difference between the two efficiencies, 0.19 %, is the systematic uncertainty associated with the π0 mass cut.

3 Recall that the background cuts are the Btag cuts and the continuum likelihood cut.

86 a) b) ×103 ×103 tautau 400 tautau 400 uds uds ccbar ccbar B0B0bar 350 B0B0bar 350 BpBm BpBm Data Data 300 300

Number of Events Number of Events 250 250

200 200

150 150

100 100

50 50

0 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.2 0.4 0.6 0.8 1 Mass of pion candidates (GeV/c^2) Mass of chosen pion candidate (GeV/c^2)

Figure 8.8: a) π0 reconstruction after background cuts: a) Mass of all π0 candidates b)Mass of the chosen π0 candidate .

×103

Peaking Data 350

MC background 300

250 Number of Events

200

150

100

0 0 0.2 0.4 0.6 0.8 1 Mass of chosen pion candidate (GeV/c^2)

Figure 8.9: Mass of chosen π0 candidate after background cuts and sideband substitution

Number of Events Number of Events Partial before Cut after Cut Eﬃciency(%) Data 2.41113 106 714804 29.65 × MC 2.41568 106 711651 29.46 × Table 8.3: Partial eﬃciencies used to determine error associated with the π0 mass cut.

87 0 8.8 KS reconstruction and Mass Cut

The systematic error here is determined in the same way as for the π0 re-

0 construction. The KS reconstruction is applied after the background cuts, as shown in Fig 8.10 a) and b). Furthermore, a sideband substitution is applied

0 on the mass of the chosen KS candidate as shown in Fig 8.11. The value

0 of the data-MC scale factor is 99.439% and thus the uncertainty on the KS reconstruction is 1-0.99439=0.561%.

a) b) 3 3 × ×10 10 700 tautau tautau 400 uds uds ccbar ccbar 600 B0B0bar 350 B0B0bar BpBm BpBm Data Data 500 300 Number of Events Number of Events 250 400 200 300 150 200 100

100 50

0 0 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 Mass of Ks candidates (GeV/c^2) Mass of chosen Ks candidate (GeV/c^2)

0 0 Figure 8.10: Outcome of KS reconstruction: a)Mass of all KS candidates in 0 the event, b) Mass of the chosen KS candidate.

×103

400 Peaking Data

350 MC background

300

Number of Events 250

200

150

100

0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 Mass of chosen Ks candidate (GeV/c^2)

0 Figure 8.11: Mass of chosen KS candidate after applying sideband substitution.

0 As for the KS mass cut, the diﬀerence in partial eﬃciencies is again calculated on the distribution of Fig 8.11. The values are listed in Table 8.4, and the resulting error is 0.04%.

88 Number of Events Number of Events Partial before Cut after Cut Eﬃciency(%) Data 2.23254 106 1.08913 106 48.78 × × MC 2.2355 106 1.089617 106 48.74 × × 0 Table 8.4: Partial eﬃciencies used to determine error associated with the KS mass cut.

8.8.1 Summary of Systematic Errors.

Table 8.5 lists the systematic uncertainties associated with each decay mode, along with the ﬁnal value of the signal eﬃciencies. As can be readily seen, the

Btag correction is treated as a multiplicative error, and the final signal efficiencies are scaled by that value. This correction must be applied to the peaking component of the signal Monte Carlo only, with the non-peaking component excluded. However, because the non-peaking contribution is very small at the end of the signal selection, the scaling is applied to the full distribution and the resulting difference is considered negligible.

89 Source Value(%) Mode 1 (%) Value(%) Mode 2 (%) Value — 0.0136 – 0.0371 Stats 0.0005% 0.0017 ± ± ± Tracking 0.73 0.0001 0.24 0.0001 Particle ID 10.00 0.0014 1.50 0.0006 cos ΘP miss 2.50 0.0003 2.50 0.0009 Eextra 5.98 0.0008 5.98 0.0022 0 KS reconstruction 0.56 0.0001 – – π0 reconstruction – – 0.216 0.0001 0 KS mass cut 0.04 0.00001 – – π0 mass cut – – 0.19 0.0001 Btag Correction 96.12% – 96.12% – ( 0.0024) – ( 0.0024) – ± ± Total – 0.0131 – 0.0357 stats 0.0005 0.0016 ± ± ± systematic – 0.0016 – 0.0025 ± Table 8.5: Summary table of systematic errors and the ﬁnal signal eﬃciencies.

90 Chapter 9

( J/ψ νν) B →

The branching fraction for B± K∗± J/ψ , J/ψ νν, K∗± K0 π± or K∗± → → → S K± π0 is calculated using the following equation: →

Nobs Nbkg BR = − (9.1) N sig BB × where Nobs is the number of signal events observed after unblinding, Nbkg is the expected number of background events, NBB is the number of BB pairs produced in the data samples, and sig is the signal efficiency. The value of NBB, corresponding to the dataset used for this analysis, is given in the BbkLumi Script to be (470.97 0.022) 106. The signal efficiency is listed in ± × Table 7.2 and 7.3 for Mode 1 and Mode 2 decay respectively with the associated statistical error. The systematic error in these efficiencies is outlined in Table 8.1. As for the expected background estimate, it consists of two components and is calculated in the upcoming section.

91 9.1 Expected Background Estimate

The number of background events expected to survive the signal selection is estimated using Monte Carlo simulation and sideband data. The background contribution can be divided into two types: peaking and combinatoric. Table 9.1 lists the number of Monte Carlo events surviving the ﬁnal J/ψ mass cut at the end of each selection. Most of the combinatorial background is eliminated at the end of the signal selection, except for 1 uds and 1 cc event after mode 1 cuts and 1 cc event after mode 2 cuts. Furthermore, for both modes, there are less than 1 B0B0 events surviving the signal cuts. As for B+B− Monte Carlo, the number of events at the end of selection includes a peaking and non-peaking contribution. The two contributions are separated using a mES sideband substitution as discussed below. Decay Mode B+B− B0B0 cc uds τ +τ − K∗± K0 π± 4.05 1.17 0.64 0.46 1.00 0.71 1.01 0.71 0.0 → S ± ± ± ± K∗± K± π0 1.33 0.67 0.32 0.32 0.99 0.71 0.0 0.0 → ± ± ± Table 9.1: Number of surviving background Monte Carlo events at the end of each selection process.The listed uncertainties are purely statistical.

9.1.1 Combinatorial Background Estimate

To calculate the number of combinatorial background events surviving the full signal selection, a mES sideband substitution must be applied on the mass dis-

∗ tribution recoiling against the K in the J/ψ signal region (3.00 < MRecoil < 3.20 GeV/c2). As previously mentioned, the goal of a sideband substitution is to replace the combinatorial MC background with sideband data. Doing so, the dependence on MC simulation in the background estimates is eliminated along with the associated systematic errors. Fig 9.1 shows the ratio, calculated using equation (5.3), after each selection cut of Mode 1 and Mode 2 signal se-

92 lection. Recall that the sideband data must be scaled by the appropriate ratio, representing the relative size of the signal and sideband regions and the shape of the combinatorial background distribution, before substituting it in the combinatorial background estimate. Ideally, the value of this ratio should be taken at the end of the selection after all cuts, since the combinatorial background shape varies slightly as cuts are sequentially applied. However, at that stage, the sideband region has very low statistics and thus a large statistical error is associated with the calculated ratio. Therefore, for this analysis, the ratio is chosen after completing the K∗ reconstruction and before applying the K∗ mass cut. At that stage, much of the signal selection has been taken into account and the statistics are still high enough to provide a reasonable result. Thus, for Mode 1, the ratio is taken after requiring the charge of the remaining pion in the event to be opposite to that of Btag and joining it with

0 the KS candidate. To avoid any bias in this choice, a conservative uncertainty is assigned to this estimate. This way most of the values in the distribution are accounted for within error. Similarly, for Mode 2, the ratio is taken after cutting on the extra energy in the event and joining the π0 candidate with the charged kaon. Table 9.2 lists the value of the chosen ratio and its associated error, along with the combinatorial background estimate for both Mode 1 and Mode 2 signal selection.

Mode 1 Signal Selection Mode 2 Signal Selection

0.45 0.4 0.4 0.35 0.35 0.3 0.3 0.25 0.25 0.2 0.2

0.15 0.15

0.1 0.1

0.05 0.05

Btag CutsContinuumTrack Likelihood #=3Pion PIDEextra CutCosThetaKs Cut ReconstructionKs Mass K*Cut ReconctrsuctionK* Mass CutJsi Mass Cut 0 Btag CutsContinuumTrack Likelihood #=1Kaon PIDKaon ChargeCosTheta Cut Pi0 Cut ReconstructionPi0 Mass EextraCut CutK* Mass CutJsi Mass Cut

Figure 9.1: Ratio for a)Mode 1 and b)Mode 2 decay.

93 Mode Signal Region Sideband Ratio Background MC Data Estimate 1 5.34 1.46 15.00 3.87 0.253 0.026 3.80 1.05 ± ± ± ± 2 2.33 0.97 7.00 2.65 0.223 0.027 1.56 0.62 ± ± ± ± Table 9.2: Combinatorial background estimate for Mode 1 and Mode 2 decay.The listed uncertainties are purely statistical.

9.1.2 Peaking Background Estimate

To determine the peaking background estimate, the peaking component of the B+B− distribution in the ﬁnal recoil mass distribution is isolated and then scaled by a chosen correction factor. As previously mentioned, the peaking B+B− component is extracted by estimating a combinatorial contribution with the same shape as that of B0B0 and subtracting this combinatorial part from the full B+B− distribution. The correction factor is chosen using the same reasoning as in the combinatorial background estimate, after completing the K∗ reconstruction. However, in this case, systematic uncertainties must be taken into account and thus the values of table 8.5 are calculated for the peaking B+B− component. The results are listed in Table 9.3.

Mode Peaking Correction Peaking B+B− Factor Background 1 3.51 1.28 1.21 0.204 4.24 1.68 0.51 ± ± ± ± 2 1.33 0.67 0.87 0.37 1.15 0.76 0.14 ± ± ± ± Table 9.3: Peaking background estimate for Mode 1 and Mode 2 decay. The ﬁrst error is statistical and the second is systematic.

9.2 Results and Limits

The ﬁnal signal eﬃciencies, peaking and combinatorial background estimates, and the associated errors are all listed in Table 9.4 for Mode 1 and Mode 2

94 decay. These values can be inserted into (9.1), with the number of observed events, to determine the central value of (J/ψ νν). Because this is a B → sensitivity study for an ongoing BABAR analysis, the data is left blinded and the number of observed events is unknown. Therefore, a range of values is used to estimate the branching fraction. The results are shown in Table 9.5 and 9.6 for Mode 1 and Mode 2 respectively. Furthermore, the upper and lower limits of the expected branching fraction at the 90 % confidence level are also listed in Table 9.5 and 9.6 . Decay Mode Signal Efficiency (%) Expected Background Mode 1: K∗± K0 π± 0.0131 0.0017 8.04 2.04 → S ± ± Mode 2:K∗± K± π0 0.0357 0.0030 2.71 0.99 → ± ± Table 9.4: Final signal efficiencies, peaking and combinatorial background estimate for each of Mode 1 and Mode 2 decays with their associated errors.

An upper (lower) limit on (J/ψ νν) at the 90 % conﬁdence level for B → a given number of events N is the value of (J/ψ νν) for which 10 % of B → all measurements would yield a result which is less (greater) than or equal to N. For this analysis, the upper and lower limits are calculated using two diﬀerent frequentist methods: Barlow and Feldmann-Cousins[28]. With the Barlow method, the limit R is determined using the following equation[28]:

1 R± = (µ± b) (9.2) S − where µ is the Poisson mean for the number of observed events, b is the number of background events, and S is the sensitivity which is equal to the eﬃciency times NBB. The approach here is to perform a set of toy Monte Carlo experiments, where the total number of observed events is generated from a Poisson distribution with a mean µ and the trial values of S and b are generated by Gaussian

95 distributions with a standard deviation equal to σS and σb . (However, in this case, the uncertainty of b is not included because it is already accounted for in the Btag yield systematic error. [21]) The trial value of R that gives 10% of toy experiments with a value of N less (greater) than or equal to the observed value is the upper (lower) limit.[28] The only problem with the Barlow method is that it can output negative upper or lower limits. To avoid this, the Feldmann-Cousins method is also used to calculated the limits of (J/ψ νν). Here, a likelihood ratio is employed to B → rank the possible outcomes of an experiment when determining the boundaries of the acceptance region. This ratio is given by:

R P (n )/P (n best) (9.3) ≡ |B |B where P is the probability for observing n events given a branching fraction

and best is the value of which maximizes P (n ). Thus, R is a ratio of B B B |B two likelihoods-the ﬁrst is the likelihood of getting n events given a branching fraction and the second is the likelihood of getting n events given the best B physically possible branching fraction best. Every possible outcome (number B of events) n is assigned a likelihood ratio. The limits are calculated by adding n values to the acceptance region until the sum of the probabilities is 90%. At the end of an experiment, the upper and lower limits for an observed number of events no are the maximum and minimum values of that have no in B the acceptance region. To account for the uncertainties, a convolution of the Poisson distribution of P with a Gaussian in b and S is performed. The procedure is similar to that used in the Barlow method and is explained in greater detail in Reference [28]. Fig 9.2 and 9.3 show the central value and the 90 % conﬁdence limit interval of (J/ψ νν) for Mode 1 and Mode 2 B → respectively, using the Barlow and Feldmann-Cousins method.

96 ± ∗± Nobserved (J/ψ νν)/ (B K J/ψ ) B → B → Central Value Barlow Feldmann-Cousins Lower Limit Upper Limit Lower Limit Upper Limit ( 10−2) ( 10−2) ( 10−2) ( 10−2) ( 10−2) × × × × × 3 - 8.00 -12.12 -0.63 0.0 3.3 4 -6.46 -10.85 1.35 0.0 4.3 5 -4.86 -9.52 3.30 0.0 6.0 6 –3.26 -8.19 5.25 0.0 7.4 7 -1.66 -6.98 7.14 0.0 9.7 8 -0.06 -5.60 9.13 0.0 11.2 9 1.54 -4.25 10.94 0.0 13.2 10 3.14 -2.95 12.81 0.0 15.0 11 4.74 -1.56 14.67 0.0 16.8 12 6.34 -0.29 16.62 0.0 19.1 13 7.94 1.15 18.43 0.5 20.8

Table 9.5: (J/ψ νν)values with upper and lower limits for Mode 1 decay. B →

± ∗± Nobserved (J/ψ νν)/ (B K J/ψ ) B → B → Central Value Barlow Feldmann-Cousins Lower Limit Upper Limit Lower Limit Upper Limit ( 10−2) ( 10−2) ( 10−2) ( 10−2) ( 10−2) × × × × × 0 -1.59 2.00 0.02 0.0 0.75 1 -1.00 -1.60 0.89 0.0 1.41 2 -0.42 -1.20 1.70 0.0 2.18 3 0.17 -0.78 2.49 0.0 2.98 4 0.76 -0.35 3.26 0.0 3.66 5 1.34 0.10 4.01 0.0 4.55 6 1.93 0.54 4.73 0.10 5.41 7 2.52 1.00 5.50 0.56 6.09 8 3.11 1.45 6.22 0.79 6.81 9 3.69 1.93 6.91 1.21 7.50 10 4.28 2.39 7.62 1.42 8.07

Table 9.6: (J/ψ νν) values with upper and lower limits for Mode 2 decay. B →

97 Mode 1 Confidence Limit Interval

Expected background events 0.15 Central Value Barlow upper (UL) & lower (LL) limits Feldman−Cousins UL & LL 0.1 Feldman−Cousins UL & LL withOUT uncertainties

0.05

−0.05 Branching Fraction −0.1

−0.15 0 2 4 6 8 10 Number of Observed Events

Figure 9.2: Conﬁdence limit interval for Mode 1 decay using Barlow and Feldmann-Cousins method.

Mode 2 Confidence Limit Interval

Expected background events 0.8 Central Value Barlow upper (UL) & lower (LL) limits Feldman−Cousins UL & LL Feldman−Cousins UL & LL withOUT uncertainties 0.6

0.4

0.2 Branching Fraction 0

−0.2 0 2 4 6 8 10 Number of Observed Events

Figure 9.3: Conﬁdence limit interval for Mode 2 decay using Barlow and Feldmann-Cousins method.

98 Chapter 10

Conclusion

We have presented a sensitivity study on the search for J/ψ νν in B± → → ∗± ∗± 0 ± ± 0 K J/ψ , with K decaying into either KS π or K π . Hadronic B reconstruction has been employed and because this is a sensitivity study for an ongoing BABAR analysis, the data is left blinded in the signal region. The signal selection has been optimized such that very little background survives the chosen cuts. In addition, the systematic uncertainties associated with the signal selection variables and reconstruction methods have been examined. The final signal efficiency is (0.0131 0.0005)% for Mode 1, K∗± K0 π±, ± → and (0.0357 0.0017)% for Mode 2, K∗± K± J/ψ . Furthermore, with an ± → expected amount of 8 observed events, the calculated branching fraction for Mode 1 has an upper limit on (J/ψ νν) at the 90 % confidence level of B → 9.12 10−2 using the Barlow method and 11.01 10−2 using the Feldmann- × × Cousins method. Similarly, the result for Mode 2, with an expected number of 3 events, is an upper limit at the 90% confidence level of 2.49 10−2 and 2.98 × 10−2 using the Barlow and Feldmann-Cousins method respectively. The re- × sults are limited by the low efficiency of the hadronic B reconstruction method and the insufficient amount of data at the available BABAR luminosity. The

99 determined sensitivity is not an improvement to the previously quoted result by BES[18], B(J/ψ →νν) = 1.2 10−2 at 90 % conﬁdence level. However, B(J/ψ →µ+µ−) × the signal selection could beneﬁt from a larger data sample- one which is ten times larger for a more competitive result and at least three orders of magnitude greater for a precision measurement sensitive to new physics. With the approval of the SuperB project (the extension of the BABAR experiment to higher luminosities), a better limit on (J/ψ νν) can be obtained, possibly B → reaching the scale of discovery.

100 Bibliography

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[2] Martin, B. R., and G. Shaw. Particle Physics. Chichester, UK: Wiley, 2008. Print.

[3] K. Nakamura et al. (Particle Data Group), JPG 37, 075021 (2010) (URL: http://pdg.lbl.gov)

[4] Battaglia, M., A. J. Buras, P. Gambino, and A. Stocchi. “The CKM Ma- trix and the Unitarity Triangle.” Proc. of First Workshop on the CKM Matrix, CERN, Switzerland. Print.

[5] ALEPH Collaboration. Crespo, J.M et al. “Search for the neutral Higgs boson from Z0 decay.” Physics Letters B 236.2 (1990).

[6] DELPHI Collaboration. Abreu, P et al. “Search for Pair Production of Neutral Higgs Bosons in Z0 Decays.” Physics Letters B 245 (1990): 276- 88.

i [7] L3 Collaboration. Adeva, B. et al. “Search for the Neutral Higgs Boson from Z0 Decay.” Physics Letters B 24.1,2 (1990).

[8] OPAL Collaboration. Alexander et al. G.“Search for Neutral Higgs Bosons in Z0 Decays Using the OPAL Detector at LEP.” Zeitschrift Fur Physik C Particles and Fields 73.2 (1997): 189-99.

[9] Stephen P. Martin, arXiv:hep-ph/9709356 v5 (2008).

[10] Harari, Haim. “Left Right Symmetry and the Mass Scale of a Possible Right-Handed Weak Boson.” Nuclear Physics B.233 (1984): 221-31. Web.

[11] Gaitskell, Rick. “Evidence for Dark Matter”. SLAC. Aug. 2004. Lecture.

[12] Chang, L.N. “On the invisible decay of Υ (1S) and J/ψ resonances”. arXiv:hep-ph/9806487 v1 (1998).

[13] McElrath, Bob. “Light Higgles and Dark Matter at Bottom and Charm Factories.” Proceedings of the CHARM 2007 Workshop, Ithaca ,NY , Au- gust 5-8 2007.

[14] McElrath, Bob. “Invisible Quarkonium States as a Sensitive Probe for Dark Matter.” Phys.Rev.D72:103508 (2005).

[15] Rubin, P. et al. “Search for the Invisible Decays of Υ (1S).” Phys.Rev.D75:031104,2007. (2006).

[16] Tajima, et al. “Search for the Invisible Decays of Υ (1S) ”. Phys.Rev.Lett.98:132001. (2007).

[17] Abilikim,M. et al, “Search for the Invisible Decay of η and η0 in J/ψ to φ η and φ η0.” Phys.Rev.Lett.97:202002,2006.

ii [18] Abilikim, M. et al,“Search for the Invisible Decays of the J/ψ in ψ(2S) → J/ψ π+ π−.”Phys.Rev.Lett.100:192001,2008.

[19] The BABAR collaboration. B, Aubert et al. “The BABAR detector”. ariXiv:hep-ex/0105044 v1 (2001).

[20] Aubert et al, “Measurement of Decay Amplitudes of B K∗ J/ψ , B → → ψ(2S), and B χcK∗ with an Angular Analysis.” BAD 1438. 2007 →

± [21] Lindemann, Dana M.“A Search for the Decay B l ν` γ Using Hadronic → Tag Reconstruction.” Thesis. McGill University, 2009.

[22] Weinstein, A. J., and R. Stroynowski. “The TAU Lepton and Its Neu- trino.“Annual Review of Nuclear and Particle Science 43.1 (1993): 457- 528. Print.

[23] Harrison, P. F., and H. R. Quinn. BaBar Physics Book. Stanford, CA. Stanford Linear Acceleration Center, 1998. Print.

[24] ARGUS Collaboration, H. Albrecht et al., Phys. Lett. B 241, 278 (1990).

[25] “BaBar Glossary Search Tool.” SLAC National Accelerator Laboratory. Web. 28 Mar. 2011.

[26] The BABAR collaboration. Flood, Kevin, Alexandre Telnov, and Carlo Vuaslo. “Muon Identiﬁcation Using Decision Trees.” BAD 1853 .2010.

[27] The BABAR collaboration. Nugent, Ian, Michael Roney, and Robert Kowalewski. “Tau31 Tracking Eﬃciency Study for 2004.” BAD 931.2004

[28] The BABAR collaboration. Owen Long. “Search for the forbidden decay: B± K± τ µ.” BAD 1732 (v9).2008 →

iii [29] The BABAR collaboration. Thorsten Brandt . “Likelihood Based Electron Identiﬁcation.” BAD 396 (v1).2002.

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[32] Inventory of PID Selectors for “r24c” BaBar Collaboration. Web.

iv Chapter 11

Appendecies

Appendix 1: PID Selectors

A PID selector is an analysis tool which uses a speciﬁc hypothesis and information from the EMC, DCH, and DIRC to determine whether a track is a kaon, electron, pion, proton, or muon. There are two kinds of selectors used in this analysis: Likelihood (LH) selectors to identify electrons and protons and bagger decision tree (BDT) selectors for kaons and muons.

11.1 Likelihood Selector

A LH selector calculates a likelihood L(ξ) for each particle hypothesis, ξ ∈ e; π, K, p , using a set of discriminating variables. The variables are chosen { } based on pure samples of electrons, protons, kaons, and pions. The approach here is to construct a probability density function for each discriminating vari-

v able and compute the likelihood using the following equation:

L(ξ) = P (xEMC , xDCH , xDIRC ; ξ) = P (xEMC ; ξ)P (xDCH )P (xDIRC ; ξ) (11.1)

where xEMC , xDCH , xDIRC represent vectors of discriminating variables from each detector subsystem.[29] A likelihood fraction for each particle is then calculated given by:

pξLξ fL = (11.2) peLe + pπLπ + pK LK + ppLp

where pξ is a priori probability assigned to each particle.

A track is assigned as a particle ξ if it passes a cut on fL, which ranges between

0 and 1. The higher the value of the cut on fL , the tighter the likelihood selector is.

11.2 Decision Tree Selector

A decision tree is a multivariate analysis tool, used to discriminate between different classes (in this case, diﬀerent PID hypotheses) of events. It is composed of diﬀerent nodes, with each using a set of discriminating variables to achieve the best separation. As can be seen in Fig 11.1, an initial cut, initial rule, is applied to the data dividing it into two classes:R(x1) = xi < x: class=true,

Rx1 = xi > x: class=false. Each successive layer further separates the data into the two classes in question.[30]

While training a decision tree, events crossing through a node can be mis- classiﬁed. To address this issue without overtraining a data sample, a decision tree can be boosted. This is done by assigning a greater event weight, α, to

vi !"#$%$&'()*""%( ! +,-.($%(,-//"'$'01( R(x1) I'$J-8(*78"(EK&&.('&<"G(

R (x ) ! ),"(2&3&4(&5(-(.*""(67%.(( 1 2 R2(x2) (((((8&&9%(8$9"(-(%72:%-4/8"(( R (x ) R (x ) (((((&5(";"'.%(%726"#."<(.&(-(( 3 3 4 3 R5(x3) R6(x3) (((((#7.(2-%"<(-'-8=%$%>( R7(x4) R8(x4) D$0'-8(EFG(((((((H-#90*&7'<(EHG( Figure 11.1: A schematic diagram of a decision tree.[30] ! ),"*"(-*"(4-'=(2&3&4(8";"8%(.&(.,"(.*""?( ! >>>(%&(.,"*"(-*"(4-'=(%$0'-8(@(2-#90*&7'<(*"0$&'%(<"A'"<( 1− the misclassiﬁed events. The weight is given by α = , where is the error 2=(.,"(-80&*$.,4>( rate at each node.[30] Another way to improve the stability of a decision tree algorithm is bagging.->6>2";-'LM478>-#>79( In bagging, B bootstrap dataBC( samples are generated, each consisting of the n classes in question.[31] A decision tree is built for each sample and the average of these re-sampled solutions is then taken. Doing so, instabilities due to statistical ﬂuctuations in a training sample are removed.

11.3 Performance of chosen PID selectors

Fig 11.2, 11.3, 11.4, and 11.5 show the performance of each of the PID selectors used in this analysis as a function of the particle’s momentum. Furthermore, the pion fake rate of each of the selectors is also shown in Fig 11.6, 11.8, 11.7, 11.9.

vii 25.78 ≤ θ < 146.10 25.78 ≤ θ < 146.10 25.78 ≤ θ < 146.10 1 1 - 1.1 K , Data K+ - K , MC K-

∈ ∈ 1 0.9 0.9 MC ∈ / + 0.9 K , Data data

+ ∈ efficiency 0.8 K , MC efficiency 0.8 0.8 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 p [GeV/c] p [GeV/c] p [GeV/c]

Selector : TightBDTKaonMicroSelection Dataset : run6-r24c Tables created on 4/2/2009 (Data) , 4/2/2009 (MC)

Figure 11.2: Performace plot of the kaon Tight Bagged Decision Tree selector as a function of kaon momentum.[32]

22.18 ≤ θ < 137.38 22.18 ≤ θ < 137.38 22.18 ≤ θ < 137.38 1 1 1.1 0.8 0.8 ∈ ∈ 1 + + - µ µ , Data µ , Data MC µ- 0.6 µ+, MC 0.6 µ-, MC ∈ / 0.9

0.4 0.4 data ∈ efficiency efficiency 0.8 0.2 0.2 0 1 2 3 4 5 0 1 2 3 4 5 0.70 1 2 3 4 5 p [GeV/c] p [GeV/c] p [GeV/c]

Selector : BDTLooseMuonSelection Dataset : run6-r24c Tables created on 26/3/2010 (Data) , 26/3/2010 (MC)

Figure 11.3: Performace plot of the muon Loose Bagged Decision Tree selector as a function of muon momentum.[32]

22.18 ≤ θ < 141.72 22.18 ≤ θ < 141.72 22.18 ≤ θ < 141.72 1 1 1.1 e+ e-

∈ ∈ 1.05 + - 0.9 e , Data 0.9 e , Data MC e+, MC e-, MC ∈ / 1 data

0.8 0.8 ∈ efficiency efficiency 0.95

0.7 1 2 3 4 0.7 1 2 3 4 0.9 1 2 3 4 p [GeV/c] p [GeV/c] p [GeV/c]

Selector : PidLHElectronSelector Dataset : run6-r24c Tables created on 4/2/2009 (Data) , 5/2/2009 (MC)

Figure 11.4: Performace plot of the electron tight likelihood selector as a function of electron momentum.[32]

viii 25.78 ≤ θ < 146.10 25.78 ≤ θ < 146.10 25.78 ≤ θ < 146.10 p+, Data p-, Data 1.2 p+ 1.1 p+, MC p-, MC p-

∈ ∈ 1 1.1 MC

1 ∈

/ 1 data

0.8 ∈

efficiency 0.9 efficiency 0.9 0.8 1 2 3 4 5 1 2 3 4 5 0.8 1 2 3 4 5 p [GeV/c] p [GeV/c] p [GeV/c]

Selector : TightLHProtonSelection Dataset : run6-r24c Tables created on 4/2/2009 (Data) , 4/2/2009 (MC)

Figure 11.5: Performace plot of the proton tight likelihood selector as a function of proton momentum.[32]

25.78 ≤ θ < 146.10 25.78 ≤ θ < 146.10 25.78 ≤ θ < 146.10 3 π+, Data π-, Data π+ π+, MC π-, MC π-

∈ 0.05 ∈ 0.05 MC 2 ∈ / data

∈ 1

efficiency 0 efficiency 0

1 2 3 4 5 1 2 3 4 5 0 1 2 3 4 5 p [GeV/c] p [GeV/c] p [GeV/c]

Selector : TightBDTKaonMicroSelection Dataset : run6-r24c Tables created on 4/2/2009 (Data) , 4/2/2009 (MC)

Figure 11.6: Pion Fake Rate for the kaon tight bagged decision tree as a function of momentum.

22.18 ≤ θ < 137.38 22.18 ≤ θ < 137.38 22.18 ≤ θ < 137.38 0.1 π+ 0.1 π- π+ , Data , Data 1.4 π+, MC π-, MC π-

∈ ∈ 1.2 0.05 MC 0.05 ∈ / 1 data ∈ efficiency efficiency 0 0.8 0 0.6 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 p [GeV/c] p [GeV/c] p [GeV/c]

Selector : BDTLooseMuonSelection Dataset : run6-r24c Tables created on 26/3/2010 (Data) , 26/3/2010 (MC)

Figure 11.7: Pion Fake Rate for the muon loose bagged decision tree as a function of momentum.

ix 22.18 ≤ θ < 137.38 22.18 ≤ θ < 137.38 22.18 ≤ θ < 137.38 π+, Data π-, Data π+ π+, MC π-, MC 2 π-

0.004∈ 0.004∈ MC

∈ 1.5 0.002 0.002 / data ∈

efficiency efficiency 1 0 0 0.5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 p [GeV/c] p [GeV/c] p [GeV/c]

Selector : PidLHElectronSelector Dataset : run6-r24c Tables created on 4/2/2009 (Data) , 4/2/2009 (MC)

Figure 11.8: Pion Fake Rate for the electron tight likelihood selector as a function of momentum.

25.78 ≤ θ < 146.10 25.78 ≤ θ < 146.10 25.78 ≤ θ < 146.10 10 π+ 0.04 0.04 π- 8 ∈ 0.02 ∈ 0.02 MC

∈ 6

0 / π+ 0 , Data data 4

π+ π- ∈ -0.02efficiency , MC efficiency , Data -0.02 π-, MC 2 -0.04 1 2 3 4 5 1 2 3 4 5 0 1 2 3 4 5 p [GeV/c] p [GeV/c] p [GeV/c]

Selector : TightLHProtonSelection Dataset : run6-r24c Tables created on 4/2/2009 (Data) , 4/2/2009 (MC)

Figure 11.9: Pion Fake Rate for the proton tight likelihood selector as a function of momentum.

x Appendix 2: Tau 31 Method.

To determine the systematic uncertainty associated with track multiplicity at BABAR, the tau 31 method has been developed. This method utilizes τ decays, whose multiplicity is known, to determine the tracking efficiency of the detector. Here, an event is identified by a selection criteria on n-1 tracks to determine the probability of reconstructing the nth track. This probability is given by[27]: N(n tracks) (A) = (11.3) N(n-1 tracks) + N(n tracks) where is the efficiency, A is the geometric acceptance of the , N(n tracks) is the number of event where n tracks are reconstructed, and N(n-1 tracks) is the number of events where n-1 tracks where reconstructed. By calculating for both data and Monte Carlo and comparing the resulting values, the systematic uncertainty on the track multiplicity variable can be determined. This uncertainty can be represented in terms of a correction factor[27]: A ∆ = 1 Data = 1 Data (11.4) − MC − MC A

τ decays are a good candidate for a tracking eﬃciency study, because they involve an odd number of daughter tracks (due to charge conservation). These are produced in BABAR as e+e− τ +τ −. The τ decays used here are τ ± → → + − ∓ ± o ± π π h ντ and τ ρ h ντ , where h is a charged kaon or pion and is referred → to as the fourth particle. Because the τ has a high momentum, the daughter tracks all travel in the same direction resulting in a prong. The second τ decays into an electron or muon, and is geometrically separated from the ﬁrst τ. A schematic diagram of a candidate event is shown in Fig 11.10. A set of cuts are applied to select for all the tracks in a candidate event, except for the

xi Tracking Efﬁciency

Figure 11.10:• DiagramCompare of missing a candidate tracksτ decayin Data used and in MC traking for τ31 efficiency study. • No significant difference, systematic error = precision of comparison ~ 0.25%/track fourth one; i.e. only• central the pions region, and Pt > leptons 180 MeV are identified. The number of events Confirmed with ISR 4-prong events (to ~.5%/track) that pass the• selection cuts and include a fourth track is determined and the • Publication in preparation tracking efficiency given in (11.3) is calculated for both data and Monte Carlo.

xii