Searches for a Charged Higgs Boson in ATLAS and Development of Novel Technology for Future Particle Detector Systems

Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1222

DANIEL PELIKAN

ACTA UNIVERSITATIS UPSALIENSIS ISSN 1651-6214 ISBN 978-91-554-9153-6 UPPSALA urn:nbn:se:uu:diva-242491 2015 Dissertation presented at Uppsala University to be publicly examined in Polhemssalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, Friday, 20 March 2015 at 10:00 for the degree of Doctor of Philosophy. The examination will be conducted in English. Faculty examiner: Prof. Dr. Fabrizio Palla (Istituto Nazionale di Fisica Nucleare (INFN) Pisa).

Abstract Pelikan, D. 2015. Searches for a Charged Higgs Boson in ATLAS and Development of Novel Technology for Future Particle Detector Systems. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1222. 119 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-554-9153-6.

The discovery of a charged Higgs boson (H±) would be a clear indication for physics beyond the Standard Model. This thesis describes searches for charged Higgs bosons with the ATLAS experiment at CERN’s Large Hadron Collider (LHC). The first data collected during the LHC Run 1 is analysed, searching for a light charged Higgs boson (mH±

Keywords: Charged Higgs boson, Matrix Method, ATLAS, 60 GHz, future particle detector

Daniel Pelikan, Department of Physics and Astronomy, High Energy Physics, 516, Uppsala University, SE-751 20 Uppsala, Sweden.

ISSN 1651-6214 ISBN 978-91-554-9153-6 urn:nbn:se:uu:diva-242491 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-242491) List of papers

This thesis is based on the following papers, which are referred to in the text by their Roman numerals.

I The ATLAS Collaboration, + Search for charged Higgs bosons decaying√ via H → τν in top quark pair events using pp collision data at s = 7 TeV with the ATLAS detector, JHEP 1206 (2012) 039

II The ATLAS Collaboration, Search for charged Higgs bosons through the violation√ of lepton universality in ttbar events using pp collision data at s = 7 TeV with the ATLAS experiment, JHEP 03 (2013) 076

III The ATLAS Collaboration, Estimation of non-prompt and fake lepton backgrounds in√ ﬁnal states with top quarks produced in proton-proton collisions at s = 8 TeV with the ATLAS detector, ATLAS-CONF-2014-058

IV Daniel Pelikan, Nils Bingefors, Richard Brenner, Dragos Dancila, Leif Gustafsson, Wireless data transfer with mm-waves for future tracking detectors, 2014 JINST 9 C11008

V Daniel Pelikan, Nils Bingefors, Richard Brenner, Dragos Dancila, Leif Gustafsson, Radial transfer of tracking data with wireless links, PoS(TIPP2014)095 List of papers not included in this thesis:

VI The ATLAS Collaboration, Study of discriminating variables for charged Higgs boson searches in tt¯ events with leptons, using 35/pb of data from the ATLAS detector, ATLAS-CONF-2011-018

VII The ATLAS Collaboration, Search for a charged Higgs boson decaying via H+ → τlep + ν in tt¯ events with one or two light√ leptons in the ﬁnal state using 1.03/fb of pp collision data recorded at s = 7 TeV with the ATLAS detector, ATLAS-CONF-2011-151

VIII The ATLAS Collaboration, ± Search for charged Higgs bosons decaying√ via H → τν in tt¯ events using 4.6 f b−1 of collision data at s = 7 TeV with the ATLAS detector, ATLAS-CONF-2012-011

IX Daniel Pelikan, Search for charged Higgs bosons in ATLAS, EPJ Web of Conferences 28, 12057 (2012) Hadron Collider Physics Symposium (HCP) 2011

Reprints were made with permission from the publishers. Contents

1 Introduction ...... 9

2 Theoretical background ...... 11 2.1 The Standard Model of particle physics ...... 11 2.1.1 The particles of the Standard Model ...... 11 2.1.2 The Higgs mechanism ...... 14 2.2 Beyond the Standard Model (BSM) physics ...... 16 2.2.1 Phenomena not explained by the Standard Model ...... 16 2.2.2 Supersymmetry ...... 17 2.2.3 The charged Higgs bosons ...... 20 2.2.4 Production and decay of charged Higgs bosons ...... 22

3 The CERN laboratory ...... 34 3.1 Scientiﬁc achievements made by CERN ...... 34 3.2 The accelerator infrastructure ...... 34 3.2.1 Linac-2 ...... 36 3.2.2 Linac-3 ...... 36 3.2.3 Linac-4 ...... 36 3.2.4 Proton Synchrotron Booster (PSB) ...... 36 3.2.5 Proton Synchrotron (PS) ...... 36 3.2.6 Super Proton Synchrotron (SPS) ...... 36 3.3 The Large Hadron Collider (LHC) ...... 37 3.4 The four experiments at the LHC ...... 38

4 The ATLAS detector system ...... 39 4.1 Conventions ...... 39 4.2 The inner detector ...... 41 4.3 The calorimeters ...... 42 4.4 The muon spectrometer ...... 44 4.5 The trigger system ...... 46

5 Physics analysis in ATLAS ...... 47 5.1 Charged Higgs boson searches in ATLAS ...... 47 5.1.1 Measurement of discriminating variables for charged Higgs boson searches ...... 47 5.1.2 Charged Higgs boson searches in the single- and di-lepton channels ...... 48 5.1.3 Combination of the most sensitive channels for charged Higgs boson searches ...... 49 5.1.4 Charged Higgs boson searches through the violation of lepton universality ...... 50 5.1.5 Charged Higgs boson searches with the 2012 dataset ... 51 5.2 The Matrix Method ...... 51 5.2.1 The Matrix Method related to top quark and charged Higgs boson physics in ATLAS ...... 52 5.2.2 Physics analyses ...... 53

6 Future data readout challenges at LHC ...... 58 6.1 Introduction ...... 58 6.2 Wireless technology in future detector systems ...... 59 6.2.1 Choice of the frequency band for wireless data links ... 60 6.2.2 Connection concept ...... 61 6.2.3 Requirements on the antenna system ...... 62 6.3 Radiation damage to antenna substrate ...... 63 6.3.1 Effect of changes in the dielectric constant ...... 63 6.3.2 Radiation damage studies ...... 64 6.4 Outlook ...... 65

7 Wireless technology ...... 66 7.1 Electromagnetic waves ...... 66 7.2 The scattering parameter ...... 67 7.3 Antenna characteristics ...... 71 7.4 The transmission line ...... 72 7.4.1 Transmission line types ...... 72 7.4.2 Characteristic impedance of a transmission line ...... 73 7.4.3 Matched and unmatched transmission line ...... 74 7.4.4 The Smith chart ...... 75 7.4.5 Impedance matching ...... 76 7.5 Signal modulation ...... 78 7.6 The patch antenna ...... 82 7.6.1 Design steps for a patch antenna ...... 82 7.6.2 Impedance matching ...... 85 7.6.3 Design of the feeding-line ...... 86 7.6.4 Antenna simulation ...... 87 7.7 Fabrication of the antennas ...... 90 7.8 Test setup for passive repeater antennas ...... 92

8 Summary of papers ...... 95

9 Conclusion ...... 97

10 Summary in Swedish - Sammanfattning på svenska ...... 99

11 Acknowledgements ...... 102

References ...... 107

1. Introduction

One of the great philosophical questions of mankind is “Where do we come from?”. Science is trying to answer this question with the help of evolution in biology, the Big Bang in physics and many other theories. The question “Where do we come from?” can be reduced to the question “What are we made of?”. This leads to the topic of particle physics, the study of the smallest building blocks of our universe and their interaction with each other. In order to answer the question “Where do we come from?” we first need to answer a set of more fundamental questions. Part of this thesis is trying to answer some of them. The most fundamental particles that we believe exist, and their interactions with each other, are summarized in the Standard Model of particle physics. The Large Hadron Collider (LHC) and the detectors ATLAS and CMS were built to search for new physics and hunt the last missing particle of the Stan- dard Model, the Higgs boson. It was discovered in 2012 and the discovery was honoured with a Nobel Prize one year later. But there are more open questions which need to be answered. The Standard Model is not believed to be the final theory and scientists expect to find new physics beyond the Standard Model. For instance, the Standard Model does not explain gravity and is not a Grand Unified The- ory (GUT). One possible extension of the Standard Model is supersymmetry, which can include gravity, can explain dark matter, the other 95% of matter which are not Standard Model Matter, furthermore supersymmetry has the potential to be a Grand Unified Theory. Supersymmetry requires at least two Higgs doublets leading to five Higgs bosons, where two are charged and three are neutral, compared to one neutral state in the Standard Model. This thesis presents searches for charged Higgs bosons with the ATLAS experiment. Their discovery would be a clear indication for physics beyond the Standard Model. Searches for light charged Higgs bosons (lighter than the top quark mass) were performed in different channels from the beginning of LHC Run 1 until its end. With more and more data being accumulated, better exclusion limits were set and the search for the heavy charged Higgs bosons was started. The ATLAS detector system is an excellent detector for muon and electron identification, therefore many of the search channels that were chosen had leptons in their final state. One key ingredient in physics searches is the estimation of backgrounds. Some of the backgrounds are well modelled in simulation, while some others must be derived using data. One of these data driven estimated backgrounds is the amount of misidentified leptons in the final selection. This background is very difficult and computing intensive to model,

9 therefore it is estimated directly from data. The method used for the estimation is called Matrix Method. It was optimized to ﬁt the changing conditions of the ATLAS data, e.g. increasing pile-up and new detector calibrations. In order to probe physics beyond the Standard Model, colliders and experiments eventually have to reach even higher energies and interaction rates. This opens the possibility to produce particles with high masses and rare production probabilities. As a result the technology of the existing and future particle detectors has to be upgraded and research has to be done to develop these new technologies. One major problem that modern detectors face is the huge amount of information generated per collision in these systems. The high granularity of modern detectors is needed to cope with the huge amounts of generated tracks and energy deposits happening during collisions. In order to reconstruct the whole event, and not to get blinded by all the pile-up in the detector, a high resolution is essential. High granularity means many readout channels, a lot of electronics and cables needed to process or bring out the data. The electronics and cables introduce a lot of non sensitive material into the detector system and should be kept to a minimum. One way to reduce the amount of cables and connectors is the usage of wireless technology in order to read out the detector system. Other scenarios are envisaged, for example where wireless based communication between tracking hardware is placed inside the detector. In such a scenario, decisions on the interest of an event are already made before the detector is read out. With such an approach, a lot of bandwidth would be saved. The detector only needs to be read out completely if the event is really of interest for physics.

This thesis consists of two main parts, physics searches and technology development for future detectors. The physics search is introduced in chapter 2 with some theoretical background about particle physics and especially charged Higgs bosons. CERN with its accelerator infrastructure is introduced in chapter 3, and the detector system ATLAS used for the physics studies is described in chapter 4. Chapter 5 is about the physics analysis of charged Higgs bosons. The relation between physics analysis and hardware developement is explained in chapter 6, where the use of wireless technology in future detector systems is motivated by the search for new physics. Requirements on future experimental facilities and readout scenarios are presented as well as requirements on the wireless technology itself. Chapter 7 gives an introduction into wireless technology and antenna design. A summary of the papers listed in this thesis is given in chapter 8, underlining the contributions of the author. The thesis is concluded in chapter 9,followedbyasummaryinSwedishin chapter 10 for non experts.

10 2. Theoretical background

2.1 The Standard Model of particle physics

ȡȕȧȧ → Α Β ȅșȎ ΐ ΑΖΔ ǿșȎ ΐΖΒ ǿșȎ Ώ ȗȜȕȦțș → ΑΎΒ ΑΎΒ ΑΎΒ Ώ ț ȧȤȝȢ → ΐΎΑ ȩȗΐΎΑ ΐΎΑ Ȩ ΐ

ȩȤ ȗȜȕȦȡ ȨȣȤ țȠȩȣȢ

Γ Η ȅșȎ ΘΔ ȅșȎ Γ ΐΗ ǿșȎ Ώ ΐΑΔ Θ ǿșȎ ΐΎΒ ΐΎΒ ΐΎΒ Ώ γ Ώ ΐΎΑ Ș ΐΎΑ ȧ ΐΎΑ Ȗ ΐ Ώ Ȁ ȉȩȕȦȟȧ Ȁȝțțȧ ȘȣȫȢ ȧȨȦȕȢțș ȖȣȨȨȣȡ ȤȜȣȨȣȢ ȖȣȧȣȢ

Δΐΐ ȟșȎ ΐΏΔ Ζ ȅșȎ ΐ ΖΗ ǿșȎ Θΐ ΐΘ ǿșȎ ΐ ΑΎΒ μ ΑΎΒ τ Ώ ΐΎΑ ș ΐΎΑ ΐΎΑ ΐ Ȓ

șȠșȗȨȦȣȢ ȡȩȣȢ Ȩȕȩ Ȓ ȖȣȧȣȢ

ǶΑ Α șȎ ǶΏ ΐΘ ȅșȎ ǶΐΗ Α ȅșȎ ΗΏ ΒΘ ǿșȎ Ώ ν Ώ νμ Ώ ντ ɍΐ ΐΎΑ ș ΐΎΑ ΐΎΑ ΐ ȏ ȄșȤȨȣȢȧ șȠșȗȨȦȣȢ ȡȩȣȢ Ȩȕȩ ȢșȩȨȦȝȢȣ ȢșȩȨȦȝȢȣ ȢșȩȨȦȝȢȣ

ȏ ȖȣȧȣȢ ǿȕȩțș ǺȣȧȣȢȧ

Figure 2.1. Schematic illustration of the particle content of the Standard Model [1].

2.1.1 The particles of the Standard Model The Standard Model (SM) of elementary particles [2, 3, 4] was developed in the 1960s and 1970s. It is a theory describing the fundamental constituents, the building blocks of matter and their interactions through electromagnetic, strong and weak forces. The matter particles are elementary, which means that they do not have a substructure. They are called fermions and have half integer spin, they can be further categorized into leptons and quarks. The force carriers are bosons, particles with an integer spin. A schematic illustration of the particle content of the Standard Model is given in ﬁgure 2.1.

11 The fermions are organized in three families. The LEP experiments showed that there are no more than three families with light neutrinos (mν < mZ/2) in the SM [5]. Each family consists of two quarks and two leptons. The quarks can be categorized into one up-type quark and one down-type quark, the leptons into a electron like lepton and a neutrino. The up-type quark carries + 2 − 1 an electric charge of 3 e and the down type quark an electric charge of 3 e. The massive leptons (electron, muon and tau) have an electric charge of −1e. Neutrinos are electrically neutral and much lighter than the charged leptons. All particles with an electric charge interact electromagnetically. All fermions interact weakly, but the neutrinos have the weak force as their only way to interact. Quarks, unlike leptons, also carry a colour charge, which is the quanta of the strong interaction. Quarks come in three colours, “red”, “green” and “blue”, additionally they only exist in a confined state for which the sum of the colour charges is white. Baryons are bound states of three quarks, or three anti- quarks. Mesons are composed of a quark and anti-quark pair. In other words, the colour white can be achieved by combining one of each red, green and blue (or anti-red, anti-green and anti-blue) quarks, or by adding a colour and the corresponding anti-colour. The gauge bosons are the force carriers. The photon, γ is the carrier of the electromagnetic force, the W and Z bosons are the carriers of the weak force and the gluons, g are the carriers of the strong force. The Higgs boson is the last boson in the SM, and was discovered in 2012 by the ATLAS and CMS collaborations [6, 7]. It is different from the gauge bosons and its role in the SM will be explained in 2.1.2. Figure 2.2 shows the distribution of the four-lepton invariant mass m4l measured by ATLAS and the invariant mass of diphoton candidates measured by CMS, as a selection of channels in which the Higgs boson with a mass of around 125 GeV was discovered. These are the golden channels for Higgs boson seaches, since the backgrounds in these channels are very low. In order to get enough sensitivity to claim a discovery, both experiments combined several channels (H → γγ, H → ZZ, H → WW, H → ττ, H → bb). The local p0 value [8] with respect to the Higgs boson mass of the combination is shown in figure 2.3 for both ATLAS and CMS. The p0 value is a measure of the significance at which the null hypothesis (SM without a Higgs boson) would be rejected. The smaller the p0-value, the stronger the evidence to favour an alternative hypothesis. Lines of sigma levels (the number of statistical fluctuations of the background) are shown in the plot to guide the translation from p0-value to sigma level [9]. As can be seen almost 6σ in ATLAS and 5σ in CMS are reached. The 5σ level means that a new particle was discovered, with 99.9999% probability and < 0.0001% probability it is just a background fluctuation.

12 &06 V 7H9/ IE V 7H9/ IE

Data 9

ATLAS H (*) 8QZHLJKWHG 25 Background ZZ (*) * H→ZZ →4l Background Z+jets, tt Signal (m =125 GeV) 20 H YHQWV Events/5 GeV Syst.Unc. ( ∫ -1 15 s = 7 TeV: Ldt = 4.8 fb P γγ *H9 s = 8 TeV: ∫Ldt = 5.8 fb-1 10 'DWD 6%)LW %)LW&RPSRQHQW 5 ±σ ± σ 0 6 6% :HLJKWHG(YHQWV*H9 100 150 200 250 P γγ *H9 m4l [GeV] (a) ATLAS (b) CMS

Figure 2.2. Four-lepton invariant mass, m4l, for the selected candidates, measured in ATLAS (left). The data with error bars is shown in black while the background and signal expectation from simulation are shown in colours [6]. Invariant mass distribution of di-photon candidates in CMS (right) [7]. Note that these plots are not with the full 2012 dataset, these are the plots from the discovery paper, plots with the full 2012 dataset can be found in: [10, 11].

CMS s = 7 TeV, L = 5.1 fb-1 s = 8 TeV, L = 5.3 fb-1 1 1σ 2σ 0 10-2 ATLAS 2011 - 2012 3σ 1 -1 10 10-4 σ Local p -2 4 10 2 σ Local p-value -3 10 3 σ -6 ∫ -1 10 σ 10-4 s = 7 TeV: Ldt = 4.6-4.8 fb 5 -5 -1 4 σ 10 s = 8 TeV: ∫Ldt = 5.8-5.9 fb -8 Combined obs. 10-6 10 Exp. for SM H 6σ 10-7 5 σ H γγ→ Sig. Expected → 10-8 -10 H ZZ Observed 10 H → WW -9 H ττ→ 10 6 σ -10 H → bb 7σ 10 10-12 110 150 200 300 400 500 110 115 120 125 130 135 140 145 m [GeV] H mH (GeV) (a) ATLAS (b) CMS

Figure 2.3. Combined search results of the observed (solid) local p0 as a function of the Higgs boson mass mH and the expectation (dashed) for a SM Higgs boson signal hypothesis at the given mass for ATLAS (left) [6]. On the right side the observed local p0 for the ﬁve decay modes (H → γγ, H → ZZ, H → WW, H → ττ, H → bb)which were combined and the overall combination as a function of the SM Higgs boson mass [7]. Note that these plots are not with the full 2012 dataset, these are the plots from the discovery paper.

13 2.1.2 The Higgs mechanism In a local gauge theory the gauge boson ﬁelds are massless, because of the gauge symmetry. From experiments it is known [12, 13, 14, 15] that the gauge bosons, except the photon and gluons, have masses. Introducing explicit mass terms in the SM generates problems with gauge invariance and renormalization, making it impossible to predict observables with good accuracy. Hence, there has to be a different mechanism to introduce mass into the SM. This can be done by introducing spontaneous symmetry breaking [16, 17]. Particle physics is based on Quantum Field Theory (QFT) [18] and the Higgs mechanism will be derived on the principals of QFT in the following: A complex Higgs SU (2) doublet Φ (x) Φ(x)= a (2.1) Φb(x) is included in the SM, with a SU (2) ×U(1) invariant Lagrangian:

H μ † L (x)=[D Φ(x)] [Dμ Φ(x)] −V(Φ), (2.2) where Φ† is the Hermitian adjoint of Φ and V (Φ) is the Higgs potential of the form: V (Φ)=μ2(Φ†(x)Φ(x)) + λ(Φ†(x)Φ(x))2. (2.3) With the boundary conditions μ2 < 0andλ > 0, the potential becomes the Mexican hat shaped potential shown in ﬁgure 2.4. Dμ is the gauge covariant derivative, containing the interaction terms which lead to the gauge bosons W, Z and γ. μ and λ are real parameters.

Figure 2.4. The Higgs potential, the minimum has a non zero value.

The Mexican hat potential has a continuum of minima. The electroweak symmetry can be broken by choosing one minimum using the freedom of a

14 global SU (2) rotation. A convenient choice for such a vacuum state is: Φ0 μ2 Φ = a = √1 0 = − 0 Φ0 with v λ (2.4) b 2 v Expanding around the vacuum state gives: η ( )+ η ( ) Φ( )= √1 1 x i 2 x x + σ( )+ η ( ) (2.5) 2 v x i 3 x where ηi(x) and σ(x) are scalar fields. Using this equation in the Lagrangian yields mass terms, by spontaneous symmetry breaking, for the gauge bosons. After diagonalising, the W and Z bosons aquire masses, while the photon γ remains massless. The surviving μ2 field σ(x), with a vacuum expectation value of v = − λ ≈ 246 GeV [1], the average expected value in the vacuum, gives rise to a massive, electrically neutral, spin-0 particle, called the Higgs boson. It should be noted that the vacuum state is not SU (2) gauge invariant, even though the Lagrangian is. This is called spontaneous symmetry breaking. More details of the derivation can be found in [18]. Yukawa couplings, the interactions between a scalar field and a Dirac field, i.e. between the Higgs field and the fermions, indicates the mass scale of the quarks and leptons in the SM. The fermion masses can be generated using the scalar field Φ, with hyper- ∗ charge Y = 1, and the isodoublet Φ˜ = iτ2Φ with a hypercharge Y = −1. τ2 is the second Pauli matrix1. For any fermion generation, the SU (2)L × U(1)Y invariant Yukawa La- grangian can be introduced [19]:

LF = −λeL¯ΦeR − λdQ¯ΦdR − λuQ¯Φ˜ uR + h.c. (2.6) where L¯ and Q¯ are the isodoublets of the left-handed fermions for leptons and quarks, respectivly and eR, uR and dR are the isosinglets of the right- handed fermions for leptons, up-type quarks and down-type quarks. After gauge transformation the Lagrangian can be written in the form: 1 LF = −√ λ f (v + σ) f¯L fR + h.c. (2.7) 2

The constant term in front of the fermion isosinglets f¯L fR is the mass of the fermion:

λev λuv λdv me = √ , mu = √ , md = √ (2.8) 2 2 2 01 0 −i 10 1Pauli matrices: τ = , τ = , τ = 1 10 2 i 0 3 0 −1

15 2.2 Beyond the Standard Model (BSM) physics Even though the SM is a very successful theory, it is not believed to be the ﬁnal theory for describing matter and the fundamental interactions. It is regarded as a theory which is valid up to a certain energy level. There are other theories beyond the SM which try to explain phenomena which can not be accounted for by the SM. Example of these theories are supersymmetric models (see section 2.2.2) like the Minimal Supersymmetric Standard Model (MSSM) [20] and Next-to-Minimal Supersymmetric Standard Model (NMSSM) [21], Little Higgs models [22], String Theory [23], Technicolour [24] and Extra Dimen- sion [25]. All these theories contain the SM, but are more general. Which of these theories best describes physics beyond the SM, can only be veriﬁed experimentally.

2.2.1 Phenomena not explained by the Standard Model There are several phenomena which can not be explained by the SM but with a possible explanation or solution in one of the extensions of the SM. The most prominent ones are mentioned in the following: Dark matter and dark energy: Observations of the cosmic microwave background show that the SM can explain around 5% of the energy content in the universe. It is believed that around 27% is dark matter and 68% is dark energy [26]. The existence and properties of dark matter are studied from its gravitational effects on visible matter, radiation and large-scale structures of the universe. Dark Energy is used to explain the acceleration of the expansion of the universe. Matter anti-matter asymmetry: The universe is mainly made of matter, e.g. particles, not anti-particles. The SM predicts that matter and anti-matter were produced in almost equal amounts in the Big Bang. Charge Parity (CP) Violation in the SM, the effect that matter does not exactly behave in the same way as anti-matter under CP transformation, can account for some but not the full SM matter in our universe. Hence the reason for the matter anti-matter asymmetry must be phenomena not explained by the SM [27]. Three generations: From the Z-boson measurements it is known that there are exactly three generations of matter particles. However, the SM does not explain why [5]. Grand Unification Theory (GUT): There are three gauge symmetries in the SM corresponding to the three fundamental forces. The coupling constants of these interactions vary with energy and become approximately equal around 1016 GeV. That is why it is expected that the three symmetries unite into one single gauge symmetry above this energy. Below the threshold of around 1016 GeV the symmetry is spontaneously broken into the three SM symmetries [28]. This unification can be included in supersymmetric models, see figure 2.5.

16 (a) Standard Model (b) SUSY Model Figure 2.5. Evolution of the SU(3) × SU(2) ×U(1) gauge couplings to high energy scales, using the one-loop renormalization group equation of the SM (left) and the supersymmetric generalization of the SM (right) [28].

Hierarchy problem: In the SM, masses of particles are introduced by spontaneous symmetry breaking caused by the Higgs field. Due to the presence of virtual particles, the Higgs mass requires large quantum corrections in the SM. These corrections are significantly larger than the measured Higgs boson mass, which requires that the mass parameter of the Higgs boson in the SM is fine-tuned in order to cancel the quantum corrections. This requirement of fine-tuning is considered unnatural. Quantum gravity: Gravity is not included in the SM. Adding gravity to the SM is not possible as it generates unphysical effects like particle velocities higher than the speed of light, and further modifications would be needed. The most successful theory (General Relativity) is incompatible with the SM [29]. Gravity acts on a macroscopic scale, therefore the SM predictions are not af- fected by it. Neutrino mass: In the SM neutrinos are massless and cannot change flavour. The observed number of electron neutrinos arriving from the sun is much smaller than the number predicted by the Standard Solar Model [30], this is called the solar neutrino problem. To solve this problem neutrinos need to have mass, in order to oscillate between flavours [31].

2.2.2 Supersymmetry Some of the problems described in section 2.2.1 can be solved by supersymmetry (SUSY). SUSY is a proposed extension of space-time described by the Poincaré group, which relates boson and fermion ﬁelds to each other. Each particle from one group has a “superpartner” in the other group, with a spin difference of a half-integer. This generates at least a doubling of the SM particle spectrum. If SUSY exists, and would be unbroken, every particle in the

17 SM would have a superpartner. This superpartner would have exactly the same mass as its SM counterpart and should have therefore already been discovered. This means that, assuming SUSY exists, it has to be broken. Superpartners could exist with higher masses compared to SM particles. Considering SUSY as a true symmetry of nature, the Hierarchy problem would be solved since the quantum corrections are cancelled by those from the corresponding superpartners above the SUSY breaking scale. Also the dark matter problem can be solved since SUSY can provide a dark matter candidate particle. The light- est supersymmetric particle, provided there exists a conservation law which forbids its decay into SM particles, could be a good candidate for dark matter. SUSY is also a Grand Uniﬁcation Theory, since within SUSY the weak, strong and electromagnetic interactions can be uniﬁed at high-energy [28]. Also quantum gravity can be included in Local Supersymmetric Models.

Minimal Supersymmetric Standard Model The Minimal Supersymmetric Standard Model (MSSM) is the most economic implementation of SUSY beyond the SM in terms of new particles and additional parameters. It is one of the best studied candidates for physics beyond the SM and was introduced in 1981 to stabilize the weak scale and solving the hierarchy problem [32]. As described in the previous section, SUSY associates bosons with fermions. In the MSSM, the supersymmetric scalars are named after the corresponding fermion in the SM. For each fermion in the SM, there are two scalar fermions (sfermion) in the MSSM to account for left-handed and right-handed states in the SM. For the gauge bosons in the SM, there are half-integer spin gaugions in the MSSM. These superpartners are named after the gauge eigenstate in the SM with an added “-ino” sufﬁx: Bino, Wino and gluino. The Bino and the Wino mix with the half-integer spin superpartners of the Higgs boson, the χ0,χ0,χ0,χ0 Higgsinos. There are four Neutralinos mass eigenstates ( 1 2 3 4 ), which are fermions and are electrically neutral. They are a mixture of the Bino, the neutral Wino and the neutral Higgsinos. The two Chargino mass eigenstates χ±,χ± ( 1 2 ) are electrically charged fermions. They are a mixture of the charged Wino and charged Higgsinos. A single Higgsino would lead to a gauge anomaly, i.e. not a good symmetry. If two Higgsinos are added, this gauge anomaly is solved. The simplest approach is one with two Higgsinos and two scalar Higgs doublets. Also in order to have Yukawa couplings between the Higgs boson and both down- and up-type quarks, two scalar Higgs doublets are needed. The strength of the mixing of left-handed and right-handed sfermions is given by the mass of the corresponding SM fermion. The particle content of the MSSM is given in table 2.1. So far no evidence for SUSY has been observed [34, 35, 36, 37, 38, 39, 40] as can be seen in ﬁgure 2.6.

18 h aes[ papers the 2.6. Figure

ATLAS SUSY Searches* - 95% CL Lower Limits ATLAS√ Preliminary Status: ICHEP 2014 s =7,8TeV − e,μ,τ,γ Emiss L dt[fb 1] Model Jets T Mass limit Reference

MSUGRA/CMSSM 0 2-6 jets Ye s 20.3 q˜, g˜ 1.7 TeV m(q˜)=m(g˜) 1405.7875 MSUGRA/CMSSM 1 e,μ 3-6 jets Ye s 20.3 g˜ 1.2 TeV any m(q˜) ATLAS-CONF-2013-062 34

iiso UYsace rmALS h lti oplto from compilation a is plot The ATLAS. from searches SUSY on Limits MSUGRA/CMSSM 0 7-10 jets Ye s 20.3 g˜ 1.1 TeV any m(q˜) 1308.1841 χ0 χ˜0 st . nd . q˜q˜, q˜→q ˜1 0 2-6 jets Ye s 20.3 q˜ 850 GeV m( 1)=0 GeV, m(1 gen ˜q)=m(2 gen ˜q) 1405.7875 , χ0 χ˜0 g˜g˜, g˜→qq¯ ˜1 0 2-6 jets Ye s 20.3 g˜ 1.33 TeV m( 1)=0 GeV 1405.7875 35 ± ± χ ±χ0 ,μ χ˜0 < χ˜ χ˜0 g˜g˜, g˜→qq ˜1 →qqW ˜1 1 e 3-6 jets Ye s 20.3 g˜ 1.18 TeV m( 1) 200 GeV, m( )=0.5(m( 1)+m(g˜)) ATLAS-CONF-2013-062 χ0 ,μ χ0 g˜g˜, g˜→qq(/ν/νν) ˜ 2 e 0-3 jets - 20.3 g˜ 1.12 TeV m( ˜1)=0GeV ATLAS-CONF-2013-089

, 1 GMSB (˜ NLSP) 2 e,μ 2-4 jets Ye s 4 . 7 g˜ 1.24 TeV tanβ<15 1208.4688 36 GMSB (˜ NLSP) 1-2 τ +0-1 0-2 jets Ye s 2 0 . 3 g˜ 1.6 TeV tanβ>20 1407.0603 γ χ0 GGM (bino NLSP) 2 - Ye s 20.3 g˜ 1.28 TeV m( ˜1)>50 GeV ATLAS-CONF-2014-001 , 0 GGM (wino NLSP) 1 e,μ+ γ - Ye s 4 . 8 g˜ 619 GeV m(χ˜ )>50 GeV ATLAS-CONF-2012-144

Inclusive Searches 1 37 γ χ0 GGM (higgsino-bino NLSP) 1 b Ye s 4.8 g˜ 900 GeV m( ˜1)>220 GeV 1211.1167 GGM (higgsino NLSP) 2 e,μ(Z) 0-3 jets Ye s 5 . 8 g˜ 690 GeV m(NLSP)>200 GeV ATLAS-CONF-2012-152 , − Gravitino LSP 0 mono-jet Ye s 10.5 1/2 scale 645 GeV m(G˜)>10 4 eV ATLAS-CONF-2012-147

38 F χ0 χ˜0 < g˜→bb¯ ˜1 03b Ye s 2 0 . 1 g˜ 1.25 TeV m( 1) 400 GeV 1407.0600 , 0 0 → χ˜ 0 7-10 jets Ye s 20.3 g˜ 1.1 TeV m(χ˜ ) <350 GeV 1308.1841 gen. g˜ tt¯ 1 1 39

med. 0 0 → ¯χ˜ 0-1 e,μ 3 b Ye s 2 0 . 1 g˜ 1.34 TeV m(χ˜ )<400 GeV 1407.0600 rd g˜ tt 1 1 ˜ g + 0 3 χ ,μ χ < g˜→bt¯˜1 0-1 e 3 b Ye s 20.1 g˜ 1.3 TeV m( ˜1) 300 GeV 1407.0600 , 0 χ0 40 ˜ ˜ ˜ → χ˜ 0 2 b Ye s 2 0 . 1 b˜ 100-620 GeV m( ˜ )<90 GeV 1308.2631 b1b1, b1 b ±1 1 1 χ ,μ ˜ χ± χ0 b˜1b˜1, b˜1→t ˜1 2 e (SS) 0-3 b Ye s 20.3 b1 275-440 GeV m( ˜1 )=2 m( ˜1) 1404.2500 ± 0 ]. → χ ,μ ˜ χ t˜1t˜1(light), t˜1 b ˜1 1-2 e 1-2 b Ye s 4.7 t1 110-167 GeV m( ˜1)=55 GeV 1208.4305, 1209.2102 χ0 ,μ ˜ χ˜0 << χ˜± t˜1t˜1(light), t˜1→Wb˜1 2 e 0-2 jets Ye s 20.3 t1 130-210 GeV m( 1)=m(t˜1)-m(W)-50 GeV, m(t˜1) m( 1 ) 1403.4853 0 0 ˜ ˜ ˜ → χ˜ 2 e,μ 2jets Ye s 20.3 t˜ 215-530 GeV m(χ˜ )=1 GeV 1403.4853 t1t1(medium), t1 t 1± 1 1 → χ χ0 < χ± χ0 t˜1t˜1(medium), t˜1 b ˜1 0 2 b Ye s 20.1 t˜1 150-580 GeV m( ˜1) 200 GeV, m( ˜1 )-m( ˜1)=5 GeV 1308.2631 χ0 ,μ ˜ χ˜0 t˜1t˜1(heavy), t˜1→t ˜1 1 e 1 b Ye s 20 t1 210-640 GeV m( 1)=0 GeV 1407.0583 gen. squarks χ0 ˜ χ˜0 t˜1t˜1(heavy), t˜1→t ˜1 0 2 b Ye s 20.1 t1 260-640 GeV m( 1)=0 GeV 1406.1122

rd χ0 χ0 ˜ ˜ ˜ → ˜ 0 mono-jet/c-tag Ye s 20.3 t˜1 90-240 GeV m(t˜ )-m( ˜ )<85 GeV 1407.0608 3 direct productiont1t1, t1 c 1 1 1 ,μ χ0 t˜1t˜1(natural GMSB) 2 e (Z) 1 b Ye s 2 0 . 3 t˜1 150-580 GeV m( ˜1)>150 GeV 1403.5222 → + ,μ χ0 t˜2t˜2, t˜2 t˜1 Z 3 e (Z) 1 b Ye s 20.3 t˜2 290-600 GeV m( ˜1)<200 GeV 1403.5222 χ0 ,μ χ0 ˜L,R˜L,R, ˜→ ˜1 2 e 0 Yes 20.3 ˜ 90-325 GeV m( ˜1)=0 GeV 1403.5294 + − + χ± 0 ± 0 χ˜ χ˜ , χ˜ →ν˜ (ν˜) 2 e,μ 0 Ye s 20.3 ˜ 140-465 GeV m(χ˜ )=0 GeV, m(,˜ ν˜)=0.5(m(χ˜ )+m(χ˜ )) 1403.5294 +1 −1 +1 ±1 1 1 1 χ χ χ →τν τν τ - χ˜ χ˜0 τ, ν χ˜± χ˜0 ˜ 1 ˜1 , ˜1 ˜ ( ˜) 2 Ye s 2 0 . 3 1 100-350 GeV m( 1)=0 GeV, m(˜ ˜)=0.5(m( 1 )+m( 1)) 1407.0350 χ±χ0 ,μ χ±, χ0 χ± χ0 χ0 χ± χ0 ˜ ˜ →˜ ν˜ (˜νν),ν˜˜ (˜νν) 3 e 0 Ye s 20.3 ˜ ˜ 700 GeV m( ˜1 )=m( ˜2), m( ˜1)=0, m(,˜ ν˜)=0.5(m( ˜1 )+m( ˜1)) 1402.7029 EW 1 2 L L L 1 2 ± ± 0 ± direct χ χ0 χ0 χ0 ,μ χ , χ χ χ0 χ0 ˜ ˜ →W ˜ Z ˜ 2-3 e 0Yes20.3˜ ˜ 420 GeV m( ˜1 )=m( ˜2), m( ˜1)=0, sleptons decoupled 1403.5294, 1402.7029 ±1 2 1 1 1± 2 ± χ χ0→ χ0 χ0 1 ,μ χ˜ , χ˜ 0 χ˜ χ˜0 χ˜0 ˜ 1 ˜2 W ˜1h ˜ 1 e 2 b Ye s 20.3 1 2 285 GeV m( 1 )=m( 2), m( 1)=0, sleptons decoupled ATLAS-CONF-2013-093 χ0χ0 χ0 → ,μ χ˜ 0 χ˜0 χ˜0 χ˜0 ,˜ ν χ˜0 χ˜0 ˜ 2 ˜ 3, ˜ 2,3 ˜R 4 e 0 Yes 20.3 2,3 620 GeV m( 2)=m( 3), m( 1)=0, m( ˜)=0.5(m( 2)+m( 1)) 1405.5086 + − ± ± χ˜ χ˜ χ˜ χ˜ χ˜± χ˜0 = τ χ˜± = Direct 1 1 prod., long-lived 1 Disapp. trk 1 jet Ye s 20.3 1 270 GeV m( 1 )-m( 1) 160 MeV, ( 1 ) 0.2 ns ATLAS-CONF-2013-069 χ0 Stable, stopped g˜ R-hadron 0 1-5 jets Ye s 2 7 . 9 g˜ 832 GeV m( ˜1)=100 GeV, 10 μs<τ(˜g)<1000 s 1310.6584 τ χ0→τ , μ τ ,μ 1-2 μ -- χ˜ 0 100.2×m( ˜ ), λ 0 1405.5086 1 1 1 1 1 e ±1 1 1 121 RPV + − + ± χ χ χ → χ0, χ0→ττν , τν 3 ,μ+ τ - χ˜ χ˜0 > × χ˜ λ ˜ 1 ˜1 , ˜1 W ˜1 ˜ 1 ˜e e ˜τ e Ye s 20.3 1 450 GeV m( 1) 0.2 m( 1 ), 133 0 1405.5086 g˜→qqq 0 6-7 jets - 20.3 g˜ 916 GeV BR(t)=BR(b)=BR(c)=0% ATLAS-CONF-2013-091 g˜→t˜1t, t˜1→bs 2 e,μ(SS) 0-3 b Ye s 20.3 g˜ 850 GeV 1404.250

Scalar gluon pair, sgluon→qq¯ 0 4jets - 4.6 sgluon 100-287 GeV incl. limit from 1110.2693 1210.4826 Scalar gluon pair, sgluon→tt¯ 2 e,μ(SS) 2 b Ye s 14.3 sgluon 350-800 GeV ATLAS-CONF-2013-051 WIMP interaction (D5, Dirac χ) 0 mono-jet Ye s 1 0 . 5 M* scale 704 GeV m(χ)<80 GeV, limit of<687 GeV for D8 ATLAS-CONF-2012-147 Other √ √ √ s =7TeV s =8TeV s =8TeV 10−1 1 full data partial data full data Mass scale [TeV] 19 *Only a selection of the available mass limits on new states or phenomena is shown. All limits quoted are observed minus 1 σ theoretical signal cross section uncertainty. Table 2.1. The proposed particles in the MSSM [33].

Names Spin R-parity (PR) Gauge Eigenstates Mass Eigenstates + 0 0 + − 0 0 0 ± Higgs bosons 0 1 Hu Hd Hu Hd h H A H uL uR dL dR (same) squarks 0 −1 sL sR cL cR (same) tL tR bL bR t1 t2 b1 b2 eL eR νe (same) sleptons 0 −1 μL μR νμ (same) τL τR ντ τ1 τ2 ντ / − 0 0 0 0 χ0 χ0 χ0 χ0 neutralinos 1 2 1 B W Hu Hd 1 2 3 4 / − ± + − χ± χ± charginos 1 2 1 W Hu Hd 1 2 gluino 1/2 −1 g (same) goldstino 1/2 − (gravitino) (3/2) 1 G (same)

2.2.3 The charged Higgs bosons Charged Higgs bosons are predicted by many models beyond the SM. The Two-Higgs-Doublet Model (2HDM) is an extension of the SM and together with the MSSM one important extension of the Higgs sector. As described in the previous section, the MSSM requires at least two Higgs doublets to prevent gauge anomalies. Because of this, two charged Higgs bosons and three neutral Higgs bosons exist in this 2HDM model after absorption of three degrees of freedom to give mass to W +, W − and Z gauge bosons. But also theories with even more than two Higgs doublets exist. For example the NMSSM [21] contains two Higgs doublets and a Higgs singlet, leading to seven Higgs bosons. A problem that arrises when adding too many Higgs ﬁelds is that the relation between the W and Z mass,

mW 2 mZ = with θW the Weinberg angle [41] (2.9) tanθW without ﬁne-tuning, is not represented correctly [42]. SUSY favours a 2HDM as the minimal necessary extension. In the 2HDM, the Higgs mechanism works similarly to the SM Higgs mechanism, as described in section 2.1.2.

The Two-Higgs-Doublet Model One extension of the Higgs sector is to consider two Higgs doublets [43, 44]. By introducing two complex, SU (2) doublet scalar ﬁelds Φ1 and Φ2 with hypercharge Y = 1 the Higgs potential can be written as [45]:

2The Weinberg angle also called weak mixing angle is a parameter in electroweak interaction theory. Spontaneous symmetry breaking rotates the original W 0 and B0 vector boson plane by the Weinberg angle, producing as a result the Z0 boson, and the photon.

20 (Φ ,Φ )= 2 Φ†Φ + 2 Φ†Φ − 2 Φ†Φ + V 1 2 m11 1 1 m22 2 2 m12 1 2 h.c. (2.10) 2 † † 1 † + λ4 Φ Φ2 Φ Φ1 + λ5 Φ Φ2 1 2 2 1 + λ Φ†Φ + λ Φ†Φ Φ†Φ + 6 1 1 7 2 2 1 2 h.c

In this potential λi are real parameters and mij are parameters related to mass. The minimum of the potential is given when all λi ≥ 0 by: 1 0 1 0 < Φ1 >= √ ,<Φ2 >= √ (2.11) 2 v1 2 v2 The potential is gauge invariant, which guarantees the correct pattern of electroweak symmetry breaking over a large range of parameters. Φ1 and Φ2 contain the physical Higgs bosons. √ 1 2(G+ cosβ − H+ sinβ) Φ = √ , (2.12) 1 vcosβ − hsinα + H cosα + i(G0 cosβ − Asinβ) 2 √ 1 2(G+ sinβ + H+ cosβ) Φ2 = √ (2.13) 2 vsinβ − hcosα + H sinα + i(G0 sinβ + Acosβ)

G+ and G0 are charged and neutral Goldstone bosons, the parameter α is the mixing angle between the mass eigenstates h and H,tanβ is the ratio of the vacuum expectation values v1 and v2, one of the key parameters of this model: v tanβ = 2 (2.14) v1 A detailed description of the derivations leading to equation (2.10)-(2.14)can be found in [45, 46]. There exist four types of 2HDM model (I - IV). They differ in the way the up-type quarks, down-type quarks and leptons couple to (and get mass from) the two Higgs doublets ﬁelds Φ1 and Φ2. One example how the physical Higgs bosons in the 2HDM couple to fermions is: 1 ( f ) ( f ) √ F¯ κ sin(β − α)+ρ cos(β − α) fRh, (2.15) 2 the couplings of H, H± and A are left out for simplicity. ¯ ¯ F stands for the isodoublets L and Q of the left-handed√ fermions, fR are the ( ) κ( f ) = 2m f = 2 + 2 right handed isosinglets eR, uR and dR, v with v v1 v2. The different types correspond to the different expressions for ρ( f ) in table 2.2.

21 Table 2.2. Coupling of the two Higgs doublets Φ1 and Φ2 in the 2HDM to the leptons (eR) and up-type (uR) and down-type quark (dR). The coupling strength is described by the Yukawa-matrices ρ. (u) (d) (e) uR dR eR ρ ρ ρ (u) (d) (e) Type I Φ2 Φ2 Φ2 κ cotβκcotβκcotβ (u) (d) (e) Type II Φ2 Φ1 Φ1 κ cotβ −κ tanβ −κ tanβ (u) (d) (e) Type III (Flipped) Φ2 Φ1 Φ2 κ cotβ −κ tanβκcotβ (u) (d) (e) Type IV (Lepton-speciﬁc) Φ2 Φ2 Φ1 κ cotβκcotβ −κ tanβ

MSSM Higgs Sector The MSSM is a Type-II 2HDM where the vacuum expectation values of the two Higgs ﬁelds are given by: 0 0 < Φ1 >= ,<Φ2 >= (2.16) v1 v2

The phase of the Higgs doublet ﬁelds are chosen so that v1 and v2 are real and non-negative. There is no CP violation in the Higgs sector. For v1,v2 > 0 the parameter tanβ is limited by 0 ≤ β ≤ π/2.

The 2HDM model has ﬁve physical Higgs bosons: • two charged Higgs bosons H±; • 0 0 > two neutral CP-even Higgs boson scalars H and h where mH0 mh0 ; • one neutral Higgs boson A0 which is a CP-odd pseudoscalar.

At tree level in the MSSM, the properties of the ﬁve Higgs bosons can be expressed by only two parameters. Commonly used are tanβ and one of the Higgs masses. 0 ± β An expression relating the two gauge boson masses (mZ, mW ), tan and the Higgs boson mass mA is given by [47]: 1 m2 = m2 + m2 ∓ (m2 + m2 )2 − 4m2 m2 cos2 2β (2.17) h0,H0 2 A Z0 A Z0 A Z0

2 = 2 + 2 mH± mA0 mW ± (2.18)

2.2.4 Production and decay of charged Higgs bosons

Charged Higgs bosons with a mass lighter than the top quark mass mt are dominantly produced at the LHC through gluon-gluon fusion in which top quark pairs are created with at least one top quark decay into a light charged Higgs boson instead of a W

gg → tt¯ → H+bW −b¯, H+bH−b¯ and W +bH−b¯. (2.19)

22 For higher charged Higgs boson masses, the charged Higgs boson is directly produced. In the four-flavour scheme (4FS) there are no b quarks in the initial state, they are non-partonic [48], and therefore the lowest-order QCD production processes are gluon-gluon fusion and quark-antiquark annihilation, gg → tbH± and qq¯ → tbH±, (2.20) respectively. In the five-flavour scheme (5FS), the leading order process for the inclusive tbH± cross-section is gluon-bottom fusion, gb → tH±. (2.21) If all orders in perturbation theory were taken into account the 4FS and the 5FS would be identical, but the way of ordering the perturbative expansion is different. At any finite order, the two schemes include different parts of the all-order result which makes the cross-section predictions not fit exactly and leads to ambiguities [49]. The Feynman diagrams of the production processes for the light and heavy charged Higgs bosons are shown in figure 2.7.

g b g H+ g b

H+ ¯b g t ¯b∗ H+

t¯ W − t

g ¯b ¯b t¯ t¯ g Figure 2.7. Production of light charged Higgs bosons in tt¯ pairs via gluon-gluon fusion (left), the production of heavy charged Higgs bosons in gluon-b-quark fusion (center) and gluon-gluon fusion (right).

The MSSM parameter space has a large number of free parameters making a compleate scan impractical in experimental and phenomenological studies. Therefore charged Higgs boson searches are often interpreted in benchmark scenarios. In these scenarios only the two parameters that enter the Higgs sec- β tor tree-level predictions, MH± and tan are varied. Other SUSY parameters, entering via radiative corrections, are fixed to particular benchmark values, exhibiting certain features of the MSSM charged Higgs boson phenomenol- max ogy. One of these benchmark scenarios is the mh scenario, described in the next section in detail, which is used for some of the performance plots in this section. Charged Higgs bosons lighter than the top quark mass decay dominantly to τν as can be seen in figures 2.8 and 2.9. The cross-section and branching ratio for a top quark decaying into a charged Higgs boson as a function of the H± mass and tanβ is shown in figure 2.10.

23 Figure 2.8. Branching ratios of the MSSM charged Higgs bosons with tanβ = 3[50].

0 0 10 10

-1 -1

10 LHC Higgs XS WG 2013 10 LHC Higgs XS WG 2013 ) ) +- +- max max -2 β -2 β mh , tan = 10 mh , tan = 50 10 ± 10 ± BR(H -> tb) BR(H -> tb) BR(H BR(H BR(H -> cs) BR(H -> cs) τ ν τ ν BR(H -> τ) BR(H -> τ) μ ν μ ν BR(H -> μ) BR(H -> μ) -3 -3 10 10

-4 -4 10 10 100 200 300 400 500 600 100 200 300 400 500 600 +- +- MH [GeV] MH [GeV] (a) BR for tanβ = 10 (b) BR for tanβ = 50 max Figure 2.9. Branching ratios of the charged MSSM Higgs boson in the mH scenario as a function of charged Higgs boson mass. The left (right) column shows the results for tanβ = 10(50) [51].

24 40 ) 0.1 ±

max bH 0.09 mh : mt(mt) = 166.8 GeV, mb(mt) = 2.31 GeV FeynHiggs → tanβ = 5 0.08 tanβ = 10 b) * 2 [pb] HDECAY LHC HIGGS XS WG 2011 WG XS HIGGS LHC BR(t 30 LHC Higgs XS WG 2011 + tanβ = 30 0.07 tanβ = 50 μ 0.06 = 200 GeV 0.05 20 b) BR(t -> W + 0.04

= 100 GeV ± 0.03 H m ± = 120 GeV H 10 0.02 m ± = 140 GeV m H 0.01 ± = 160 GeV mH (pp -> tt) BR(t H

σ 0 0 1020304050 0 β 100 110 120 130 140 150 160 tan ± MH [GeV] ± ± ± (a) σtt · BR(t → bH ) · BR(t → bW ) · 2 (b) BR(t → bH ) ± ± Figure 2.10. Left: The cross-section σtt · BR(t → bH ) · BR(t → bW ) · 2 including uncertainties, where different tanβ regions are indicated with different colours. Right: ± The branching fraction BR(t → bH ) calculated with FEYNHIGGS and HDECAY as a function of tanβ [52].

A charged Higgs boson that is heavier than the top quark, will in the MSSM decay dominantly into tb. The cross-section for direct heavy charged Higgs boson production is shown in ﬁgure 2.11. In this plot the 4FS and the 5FS are combined according to the Santander matching [51, 49]. The 4FS and 5FS calculations provide the unique description of the cross-section in the / → / → ∞ asymptotic limits mH± mb 1andmH± mb , respectively. For charged Higgs boson masses away from these asymptotic regions both schemes can be used but include different types of higher-order contributions. The Santander matching interpolates between the asymptotic limits of very light and very heavy charged Higgs bosons.

Benchmark scenarios in charged Higgs boson searches max The mh scenario deﬁnes a benchmark point optimized to maximize the theoretical upper bound on mh for a given tanβ and ﬁxed mt and the soft SUSY breaking parameter MSUSY . This benchmark point provides the largest parameter space in the mh direction and conservative exclusion limits for tanβ.

max The mh scenario used in the ATLAS papers I and II is deﬁned in [53]. max Other versions of the mh scenario exists with small variations a sign change max max in the description of mh between [54]and[53] and the (constrained) mh max scenario [55]. Further an (updated) mh scenario [56] exists, taking the discovered Higgs boson into account. Details about the different benchmark points should be taken from the publications dedicated to this scenario [53, 54, 55, 56].

25 [pb]

+ s=8 TeV tH β → -1 tan =30

pp 10 LHC HIGGS XS WG 2013

σ NLO, matched

10-2 matched 4FS 5FS 200 250 300 350 400 450 500 550 600

MH+ [GeV]

Figure 2.11. Next to leading order (NLO) cross-section prediction for pp → tH− + X at the LHC with 8 TeV for a 2HDM with tanβ = 30: The Santander matching is used for these predictions. Shown is the central prediction together with an estimate of the theoretical uncertainties [51].

max The allowed mass of the light CP-even Higgs boson in the mh scenario is only in a small region of the mA − tanβ plane when taking into account the discovery of the SM-like Higgs boson at around 125 GeV [56], this is shown max in ﬁgure 2.12.Themh scenario was designed to maximize the value of mh, in the decoupling region this scenario yields mh values that are higher than the ones of the observed boson. max Due to this, a modiﬁcation of the mh scenario was suggested by theo- mod reticians, called the mh scenario [56]. Two variants of this scenario exist mod+ mod− mh and mh , with a sign and absolute value difference on the parameter Xt /MSUSY ,whereXt is the stop mixing parameter. This scenario is now used in the latest ATLAS charged Higgs boson search [58]. A detailed description mod on the mh scenario, as well as other suggested benchmark scenarios can be found in [56].

Experimental constraints - direct searches For decades charged Higgs bosons have been searched for, at the colliders LEP [59], Tevatron [60] and LHC using the ATLAS [61, 62, 63, 58]and CMS [64, 65, 66] experiments. At tree level, the Higgs sector in the MSSM has only two free parameters, tanβ and one of the Higgs masses, see section 2.2.3. At loop level, due to a large number of MSSM parameters, there are additional contributions. In order to be able to present results in a two dimensional histogram, benchmark

26 β 80 -1

tan ATLAS s=8 TeV, ∫ L dt = 19.5 - 20.3 fb 70 MSSM mmax scenario, M = 1 TeV, h/H/A ττ→ h SUSY

60 Obs 95% CL limit Exp 95% CL limit 1 σ σ 50 2 =700 GeV H

Obs 95% CL limit m ± σ 1 theory =500 GeV H

40 m

mh = 130.2 GeV =300 GeV H

30 m

=170 GeV m = 130 GeV H h 20 m = 122 GeV h m

10 m = 128 GeV h

mh = 125 GeV 100 200 300 400 500 600 700 800 900 1000

mA [GeV]

Figure 2.12. Expected (dashed line) and observed (solid line with markers) 95% CL β max upper limits on tan as a function of mA for the mh scenario of the MSSM. Values of tanβ above the lines are excluded. The vertical dashed line at 200 GeV indicates the transition point between low- and high-mass categories. Lines of constant mh and mH are also shown in red and blue colour, respectively [57]. scenarios are defined. These scenarios fix all parameters except tanβ and one of the Higgs boson masses. One often used scenario is the mh-max scenario, described before. Theoretical limits for the lowest possible mass of the charged Higgs boson are given by equation (2.18). Experimental exclusion limits are set by the LEP > . experiments at mH± 79 3 GeV at 95% confidence level independently of the branching ratios [67], assuming BR(cs¯)+BR(τν)=1. For BR(τν)=1theset limits are 87.8 GeV. For heavier charged Higgs bosons the best current limits are set by the ATLAS and CMS experiments. • ATLAS: < ± < For the mass range 80 GeV mH 160 GeV, 95% confidence level upper limits on B(t → H+b) are set in the range 0.23 − 1.3%, and for < ± < the mass range 180 GeV mH 1000 GeV, 95% confidence level upper limits are set on the production cross-section of a charged Higgs boson in the range 0.0045 − 0.76 pb, both with the assumption that B(H± → τν)=1[58]. • CMS: In the mass range 80 GeV to 160 GeV,95% confidence level upper limits on B(t → H+b) are set in the range 0.16 − 1.2% and for the mass range < < 180 GeV mH± 600 GeV, 95% confidence level upper limits are set on the production cross-section of a charged Higgs boson in the range 0.026 − 0.38 pb, both with the assumption that B(H± → τν)=1[66].

27 Figure 2.13 presents the limits on the branching ratio measured by ATLAS for light charged Higgs boson (a) and the limit on the cross-section for the heavy charged Higgs boson (b). Similar plots are shown for CMS in figure 2.14. max mod± In figure 2.15 the interpretation of the limits in the mh and mh scenarios from ATLAS are shown, figure 2.16 shows the similar plots for CMS.

1 ν + ATLAS Data 2012 ATLAS Data 2012 τ→ Observed CLs ) [pb] Observed CLs -1 ν 10 -1

∫Ldt = 19.5 fb + ∫Ldt = 19.5 fb + Expected τ→ Expected H ± σ ± σ 10-1 1 s = 8 TeV 1 s = 8 TeV + B

× ± 2σ 1 ± 2σ + B(H × + bH

H -1 → -2 σ 10

t 10 B

10-2

10-3 -3 80 90 100 110 120 130 140 150 160 10 200 300 400 500 600 700 800 900 1000 mH+ [GeV] mH+ [GeV]

(a) Light charged Higgs (b) Heavy charged Higgs Figure 2.13. The expected and observed 95% CL upper limits measured in ATLAS for the light (left) and heavy (right) charged Higgs boson searches [58]. The vertical axis shows the branching ratio (a) and cross-section (b) as a function of the charged Higgs boson mass. The dashed line represents the expected average limit with absence of a charged Higgs boson. The green and yellow bands indicate the corresponding 68% and 95% uncertainty of those values. The solid line represents the observed limit from data, the black dots indicate the mass points used for the measurement.

19.7 fb-1 (8 TeV) 19.7 fb-1 (8 TeV) 0.025 1 ντ→ + + + + + + CMS t → H b, H τ→ ντ CMS pp → (b)Ht , H τ→ ντ + Preliminary τ +jets final state (pb) 0.9 Preliminary τ +jets final state H h h ντ→ B 0.02 Observed 0.8 Observed × + b Expected median ± 1σ Expected median ± 1σ + H

H Expected median ± 2σ 0.7 Expected median ± 2σ B → t × +

B 0.015 H 0.6 σ 0.5 0.01 0.4 0.3 0.005 0.2

95% CL limit on 0.1 95% CL limit for 0 0 80 90 100 110 120 130 140 150 160 200 250 300 350 400 450 500 550 600 mH+ (GeV) mH+ (GeV) (a) Light charged Higgs (b) Heavy charged Higgs Figure 2.14. The expected and observed 95% CL upper limits measured in CMS for the light (left) and heavy (right) charged Higgs boson searches [66]. The vertical axis shows the branching ratio (a) and cross-section (b) as a function of the charged Higgs boson mass. The dashed line represents the expected average limit with absence of a charged Higgs boson. The green and yellow bands indicate the corresponding 68% and 95% uncertainty of those values. The solid line represents the observed limit from data, the black dots indicate the mass points used for the measurement.

28 β 60 β 60 Median expected exclusion tan tan 50 Observed exclusion 95% CL 55 ATLAS Observed +1σ theory σ -1 40 Observed -1 theory 50 ∫Ldt = 19.5 fb ATLAS s=8 TeV -1 30 ∫Ldt = 19.5 fb 45 Data 2012 max MSSM mh scenario 20 s=8 TeV 40 Median expected exclusion Data 2012 Observed exclusion 95% CL MSSM mmax scenario 10 h 35 Observed +1σ theory Observed -1σ theory 0 30 80 90 100 110 120 130 140 150 160 200 220 240 260 280 300

+ + mH [GeV] mH [GeV] max max (a) Light charged Higgs mh (b) Heavy charged Higgs mh

β 60 β 60 Median expected exclusion tan tan 50 Observed exclusion 95% CL 55 ATLAS Observed +1σ theory σ -1 40 Observed -1 theory 50 ∫Ldt = 19.5 fb ATLAS s=8 TeV -1 30 ∫Ldt = 19.5 fb 45 Data 2012 mod+ MSSM mh scenario 20 s=8 TeV 40 Median expected exclusion Data 2012 Observed exclusion 95% CL MSSM mmod+ scenario 10 h 35 Observed +1σ theory Observed -1σ theory 0 30 80 90 100 110 120 130 140 150 160 200 220 240 260 280 300

+ + mH [GeV] mH [GeV] mod+ mod+ (c) Light charged Higgs mh (d) Heavy charged Higgs mh

β 60 β 60 Median expected exclusion tan tan 50 Observed exclusion 95% CL 55 ATLAS Observed +1σ theory σ -1 40 Observed -1 theory 50 ∫Ldt = 19.5 fb ATLAS s=8 TeV -1 30 ∫Ldt = 19.5 fb 45 Data 2012 mod- MSSM mh scenario 20 s=8 TeV 40 Median expected exclusion Data 2012 Observed exclusion 95% CL MSSM mmod- scenario 10 h 35 Observed +1σ theory Observed -1σ theory 0 30 80 90 100 110 120 130 140 150 160 200 220 240 260 280 300

+ + mH [GeV] mH [GeV] mod− mod− (e) Light charged Higgs mh (f) Heavy charged Higgs mh Figure 2.15. Interpretation of the limits on the branching fractions measured in ATLAS of the light charged Higgs boson (left) and the heavy charged Higgs boson max mod+ mod− (right), in the context of the MSSM mh (a, b), mh (c, d) and mh (e, f) scenarios [58].

29 19.7 fb-1 (8 TeV) 19.7 fb-1 (8 TeV) β β 60 CMS 60 CMS Preliminary Preliminary tan tan

+ + + 50 t → H b, H τ→ ντ 50 τ +jets final state + + + h pp → (b)Ht , H τ→ ντ MSSM updated mmax τ +jets final state h h Observed MSSM updated mmax 40 40 h Observed ±1σ (th.) Observed 30 Excluded 30 Observed ±1σ (th.) Expected median ± 1σ Excluded Expected median ± 2σ Expected median ± 1σ mMSSM ≠ 125±3 GeV Expected median ± 2σ 20 h 20 MSSM mh ≠ 125±3 GeV 10 10

0 0 90 100 110 120 130 140 150 160 200 250 300 350 400 450 500 550 600 mH+ (GeV) mH+ (GeV) max max (a) Light charged Higgs mh (b) Heavy charged Higgs mh

19.7 fb-1 (8 TeV) 19.7 fb-1 (8 TeV) β β 60 CMS 60 CMS Preliminary Preliminary tan tan

+ + + 50 t → H b, H τ→ ντ 50 τ +jets final state h mod+ mMSSM mMSSM + + h + pp → (b)Ht , H τ→ ντ 40 Observed 40 τ +jets final state h mMSSM mMSSM mod+ Observed ±1σ (th.) h 30 Excluded 30 Observed Expected median ± 1σ Observed ±1σ (th.) Expected median ± 2σ Excluded mMSSM ≠ 125±3 GeV Expected median ± 1σ 20 h 20 Expected median ± 2σ mMSSM ≠ 125±3 GeV 10 10 h

0 0 90 100 110 120 130 140 150 160 200 250 300 350 400 450 500 550 600 mH+ (GeV) mH+ (GeV) mod+ mod+ (c) Light charged Higgs mh (d) Heavy charged Higgs mh

19.7 fb-1 (8 TeV) 19.7 fb-1 (8 TeV) β β 60 CMS 60 CMS Preliminary Preliminary tan tan

+ + + 50 t → H b, H τ→ ντ 50 τ +jets final state h mod- mMSSM mMSSM + + h + pp → (b)Ht , H τ→ ντ 40 Observed 40 τ +jets final state h mod- Observed ±1σ (th.) mMSSM h 30 Excluded 30 Observed Expected median ± 1σ Observed ±1σ (th.) Expected median ± 2σ Excluded MSSM ≠ 125±3 GeV 20 mh 20 Expected median ± 1σ Expected median ± 2σ mMSSM ≠ 125±3 GeV 10 10 h

0 0 90 100 110 120 130 140 150 160 200 250 300 350 400 450 500 550 600 mH+ (GeV) mH+ (GeV) mod− mod− (e) Light charged Higgs mh (f) Heavy charged Higgs mh Figure 2.16. Interpretation of the limits on the branching fractions measured in CMS of the light charged Higgs boson (left) and the heavy charged Higgs boson (right), in max mod+ mod− the context of the MSSM mh (a, b), mh (c, d) and mh (e, f) scenarios [66].

30 Experimental constraints - indirect searches The charged Higgs boson enters measurements of some parameters at tree level or through loops. Small deviations from the SM predictions in precision measurements can be indications of charged Higgs bosons or BSM physics. Similarly precission measurements can set constraints on the charged Higgs boson. Exclusion limits can be obtained indirectly by studying ﬂavour physics, measurement of the electron electric dipole moment or other precision measurements [68]. The set limits, though, are highly model dependent and cannot replace direct searches. What is excluded by one model can be allowed by another model. 3 Taking B → Xsγ as an example, which decays via b → sγ, a charged Higgs boson or SUSY particles could contribute via the penguin loop as shown in ﬁgure 2.17. This would change the branching fraction with respect to the SM-only scenario and can therefore be used to probe physics beyond the SM. Comparing the observed branching ratio with the calculated branching ratio from a certain model can give predictions on the reliability of the model. The combined average experimental limit determined by the Heavy Flavour Averaging Group [69]is: −6 BR(B → Xsγ)=(355 ± 24 ± 9) × 10 (2.22)

In the paper [70], indirect mass constraints at 95% C.L. are set via B → Xsγ, excluding charged Higgs bosons in the 2HDM type II up to 295 GeV.

q˜ t t

± − bsW bsH± bsχ˜

(a) Standard Model (b) charged Higgs (c) charginos, squarks Figure 2.17. Contribution to b → sγ transition in the SM (a), from a charged Higgs boson (b) and from charginos and squarks (c). The loose photon is to be attached in all possible positions.

Further constraints which can be used in indirect searches are described in the following: • Bu → τντ : This process can be mediated at tree level by a charged Higgs boson. It is helicity suppressed in the SM. Measurements have been performed by the Belle and BaBar experiments:

( + → τ+ν )=( . +0.53 ± . ) × −4 [ ] BR B τ 1 83−0.49(stat.) 0 24(sys.) 10 71 (2.23) ( − → τ−ν )=( . +0.38 +0.29 ) × −4 [ ] BR B ¯τ 1 54−0.37(stat.)−0.31syst. 10 72 (2.24)

3 + = ¯ 0 = ¯ 0 = ¯ + = ¯ ∗ B-mesons: B ub, B db, Bs sb, Bc cb similarly for B ’s [1], a possible subscript indicates the quark content.

31 • B → Dτντ 4: The ratio between B → Dν,when is either an electron or a muon, and B → Dτντ is sensitive to new physics. For example contributions from the charged Higgs boson in models with BSM physics. The semileptonic decay B → Dν depends on the CKM matrix element |Vcb| which is known to a good precision [68]. The ratio was measured by the BaBar collaboration [73].

BR(B → Dτντ) R(D)= =(0.440 ± 0.058 ± 0.042) (2.25) BR(B → Dν)

The ratio for R(D∗) was measured to be 0.332 ± 0.024 ± 0.018. The combination of R(D) and R(D∗) excludes the type II 2HDM charged β/ Higgs boson with a 99.8% conﬁdence level for any value of tan mH+ > < above mH+ 10 GeV [73]. Values for mH+ 10 GeV are excluded by B → Xsγ. • Ds → τντ : The combined average experimental limit determined by the Heavy Flavour Averaging Group [69]is:

−2 BR(Ds → τντ)=5.44 ± 0.22 × 10 (2.26) + − • Bd,s → μ μ : These decays can be enhanced or supressed from Higgs- mediated contributions, they are helicity suppressed in the SM. Limits on the branching fraction were set by a combination of the ATLAS, CMS and LHCb experiment [74]:

+ − −9 BR(Bs → μ μ ) < 4.2 × 10 , (2.27) + − −10 BR(Bd → μ μ ) < 8.1 × 10 . (2.28) In the CMSSM (Constrained Minimal Supersymmetric Model) [75, 76], as an example, certain areas in the parameter space can be excluded by the previously mentioned constraints [77]. Figure 2.18 shows constrained areas − β in the mH+ tan plane. ∗ The 2HDM type-II model is excluded by B → Dτντ and B → D τντ measurements because they can not be explained in this model simultaneously [78]. Charged Higgs bosons though, still can exist in other models that have more parameters.

4 + = ¯ 0 = + = ∗+ = ¯ ∗0 = D-mesons: D cd, D du¯, Ds cs¯, D cd (different parity), D du¯ (different parity) [1], a possible subscript indicates the quark content.

32 Allowed Direct b→ s γ ντ→ Bu μ→ + μ- Bs B → D ντ K νμ→

Figure 2.18. Combined exclusion in CMSSM models by different constraints. The constraints are applied in the order they appear in the legend, and the colour coding corresponds to the ﬁrst constraint by which a point is excluded [77].

33 3. The CERN laboratory

The world largest laboratory for particle physics CERN1 (Conseil Européen pour la Recherche Nucléaire), is located to the north-west of Geneva on the French-Swiss border. It was founded on the 29th of September 1954. Today, CERN has twenty-one member states and several hundred universities world- wide participating in the research conducted there. At the beginning CERN was a laboratory for nuclear research but the energy frontier quickly moved on to higher energies to study more fundamental particles. CERN is the provider of the particle accelerators and other main infrastructure needed to push the high energy frontier. The experiments at the accelerators are constructed by international collaborations. Although mostly associated with particle physics, CERN also contributes to achievements in computing science and engineering science. For example, the World Wide Web was invented at CERN.

3.1 Scientiﬁc achievements made by CERN CERN has played an important role for our understanding of fundamental forces and basic constituents of matter. Its research has been awarded with several Nobel prices [79]. Some of the major achievements are: • 1973: The discovery of neutral currents [80, 81, 82]; • 1983: The discovery of the W and Z bosons [12, 13, 14, 15]; • 1989: The determination of the number of light neutrino families [5]; • 1995: The ﬁrst creation of anti-hydrogen atoms [83]; • 1999: The discovery of direct CP-violation [84]; • 2012: The observation of a Higgs boson at 125 GeV [6, 7];

3.2 The accelerator infrastructure CERN is the provider of the acceleration and de-acceleration infrastructure, producing particles at different energies for the experiments. The interplay between the different accelerator stages at CERN is shown in ﬁgure 3.1. The various accelerators in the LHC complex are listed and described in the following:

1the European Organization for Nuclear Research

34 Figure 3.1. CERN accelerator complex [85]. The accelerators relevant for physics at the LHC are described in the text.

35 3.2.1 Linac-2 The Linac-2 [86] linear accelerator, accelerates protons after the ionization of hydrogen to an energy of 50 MeV with a pulse length of 1 Hz and a current of 175 mA. Its main purpose is to be a pre-accelerator for the Proton Synchrotron Booster (PSB).

3.2.2 Linac-3 The Linac-3 [87] linear accelerator is a second linear accelerator at CERN, for heavy ions instead of protons. After striping off all electrons, it accelerates ions to an energy of 4.2 MeV/nucleon. Subsequently, the ions are injected into the Low Energy Ion Ring (LEIR).

3.2.3 Linac-4 The Linac-4 [88] is a future linear proton accelerator, that will replace Linac-2 in 2017/2018. Its construction was approved in 2007 and it is needed in order to provide enough protons to be able to reach the design luminosity of the LHC. Protons will be accelerated to an energy of 160 MeV.

3.2.4 Proton Synchrotron Booster (PSB) The Proton Synchrotron Booster [89] is one of the pre-accelerators at CERN. It receives the protons from Linac-2 and accelerates them to an energy of 1.4 GeV. The protons are subsequently injected into the Proton Synchrotron or delivered to Isolde [90] to produce radioactive ion beams.

3.2.5 Proton Synchrotron (PS) The Proton Synchrotron [91] is a key accelerator at CERN. It gets protons from the PSB or ions from the LEIR and accelerates them to higher energies. Protons can reach energies up to 28 GeV and ions up to 72 MeV/nucleon. The Proton Synchrotron acts as a pre-accelerator for the Super Proton Synchrotron. Its protons can also be used for anti-proton production for the Anti-proton De- accelerator (AD), production of neutrons and beam delivery to the East Area of CERN.

3.2.6 Super Proton Synchrotron (SPS) The Super Proton Synchrotron is the second largest accelerator at CERN. It is 6.9 km in circumference and can accelerate protons to energies up to 450 GeV. Before the LHC era, it was used as the proton-anti-proton collider for the UA1

36 and UA2 experiments. Today it acts as a pre-accelerator for the LHC, but it also has delivered protons for the neutrino beam to Gran Sasso (CNGS) and it provides a proton beam for the ﬁxed target experiments in the North Area of CERN. There are plans to further upgrade the SPS to a Super-SPS in order to reach the design luminosity in LHC.

3.3 The Large Hadron Collider (LHC) The Large Hadron Collider [92] provides the highest collision energy in the world, required for precision studies of the Standard Model and to probe new physics beyond it. The LHC is built in the former Large Electron Positron collider (LEP) tunnel with a circumference of 27 km, which allows operation at a centre-of-mass energy of up to 14 TeV for proton-proton collisions and a luminosity of 1034 cm−2s−1. In addition to proton-proton collisions, the LHC provides heavy ion collisions for studies of quark-gluon plasma. More than 10 000 scientists and engineers from hundreds of universities are using the beams of the LHC for their research. This work is done by four collaborations ALICE, ATLAS, CMS, LHCb, each with an experimental facility at four points along the LHC ring, the locations are shown in ﬁgure 3.2.

Figure 3.2. Schematic of the LHC ring, with the positions of the experiments [92, 93].

The start-up of the LHC was on the 10th of September 2008, but was stopped after a short time due to a major accident with the magnet system. On the 20th of November 2009, the LHC restarted and successfully collided

37 protons after a few days. The ﬁrst collisions were at an energy per beam of 450 GeV, the injection energy of the SPS. The beam energy was increased in steps and after the winter shut-down in 2009/2010, the energy per beam reached 3.5 TeV, half of the design energy of the LHC. In 2012 a further increase to 4 TeV per beam was achieved. More than 5 fb−1 of integrated luminosity were recorded at a centre-of-mass energy of 7 TeV and more than 21 fb−1 of data with a centre-of-mass energy of 8 TeV. At the end of 2012, the LHC was shut down for maintenance and is ready to restart in 2015 with a collision energy of 13 TeV.

3.4 The four experiments at the LHC ALICE (A Large Ion Collider Experiment) [94] is a heavy ion experiment designed to study the conditions of the universe directly after the Big Bang. Heavy ion runs are used to produce temperatures 100 times higher than inside the sun to produce quark-gluon plasma. The expansion and cooling down of this plasma is studied in order to understand how the universe was formed.

CMS (Compact Muon Solenoid) [95] is in size the second biggest experiment at the LHC. It is a general purpose detector, designed for searching the Higgs boson, for supersymmetry, dark matter and for precision measurements of the Standard Model. The detector is built inside a big 4 T solenoid magnet. CMS was the only detector at the LHC built over ground and installed in 15 slices in the CMS cavern. The detector system has a length of 21 m, a width of 15 m and a height of 15 m. It weighs 12500 t.

LHCb (Large Hadron Collider beauty) [96] is a detector system designed to study the B-mesons in detail. The focus is the study of the matter-antimatter symmetry and rare decays of B-mesons, which are sensitive to new physics beyond the Standard Model. It is the smallest detector at the LHC build as a single arm spectrometer detecting particles propagating in the forward direction. The experiment does not use the full luminosity of the LHC to avoid pile-up2 events.

ATLAS (A Toroidal LHC ApperatuS) [98] is the largest detector at the LHC. It is like CMS a general purpose detector with the same physics goals. More details about the ATLAS detector system, which was used to collect the data used in this thesis, are described in the next chapter.

2pile-up: In high-luminosity colliders, there is a non-negligible probability that one single bunch crossing may produce several separate events, so-called pile-up events. [97]

38 4. The ATLAS detector system

ATLAS [98] is a forward-backward symmetric detector with respect to the interaction point, as shown in ﬁgure 4.1. It is designed to handle the high interaction rates, radiation doses, particle multiplicities and energies at the LHC. The detector system is the result of over 15 year long collaboration between several thousands of physicists, engineers, technicians and students. ATLAS offers a rich set of opportunities for new physics, high precision measurements of the Standard Model and the possibility to study strongly interacting matter at high energy densities. For example top quarks [99, 100] will be produced at large rates making study of its spin and couplings possible. The search for the Standard Model Higgs boson was one of the strongest physics cases driving the requirements of the sub-systems of ATLAS. These are described in [101, 102] and summerized in table 4.1.

Table 4.1. General performance goals of the ATLAS detector [101, 102]. The units for E and pT are in GeV. Detector component Required resolution η covrage Measurement (Trigger) σ / = . ⊕ ± . Tracking pT pT 0 05%√ pT 1% 2 5 EM calorimetry σE /E = 10%/ E ⊕ 0.7% ±3.2 (±2.5) Hadronic calorimetry (jets) √ σ / = / ⊕ ± . (± . ) barrel and end-cap E E 50% √E 3% 3 2 3 2 forward σE /E = 100%/ E ⊕ 10% 3.1 < |η| < 4.9 (3.1 < |η| < 4.9) σ = = ± . (± . ) Muon spectrometer pT 10% @pT 1TeV 2 7 2 4

4.1 Conventions Conventions used in ATLAS are: • The nominal interaction point of ATLAS is deﬁned as the origin of the coordinate system. • The z-axis is deﬁned by the beam direction, the xy-plane is transverse to the z-axis. • The positive x-axis is pointing from the interaction point to the centre of the LHC ring. • The positive y-axis is pointing upwards. • The azimuthal angle φ is measured around the beam axis.

39 Figure 4.1. View of the ATLAS experiment with its sub-detectors [98].

40 • The polar angle θ is measured from the beam axis. • η η = ( θ ) The pseudo-rapidity is defined as lntan 2 . • Transverse quantities like transverse momentum pT , transverse energy miss ET and missing transverse energy ET are defined in the xy-plane. • The distance ΔR in pseudo-rapidity-azimuthal angle space is defined as ΔR = Δη2 + Δφ 2. • The 4-momentum vector P =(E, px, py, pz) can be expressed in terms of E,η,φ and pT by P =[E, pt cos(φ), pt sin(φ), pt sinh(η)] for massless particles.

4.2 The inner detector Physics measurements in ATLAS require high momentum and vertex resolu- tions, hence a high granularity to handle the large track density. The highest granularity around the vertex region is achieved using semiconductor pixel detectors, followed by a SemiConductor Tracking (SCT) detector. The total number of precision layers is limited by the material and power dissipa- tion they introduce, and the cost factor. A large number of tracking points is required for reliable pattern recognition and is achieved by a straw tube tracker/Transition Radiation Tracker (TRT) which provides the possibility of continuous track-following with much less material per point and lower costs. Additionally the electron identification and charged pion rejection capabili- ties are enhanced by the detection of transition radiation photons in the straw tubes. Further jet rejection of a factor ∼ 40 at an efficiency of better than 90% for pT > 20 GeV electrons were design parameters [103]. The inner detector plays a major role for electron identification, for γ/π0 separation in case of photon conversions, important to reduce the amount of misidentified leptons. The stand-alone performance of the inner detector is of importance for the identification of jets from b-quarks (b-tagging) used for example in the charged Higgs boson searches. All discrimination and pattern recognition need to work under the pile-up conditions occurring when running at LHC design luminosity. An overview of the inner detector is shown in figure 4.2. The inner detector is surrounded by a 2 T solenoid magnet with a length of 5.3 m and a diameter of 2.5 m. The pixel detector and the SCT, have concentric cylindrical layers in the central part and disc layers perpendicular to the beam in the end-cap, which offer a precision tracking up to |η| < 2.5. With over 80 million readout channels, the pixel detector is the most granular detector in ATLAS, capable to reconstruct the secondary vertex of b-quark decays. The SCT has around 6.3 million readout channels. The TRT system covers a pseudo-rapidity of up to |η| < 2.0 and has approximately 351000 readout channels. The combination of theses three systems provides a very robust pattern recognition and high precision in both R − φ and z coordinates. The σ / = . ⊕ design momentum resolution is pT pT 0 05%pT 1% [102].

41 Figure 4.2. Overview of the inner detector with subsystems indicated [98].

4.3 The calorimeters A calorimeter is an instrument which measures the energy of particles and their position by absorbing these particles. Characteristic interactions with matter, e.g. atomic excitation or ionization, are used to generate detectable effects. In this way, electrically charged particles but also electrically neutral particles can be detected as opposed to the inner detector, which only detects charged objects. Calorimeters are made from cell structures, aligned in form of towers, along the direction of interaction. The energy of the particles or jets is determined by integrating over the whole volume of interaction. Calorime- ters as a whole usually contain an electromagnetic system to absorb electrons and photons, followed by a hadronic system to absorb hadrons. The hadrons start their showering in the electromagnetic calorimeter, but only the hadronic calorimeters can fully stop them. Critical performance parameter for the design of the calorimeter in ATLAS are the energy resolution, the accuracy of the position and angular measurements, the ability to reconstruct e.g. the missing transverse energy with high precision, and the reconstruction of τ-leptons [104]. The capability of separation γ/π0, γ/jet and e/jet are important [103] in order to reduce misidentification rates and the resulting backgrounds. Different technologies are used in ATLAS to build a hermetic calorimeter covering the region |η| < 4.9, as shown in figure 4.3.Intheη region of the inner detector the electromagnetic calorimeter has a fine granularity (segmen- tation: Δη ∼ 0.025 − 0.1andΔΦ = 0.025 − 0.1[102]), allowing to measure electrons and photons with high precision. Outside the inner detector region,

42 Figure 4.3. Overview of the calorimeter with differnetsegments indicated [98]. the granularity of the calorimeters gets coarser, but still ﬁne enough to reconstruct jets and missing transverse energy, important for many physics signatures, for example SUSY. Calorimeters must have sufﬁcient stopping power for protecting the muon system from showers punching through.

The Electromagnetic Calorimeter: The electromagnetic calorimeter (EM) is a lead-liquid-argon sampling calorimeter, made of a barrel part (|η| < 1.475) and two end-cap parts (1.375 < |η| < 3.2). The EM calorimeter has an accordion geometry in order to cover the complete azimuthal angle φ without any azimuthal crack. 1 The total thickness of the EM calorimeter is > 22 radiation lengths (X0)inthe√ > 2 ΔE ≤ / barrel and 24 X0 in the end-caps. The energy resolution is: E 10% E (stochastic term) with a constant term < 0.7%.

The Hadronic Calorimeters: Three subsystems are used for hadronic calorimetry, based on different technologies in order to provide the best performance.

TheTilecalorimeteris a sampling calorimeter situated directly outside the

1Radiation lengths is a material characteristic, describing the energy loss of high energy, electromagnetic-interacting particles in the material. 2Stochastic term: statistical ﬂuctuations, e.g. from the shower, light yield, sampling. Con- stant term, dominant at high-energy: e.g. cell-to-cell calibration inaccuracies, intrinsic non- uniformities, radiation damage. The units for E are in GeV.

43 EM calorimeter. It uses steel as an energy absorber and scintillating tiles as active material. The barrel covers |η| < 1.0 and is completed by two extended barrels covering√ a range from 0.8 < |η| < 1.7 each. The energy resolution is: ΔE ≤ / ⊕ E 50% E 3%.

The Hadronic end-cap calorimeter is a sampling calorimeter made of two wheels per end-cap, situated directly behind the end-cap of the EM calorimeter. For the absorbing material, 25 mm parallel copper plates are used in the wheels which are closest to the interaction point, the other wheels are made from 50 mm copper plates. The copper plates have small gaps, providing space for the√ liquid argon as an active material. The energy resolution is: ΔE ≤ / ⊕ E 50% E 3%.

The Forward calorimeter is another sampling liquid argon calorimeter. It is built with three modules per end-cap, the ﬁrst uses copper for absorbing and is sensitive to electromagnetic showers. The other two layers use tung- sten and measure√ the energy of hadronic showers. The energy resolution is: σE /E = 100%/ E ⊕ 10%.

4.4 The muon spectrometer In the ATLAS muon system, the momentum of muons is determined in a large superconducting air-core toroid magnet system. It contains detector technologies for fast triggers and high precision tracking with ∼ 60 μm intrinsic resolution. Emphasis is put on reliable, high resolution, stand-alone performance over a pT range from 5 GeV to 1000 GeV [103]. Good momentum resolution is needed, above large backgrounds, for the detection of decays involving muons. The resolution can be futher improved by combining the stand alone results of the muon spectrometer with these of the inner detector. An example are light charged Higgs boson seaches, where the decay product has one or two leptons. A schematic view of the muon system is shown in ﬁgure 4.4. A large central toroid magnet bends the muons in the region |η| < 1.4. In the high-η regions (1.6 < η < 2.7), two smaller toroidal superconducting magnets are inserted. Each of the three magnets is made from eight coils which are placed symmetrically around the beam axis. A magnetic bending power of 1.4 to 5.5 Tm is provided by the barrel toroid in the range |η| < 1.4. In the end-cap region, a bending power of 1 to 7.5 Tm is provided by the end-cap magnets. The region 1.4 < |η| < 1.6 is called the transition region, where the magnetic ﬁelds overlap. Muon chambers arranged in three cylindrical layers around the beam pipe are used in the barrel region to measure muon tracks. The transition and end-cap regions are covered by three layers of muon chambers arranged along φ, meaning the centre point of the tubes are oriented tangential to the circle around the beam axis.

44 Figure 4.4. Overview of the ATLAS muon system [98].

The muon chambers The region with |η| < 2.7iscoveredbyMonitored Drift Tubes (MDT). In the high-η region the rates and background conditions are expected to be up to 30 kHz per tube at full LHC luminosity. The MDTs, which are ﬁlled with Ar/CO2 gas, have a diameter of 29.97 mm providing an average resolution of 60-80 μm. The maximal count rate of the MDT is 150 Hz/cm2.

Cathode Strip Chambers (CSC) are used in the region 2 < |η| < 2.7where the particle ﬂux and the density of tracks are highest. The CSC can handle counting rates up to 1000 Hz/cm2. The CSC system is made of two disks of eight chambers, which enable the measurement of η and φ coordinates. The CSC is ﬁlled with an Ar/CO2 mixture, the resolution reached is 60 μm.

Trigger chambers provide fast information to the Level 1 trigger logic about muon transverse momentum and bunch-crossing identiﬁcation. The trigger chambers measure the φ coordinate to give a full space trajectory in combination with the η coordinate of the MDTs. The region |η| < 2.4iscoveredusing two different types of technologies. In the barrel region |η| < 1.05, Resistive Plate Chambers (RPC) are used and, in the region 1.05 < |η| < 2.4, Thin Gap Chambers (TGC) are used.

45 4.5 The trigger system The ATLAS detector has a three-level trigger system: Level 1 (L1), Level 2 (L2) and event filter (EF) level. The levels are staged, meaning that the next level refines the event selection from the previous level by applying more precise or additional requirements. The Level 1 trigger uses high transverse momentum muons, electrons, photons, jets, τ-leptons, large missing and total transverse energies for triggering. Only reduced detector information is used in order to make a decision with a latency shorter than 2.5 μs. The rate is reduced from the Beam Cross Over (BCO) frequency of 40 MHz to 75 kHz (to be increased to 100 kHz in Run 2). The L1 trigger defines Regions Of Interest (ROI) that seed the L2 trigger. At L2, the full precision of all detector data in the ROI is used. The L2 trigger is configured to reduce the data rate to approximately 3.5 kHz with a latency less than 40 ms per event. At the EF level the data rate is further reduced to about 200 Hz for storage and offline analysis. The EF uses advanced near offline quality algorithms for processing and requires around 4 seconds per event. The stored data size is approximately 1.3 Mbyte per event [102]. A schematic layout of the trigger system is shown in figure 4.5.

Interaction rate ~1 GHz CALO MUON TRACKING Bunch crossing rate 40 MHz Pipeline LEVEL 1 memories TRIGGER < 75 (100) kHz Derandomizers Regions of Interest Readout drivers (RODs)

LEVEL 2 Readout buffers TRIGGER (ROBs) ~ 1 kHz Event builder

EVENT FILTER Full-event buffers and ~ 100 Hz processor sub-farms

Data recording Figure 4.5. Schematics layout of the trigger system [105].

46 5. Physics analysis in ATLAS

5.1 Charged Higgs boson searches in ATLAS One major task of the LHC and the ATLAS experiment is the exploration of the Higgs sector and physics beyond the SM. Several theories beyond the SM predict the existence of more than one Higgs boson (see chapter 2.2.3). The observation of a charged Higgs boson would clearly indicate physics beyond the SM. At the start up of the LHC, the upper limits on a light charged Higgs + ( + < ) ( → ) boson mH mtop , in terms of the branching fraction B t bH ,were of the order of 15-20%, as set by the Tevatron [60, 106]. The LEP experi- > . ments had excluded a charged Higgs boson below mH+ 79 3 GeV at 95% conﬁdence level [67]. The light charged Higgs boson can be produced in several extensions of the SM through the decay of a top quark into a charged Higgs boson and a bottom quark. For tanβ > 2, where tanβ is the ratio of the vacuum expectation values of the two Higgs doublets, the charged Higgs boson is assumed to predominantly decay into τν. In the region 1 < tanβ < 2, this contribution remains sizeable.

5.1.1 Measurement of discriminating variables for charged Higgs boson searches The first publication related to charged Higgs boson searches√ in ATLAS, Pa- per VI, was released after analysing 35 pb−1 of data at s = 7TeVandit summarized results of a first measurement of discriminating variables [107]. θ ∗ One of the variables was cos l defined as [108]:

2m2 4pb · pl cosθ ∗ = bl − 1 (5.1) l 2 − 2 2 − 2 mtop mW mtop mW

b l 2 b l with p · p = 2EbEl(1−cosθbl)=4EbEl sin (θbl/2),wherep and p are the 4-momenta of the lepton and the b-quark coming from the same top quark. The variable mbl is the invariant mass of the b-quark and the lepton, and θbl is the angle between them. If the top quark decays into a charged Higgs boson, instead of a W boson, the b-quark gets a smaller momentum. Also, a charged lepton arising from a leptonically decaying τ is likely to have a smaller momentum, compared to

47 a lepton coming directly from a W boson. The presence of a charged Higgs boson in a leptonic top quark decay therefore strongly reduces the invariant · θ ∗ − product pb pl and has values of cos l close to 1 as a consequence. This variable is able to discriminate between the lepton coming from τ → l + νs and a lepton coming directly from the W boson. In this first analysis, two channels were considered: • One top quark decays hadronically and the other leptonically (single- lepton analysis), • both top quarks decay leptonically (di-lepton analysis). θ ∗ Since cos l does not give any information on the charged Higgs boson H H mass, two transverse masses mT (single-lepton analysis) and mT2 (di-lepton analysis) were defined [109]. These three variables were measured in the first ATLAS data from 2010 and a good overall agreement between data and Monte Carlo simulations was observed. The amount of data at this time was not enough to draw any con- clusions about whether or not there is a charged Higgs boson.

5.1.2 Charged Higgs boson searches in the single- and di-lepton channels The search in the single- and di-lepton channels was pursued in Paper VII and the first limits were set with 1.03 fb−1 of data in 2011, when the LHC was θ ∗ running at 7 TeV [110]. With the help of the discriminating variables cos l , H H ( → +) mT and mT2, upper limits on the branching fraction B t bH between 5.2% and 14.1% were set in the H+ mass range from 90 GeV to 160 GeV. The branching fraction of a charged Higgs boson decaying into τν was assumed β max to be 100%. Limits on tan were set in the mh scenario of the MSSM. Values of tanβ larger than 30 - 40 were excluded in the H+ mass range of 90 GeV to 140 GeV. This analysis used the excellent lepton identification of the ATLAS detector, by triggering and selecting at least one isolated lepton. In order to estimate the amount of non-isolated leptons, which appear as a background in this analysis, a data-driven method was used. Non-isolated leptons arise from the semileptonic decay of b-andc-quarks and from decay in flight of π± or K-mesons. In case of misidentified electrons, they also arise from the reconstruction of a π0, photon conversion or shower fluctuations. All leptons coming from such mechanisms are referred to as misidentified leptons, as opposed to true isolated real leptons coming from e.g. W and Z decays. A data driven method, the Matrix Method, was used to estimate the contribution of this background, see section 5.2 for details. Other background contributions were modelled using Monte Carlo simulations. With more and more data collected by ATLAS it became clear that the di- lepton channel would not give enough sensitivity for further charged Higgs θ ∗ boson searches and this analysis was discontinued. The cos l distribution for

48 the H+ side in di-lepton events as well as the combined limit from the single- and di-lepton channels are shown in ﬁgure 5.1

600 -1 ATLAS Preliminary ∫Ldt = 1.03 fb 500 + mH+ = 130 GeV tt (with H ) + Br(t → bH ) = 10% tt (W+W-) Events / 0.2 400 Single top 0.4 + ATLAS Preliminary

Z + jets bH 0.35 Data 2011 s = 7 TeV

→ Observed CLs 300 Diboson t 0.3 Expected -1 ± 1σ ∫Ldt = 1.03 fb QCD & W ± 2σ 0.25 200 Data 2011 0.2

0.15 100 0.1

0.05 0

-1 -0.5 0 0.5 1 95% C.L. upper bound on Br 0 cosθ*, H+ side 90 100 110 120 130 140 150 160 mH+ [GeV] θ ∗ (a) cos l distribution. (b) Combined limit from the single- and di- lepton channels. θ ∗ + Figure 5.1. a) Reconstruction of cos l on the H side of the di-lepton events, in ATLAS data and Monte Carlo simulations. b) Upper limits on B(t → bH+) for the combined single-lepton and di-lepton channels, as a function of the charged Higgs boson mass, obtained for an integrated luminosity of 1.03/fb and with the assumption that B(H+ → τν)=100%. This paper [110] is not printed in the thesis, which is why the plots are presented here.

5.1.3 Combination of the most sensitive channels for charged Higgs boson searches In 2012 a paper on charged Higgs boson searches was published using the full 2011 dataset of 4.6fb−1 collected by ATLAS at 7 TeV [63]. This paper combines searches based on the following decay channels1: + • lepton + jets: tt¯ → bbW¯ H → bb¯(qq¯ )(τlepν) + • τ+lepton: tt¯ → bbW¯ H → bb¯(lν)(τhadν) (with l = e,μ) + • τ+jets: tt¯ → bbW¯ H → bb¯(qq¯ )(τhadν) + θ ∗ H In the lepton jets, channel the discriminating variables cos l and mT were used to discriminate between charged Higgs bosons and W bosons. In the τ+lepton and the τ+jets channels, the discriminating variables are the missing miss 2 transverse energy ET and the transverse mass mT . Limits on the branching fraction B(t → bH+) were set between 5% and 1% in the mass range from 90 GeV to 160 GeV. This was a signiﬁcant improvement over the whole charged Higgs boson mass range, compared to existing

1τ τ lep: leptonically decaying tau, had: hadronically decaying tau 2 = l miss( − φ ) mT pT ET 1 cos l,miss

49 limits provided by the Tevatron experiments, in particular for H+ masses close to the top quark mass. These combined exclusion limits were dominated by the exclusion power of the τ+jets channels, especially in the upper H+ mass range. The τ+lepton channel has a similar exclusion power compared to the τ+jets channel for low charged Higgs boson mass but a much worse exclusion power for charged Higgs boson masses close to the top quark mass. The lepton+jets channel lies somewhere in between with better exclusion limits than τ+lepton in the upper mass region, but lower compared to τ+jets and, for masses close to the W boson mass, lower limits in general [111, 112, 113]. max An interpretation of these limits was done, in the mh scenario, thereby excluding tanβ above 12-26 as well as between 1 and 2-6 for charged Higgs boson masses between 90 GeV and 150 GeV. The Matrix Method was again used to estimate the amount of misidentiﬁed leptons in the lepton + jets and τ+lepton channels. Other background contributions were determined from simulation, data driven methods or a combination of both.

5.1.4 Charged Higgs boson searches through the violation of lepton universality The following paper published by ATLAS reported on a new search for charged Higgs bosons in the τ+lepton channel through the violation of lepton universality in tt¯ events [62]. Here the 4.6 fb−1 of 7 TeV data were re-analysed. As- suming that a charged Higgs boson is produced in top quark decays, and that H+ predominantly decays into a τ−lepton and a neutrino, more ﬁnal states with taus would be found in tt¯ decays compared to the absence of a charged Higgs boson (in the SM, the top quark decays into a W boson which, with equal probability, decays into the three lepton generations). The search was performed in events with a ﬁnal state consisting of e/μ + τhad.Ratiosoftt¯ event yields between e+τhad and e+ μ, as well as between μ +τhad and μ +e events, were calculated and compared with simulation.

BR(tt¯ → bb¯ + lτ + Nν) R = had (5.2) l BR(tt¯ → bb¯ + ll + Nν)

This ratio-based method reduced the impact of common systematic uncertainties between the numerator and the denominator. With this method, upper limits on the branching fraction B(t → bH+) between 3.2% to 4.4% could be set for charged Higgs boson masses in the range from 90 GeV to 140 GeV. A combination of the results from the published τ+jets analysis and the ratio method yields upper limits on B(t → bH+) from 0.8% to 3.4% in the H+ mass max range of 90 GeV to 160 GeV. Also, the exclusion in the mh scenario could be further improved. The Matrix Method was used in order to estimate the contribution of misidentiﬁed leptons to the backgrounds.

50 5.1.5 Charged Higgs boson searches with the 2012 dataset Charged Higgs boson searches were then pursued with the 2012 ATLAS data at 8 TeV and extended to charged Higgs boson masses beyond the top quark mass. The latest ATLAS publication on charged Higgs boson searches at the time of writing is the τ+jets analysis [58]. The corresponding limits were presented in section 2.2.4, in ﬁgure 2.13.

5.2 The Matrix Method A significant background in charged Higgs boson searches, involving one or two isolated leptons, consists of events with reconstructed electrons and muons arising from the semileptonic decay of hadrons with b-orc-quarks, from the decay-in-flight of π± or K-mesons and, in the case of electrons, from π0 mesons, photon conversions or shower fluctuations. Such events are difficult to estimate from simulation. The probability that the leptons detected in such events are actually misidentified by the reconstruction software is very small and therefore huge amounts of events would have to be simulated, which in turn would use large amounts of computing resources. Also the modelling of lepton isolation in simulation is very difficult to match with reality. A better approach is therefore to estimate misidentified electrons and muons by data driven methods. One of them is the so-called Matrix Method, a method already used at the Tevatron [114]. This data driven method exploits the difference in the lepton identification between real, prompt, and misidentified or non-prompt electrons and muons. It is based on the selection of two categories of events using loose and tight lepton selection requirements while keeping the same kinematic selection as the baseline analysis. The tight selection is the one used in the baseline analysis and contains mainly real leptons. The loose selection has more relaxed isolation requirements and is enriched with misidentified and non-prompt leptons. The tight sample is a subset of the loose sample. In a data sample containing events with a single lepton, the number of events with one tight lepton (Nt ) and the number of events with one loose lepton (Nl) can be expressed as linear combinations of the number of events with a real (r) or a non-prompt, misidentified lepton ( f ):

l = l + l , N Nr Nf (5.3) t = t + t . N Nr Nf (5.4)

t l ε The ratio between Nr and Nr defines the efficiency r that a real lepton in the loose sample would pass the tight selection criteria. In the same way, the efficiency that a misidentified lepton passes the tight selection criteria is

51 Nt ε = f deﬁned as f l . This leads to the following equations: Nf t = ε l, Nr rNr (5.5) t = ε l , Nf f Nf (5.6) which can be combined together with equation (5.4): t = ε l + ε l . N rNr f Nf (5.7) By solving the equation system given by (5.3)and(5.7), and by using equation (5.6), the number of loose leptons in the tight sample can be estimated by: ε t = f (ε l − t). Nf rN N (5.8) εr − ε f

The efficiencies εr and ε f need to be known, as well as the total number of loose and tight events. The efficiencies are estimated in regions enriched with misidentified or real leptons. Not only the total number of misidentified leptons needs to be estimated, but also the shapes of various distributions need to be described correctly. For this purpose, equation (5.8) can be generalized into a weight:

ε f ωi = (εr − δi) (5.9) εr − ε f where δi is equal to 1 if the event i passes the tight event selection and 0 otherwise, and εr and ε f may depend on the properties of the event i.The weights are built in such a way that: ω = t . ∑ i Nf (5.10) i∈loose data The Matrix Method can also be used for di-lepton events. For further details, see Paper III.

5.2.1 The Matrix Method related to top quark and charged Higgs boson physics in ATLAS Even though the Matrix Method has already been used for some time, it needed further development through out the LHC Run 1. The main reasons were the change of conditions, e.g. more pile-up, but also different require- √ments at the trigger level. The data collected during 2011 had an energy of s = 7 TeV. The pileup conditions during that time were significantly different in the beginning and the end of the data taking. Also, a better understanding of the detector changed the recommendations regarding object definitions. Therefore, the efficiencies εr and ε f had to be recalculated and monitored at

52 all times. But also the parametrization, which was used to calculate the event weight, had to be adjusted at all times in order to provide the best possible description of this background. At the beginning of the 7 TeV run, the trigger menues contained no isolation requirements and the threshold was 20 GeV for electrons and 18 GeV for muons. Later in the 7 TeV run, the threshold of the electrons had to be increased to 22 GeV. When moving to 8 TeV in 2012, isolation criteria were included at the trigger level for electrons and muons. Furthermore, a combination of two triggers, with a threshold of 24 GeV and 60 GeV for electrons, and 24 GeV and 36 GeV for muons, were used. This required major changes in the parametrization of the Matrix Method, but also in the estimation of the efficiencies. At this time, the Matrix Method, which was developed for charged Higgs boson searches, was combined with studies performed in the group working on misidentified leptons in top physics, in order to handle the increasingly challenges of the Matrix Method. The outcome of this combination was Paper III, which also gave the opportunity to compare the Matrix Method with the Fitting Method (also known as jet-lepton and anti-lepton method), an alternative method for misidentified lepton estimation. The Fitting Method defines a model for the non-prompt and misidentified leptons background shape for different distributions. A maximum likelihood fit of a discriminating variable is performed on data to obtain its total normalisation. Monte Carlo simulation is used to build the templates for the shape. The two methods give comparable results within systematic uncertainties, which are between 10% and 50% for the Matrix Method and 50% for the Fitting Method.

5.2.2 Physics analyses The ﬁrst charged Higgs boson searches in LHC Run 1 were cut-based analyses. With the search for heavy charged Higgs bosons, multivariate techniques also found their way into the analyses. Paper I, II and VI - IX describe light charged Higgs boson searches where cut-based physics analyses were used. Therefore, a general description of cut- based analyses for charged Higgs boson searches is given in the following. When searching for physics processes, the overall goal is to select a subset of the total data enriched in the physics process of interest. This can be achieved by selection requirements (“cuts”) which favour a certain type of events. When the physics process of interest is identiﬁed, its signature in the detector has to be analysed: • Does the process contain leptons, or only hadronically decaying objects? • How many jets are expected in the decay, how many are b-tagged? • Does the process involve neutrinos, hence missing transverse energy? • What is the expected energy range of all decay products?

53 Once the signature is understood the cut-based analysis can be set up. In order to estimate the efﬁciency of these “cuts” and their ability to reduce backgrounds, Monte Carlo simulations are used. In charged Higgs boson searches, and other analyses, event generators like HERWIG [115], ALPGEN [116], PYTHIA [117], MC@NLO [118], POWHEG [119], AcerMC [120], SHERPA [121] are commonly used. Simulations based on different generators may result in systematic uncertainties in the modelling of physics processes.

In order to get the best background rejection, together with the best signal selection, a cut optimization is performed. Usually the first step in the analysis is event cleaning, removing those which have uncertain conditions or poorly reconstructed objects. Such events could arise from the fact that parts of the detector system were not fully operational. Jets could have wrong properties due to problems with the LAr (Liquid Ar- gon) calorimeter, or be arising from noise spikes in the calorimeter. Such requirements are usually given to the analyser from specialised working and performance groups. The next step is to choose an appropriate trigger menu and select only events that fired such triggers. If the event contains leptons, a lepton trigger could be used. For events with hadronically decaying taus, special triggers exist, usually in combination with another object (lepton or missing transverse energy). For the charged Higgs boson searches in ATLAS involving electrons or muons, a single-lepton trigger was used. Leptons are easy to trigger on and ATLAS has a very good lepton identification. Single- + lepton triggers have low pT thresholds, and hence are not pre-scaled. The H analysis team was working very closely with the top physics group, who are also using the same triggers, hence the efficiencies of the triggers were well understood. Also, systematic effects were much better understood thanks to this collaboration. Even for the selection of di-lepton events, the same single- lepton triggers were used for the charged Higgs boson searches. With different triggers, the Matrix Method would have had to be developed for each trigger separately, with subsequent problems in finding control regions for measuring the real and misidentification efficiencies. The charged Higgs boson searches did not only share the trigger studies with the top group, but also the object definitions, and performed the same or compatible overlap removals. The overlap removal is important to avoid counting the same object multiple times in the analysis. An electron can easily be reconstructed as an electron and a jet, muons can overlap with electrons, especially in the tracker, and tau objects usually need to be selected from the jet collection. The overlap removal is essentially a priority list: if objects like electrons, taus and jets overlap, which one to count as an electron, which one to count as a jet and which one as a tau? By having triggers, object selections and overlap removals in common with the top group, a lot of analysis tools could also be shared.

54 Following the trigger requirements, every selected event is required to have a certain amount of jets and b-jets, in order to account for the hadronically decaying objects in the physics signature of interest. Light charged Higgs bosons, produced through top pair production are associated with two b-jets. Additional jets could come from the decay of the W boson or other underlying events. Such a requirement removes a large amount of other physics processes which do not contain b-quarks. In physics analyses containing hadronically decaying taus, requirements that a tau object is found in every event are imposed. Since the charged Higgs boson dominantly decays to taus, this is a natural choice. Tau candidates are selected from jets with one or three associated tracks (one- or three- prong taus)3 reconstructed in the inner detector [122]. Special algorithm re- ject electrons and muons. Hadronic taus are discriminated against quark- and gluon-initiated jets by their shower shape and tracking variables. Misidentified taus are a major background in the charged Higgs boson analyses involving hadronic taus. The majority of misidentified taus in the final event selection originate from jets, with different misidentification probabilities, depending on the initial parton (light quark, heavy quark or gluon). Other sources for misidentification are electrons and muons, in which case mainly one-prong taus are misidentified. Data driven methods are used in order to estimate the amount of misidentified taus. Correcting the simulation to match the misidentification probability measured in contrrol regions of the data is one method. A Matrix Method can also be used for misidentified taus. In the decay of the W boson arising from e.g. top quarks, but also in the decay of the charged Higgs bosons, neutrinos are involved. These neutrinos miss cannot be detected by ATLAS and result in missing transverse energy (ET ). miss Therefore, in the cut-based analysis a certain amount of ET is required. This also reduces other physics processes which do not involve as much missing transverse energy as charged Higgs boson production in tt¯ events. The main background surviving the event selection for charged Higgs boson searches are mostly tt¯ events, because the final state resembles the H+ signal, as can be seen in the Feynman diagram of figure 5.2. After the final selection, an excess (or deficit) of events can indicate new physics if statistically significant. In order to enhance the signal-background separation, discriminating variables are used, where charged Higgs bosons end up dominantly in a certain region. Multi-variate analyses combining several discriminating variables into one, may also be used. However, such analyses were not performed for this thesis. After the final selection, distributions of discriminating variables are used to determine limits. These limits set constraints for example on the branching

3"prong" refers to the number of charged particles in the ﬁnal state of the tau decay. Generally, the tau decays into a single π± (1-prong) and any number of π0s, or three π± (3-prong) and any number of π0s.

55 g b g b

t W + t H+ g g

tW¯ − tW¯ −

g g ¯b ¯b (a) tt¯ background (b) charged Higgs signal Figure 5.2. The production and decay of tt¯ events (a) and the production of a light charged Higgs boson from a tt¯ decay (b). One W boson in the tt¯ decay is replaced by a charged Higgs boson. ratio of a top quark decaying into a charged Higgs boson. The limit is obtained by comparing the predictions from the SM-only hypothesis with the observed and selected events. A profile likelihood statistical analysis is performed with the test parameters of interest. The statistical treatment usually used in ATLAS is described in [123], the limit itself is derived using the CLs criterion [124]andtheasymp- totic approximation [125]. The results are presented in limit plots. An example for a neutral Higgs boson is given in figure 5.3. On the horizontal and vertical axis are the parameters of the theory under test, e.g. the mass of the Higgs boson and the cross-section ratio (σ/σSM), respectively. The solid black line shows observed limits at 95% confidence level, which represents the certainty that a Higgs boson with the given mass does not exist. The dotted black line shows the average expected limit (derived from simulation) in the absence of a Higgs boson. The green and yellow bands indicate the corresponding 68% and 95% certainty of the average expected limit. If the solid black line lies below the dotted black line, there is a deficit, indicating that less data than the expected background is observed. If it lies above, there is an excess, i.e. more data than the expected background is observed. If the solid black line lies below the red line (exclusion line at 95% CL), then the SM Higgs boson is excluded with a 95% certainty, since it is not produced with the expected cross section for that mass. If the solid black line lies above the red line and at the same time above the dotted black line, an excess is observed, indicating that there could be a Higgs boson around that mass.

56 Figure 5.3. Simpliﬁed exclusion plot made by ATLAS, for the illustration of excess, deﬁcit and exclusion in limit computations [126].

57 6. Future data readout challenges at LHC

6.1 Introduction The High Luminosity LHC (HL-LHC) will produce proton-proton collisions in 2024 with an expected instantaneous luminosity of 5×1034 cm−2s−1,which is an order of magnitude higher than at Run 1. The ATLASdetector at the LHC is expected to collect around 300 fb−1 of physics data until 2022, whereas the HL-LHC will deliver data of the order of 250 fb−1 per year [127]. The higher luminosity will increase the mean number of interactions per bunch crossing to around 140, resulting in large particle fluxes. In order to keep the good performance of vertex and track reconstruction, lepton identification and heavy flavour tagging in ATLAS under HL-LHC operation, the current tracking system must be replaced by a more granular (silicon) tracker. To take advantage of the luminosity increase for new discoveries and precision measurements in ATLAS, it is essential to improve the trigger system and the capability to reconstruct physics objects over a large acceptance range [128]. Single-lepton trigger pT -thresholds need to be kept at around 20 GeV in order to detect key-signatures like W /Z bosons and tt¯ pairs. The effect of trigger threshold on signal yields is shown in figure 6.1. At the same time, the trigger rates need to be kept low in order to be able to bring all data out of the detector. Therefore, new trigger concepts need to be implemented when upgrading ATLAS for HL-LHC. A Level-0/Level-1 trigger, i.e. a two-step first level hardware trigger architecture, is considered for that purpose. The use of calorimeter-only information for triggering will not reduce the trigger rates enough to maintain low pT -thresholds. Further information from the inner detector is needed already at L1. Sufficient trigger rate reduction can be achieved by implementing a track trigger at L1. Such a self-seeded L1Track trigger is designed as follows. A fast track reconstruction of all high momentum tracks (pT > 10 GeV) can be performed in the full coverage of the tracker without the need for external seeds. The idea is to send the positions of the hit coincidences in the inner detector layers to track finder units, which will perform a hit matching. The expected data rate at HL-LHC is around 1 Gbit/s per silicon module. The concept of the L1Track trigger is not yet fully developed and one of the main challenges is to transfer the data from the silicon modules to the central trigger processor of the detector, for which one possible approach will be presented in the following sections. Details about the Phase II upgrade plan can be found in the Letter of In- tent [128].

58 %& ' "# &&

$&"%& #"

&%'!'#"$

Figure 6.1. Acceptance of muons from tt¯, WH and SUSY processes as a function of the true muon transverse momentum [128].

6.2 Wireless technology in future detector systems In the L1Track trigger for the Phase II ATLAS upgrade data transfer is a major challenge. Tracks propagate in the radial direction of the detector, however the readout in the current detector systems is mainly routed longitudinally, i.e. parallel to the beam. This makes layer to layer communication with short con- nections complicated and a different concept has to be found. Simply connecting the different detector layers by cables in the radial direction is not feasible since that will add non-sensitive material, reducing the detector performance significantly. Figure 6.2 shows degradation of the radiation and interaction lengths in the current ATLAS detector for η > 0.7 due to the routing of services. Data transfer methods for future detectors with less material than today would indeed result in benefits. One technology solution to bring data out from the tracker is using wireless links instead of cables. Doing so, the signal can be routed more freely, en- abling to spread data links over the whole detector volume, hence avoiding the congestion currently in the transition region between the barrel and end-caps. This is especially important for the first 50 cm in the inner detector volume, where the transition between parallel data transfer and high bandwidth se- rial transfer is done. Wireless links open up new possibilities for the detector readout. The data can be transferred in the radial direction to the outside of the detector, but also local communication between detector layers which opens for putting track finding intelligence inside the tracker. This would make it

59 ) )

0 2.5 λ 0.7 Services Services TRT 0.6 TRT 2 SCT SCT Pixel 0.5 Pixel Beam-pipe Beam-pipe 1.5 0.4 Radiation length (X Interaction length ( 1 0.3 0.2 0.5 0.1

0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 |η| |η|

(a) Radiation lengths (X0) (b) Interaction lengths (λ)

Figure 6.2. Material distribution (X0, λ) at the exit of the ID envelope, including the services and thermal enclosures. The distribution is shown as a function of |η| and averaged over φ. The breakdown indicates the contributions of external services in their active volume and of individual sub-detectors [129, 130]. possible to reconstruct track primitives locally in real time [131]. Ideas on radial data transfer and inter-layer communication are shown in ﬁgure 6.3.

(a) Radial data transfer (b) Inter-layer communication Figure 6.3. Radial data transfer (left): The data is transferred via wireless links from the inside of the detector to the outside. Inter-layer communication (right): The interesting data from the four layers is collected on one layer for further processing. In this scenario extra hardware is placed on the second layer in order to decide if the event is of interest or not, and whether it should be sent outside the detector.

6.2.1 Choice of the frequency band for wireless data links In the consumer market, wireless technology can be found in many places, such as radio, terrestrial TV, satellite TV and wireless data networks. With the “internet of things” [132] it is becoming even more frequent in our everyday life. These systems operate mainly at frequencies up to 5 GHz and are not

60 suitable for wireless communication in a track trigger system, because they do not provide high enough bandwidth for all data to be transferred. Their modulation techniques are complicated and too power hungry for a tracker. Furthermore, wavelengths at 5 GHz are around 6 cm, which gives a feature size not compatible with trackers. A much more promising candidate for detector systems is the 60 GHz frequency band technology. With wavelengths of the order of 5 mm, feature sizes are significantly smaller. Also, up to 7 GHz of bandwidth is available [133]. This opens for small components [134]and high data rates with simple modulation schemes and low power consumption. The industry has discovered the advantages of 60 GHz frequency, for the increasing demand of data transfer capacity. One application that the industry is in particular interested in is the wireless transfer of high definition video between consumer products [135] over short distances, which needs a lot of bandwidth. With the 60 GHz technology, transfer over long ranges is challenging due to the high absorption of 60 GHz waves in air and most materials. This is why this technology is interesting for short distance communication in future trackers. The absorption in materials prevents signal from penetrat- ing through the different layers of the detector system. This makes it possible to re-use the same frequency at different places without interference. Fur- thermore it is of particular importance that the connection antenna to antenna should be in the far-field1, in order to benefit from directivity and gain of the antenna. Transmission distances are of the order of 10 cm in a tracker, which requires high frequencies. Of course, even higher frequencies could be used, e.g. the 80 GHz frequency band, but this would put tighter requirements on the fabrication tolerances, component costs would be higher and it would result in larger power losses in the materials. Taking this into consideration, 60 GHz seems to be the best compromise.

6.2.2 Connection concept The replacement of cables by wireless links can be achieved in a straightfor- ward way. The data of a detector layer is collected in the same way as it is now with optical links. The optical link, with a transceiver and a optical ﬁ- bre is replaced with a wireless transceiver. The transceiver chip generates a carrier wave at 60 GHz from its built-in local oscillator. One challenge is that compared to optical links, chip designs for wireless must be done for very high frequency. In the transmitter part of the chip, the detector data is modulated on the 60 GHz carrier and transmitted via an antenna through free space. Obviously less material is needed when using a wireless link.

1The far-field region is where the angular field distribution is independent on the distance to the antenna. The minimum distance where the far-field starts depends on the size of the antenna and the wavelength of the electromagnetic field [136].

61 The receiver chip gets the signal from free space through the antenna, the data is then demodulated and is digitally available for further processing units. Depending on the scenario in which the wireless link is operated, the required bandwidth is different and so is also the type of antenna.

6.2.3 Requirements on the antenna system When considerations were made about which material and antenna to use for demonstrating a wireless link suitable for trackers, it was clear that a low density design of the antenna would be optimal. Antennas of high density materials would add much non sensitive material to the detector thus should be avoided. Furthermore, the antenna should be cheap and easy to produce in large quantities. It should provide polarization and should radiate most power in one direction. The decision was to use patch antennas. A detailed description of this antenna type is given in section 7.6. The patch antenna is radiating its energy mainly in the region perpendicular to the patch and not, like for example a dipole antenna, circularly around radiating elements. Combining several patches in an array gives the possibility to increase the focussing and the gain compared to a single patch antenna. Also, for some use scenarios, it is of importance that the patch antenna has a limited bandwidth of around a few percent [137]. This makes it possible to place several data links, operating at different frequencies, close to each other without causing interference. In scenarios where fewer links are needed, but with a larger bandwidth requirement than the few percent of the patch antenna, wideband antennas are clearly better. Horn antennas [138] provide both a large gain and bandwidth, and they can be produced from Kapton foils [139], giving them a very low density. A disadvantage is their voluminous 3D structure, which may make the positioning of the components complicated. An 3D antenna made from a Kapton foil also is very sensitive to shocks, but this is a minor concern when used in a detector. Slot antennas for 60 GHz can be produced with a bandwidth of more than 7 GHz [140], on a printed circuit board (PCB) substrate. The antennas are produced in the same way as patch antennas, hence have similar advantages in terms of low material density and low fabrication cost. Vivaldi antennas are types of wideband antennas that can be used for 60 GHz. These have models that also can be produced on PCB substrate. Depending on the design, Vivaldi antennas can be constructed both with a radiation direction parallel to the substrate [141], and perpendicular to the substrate [142] like the patch and slot antennas. Other types of antennas considered are Yagi antennas [143], inverted-F antennas [144] and many more which are described in the literature [137].

62 Choice of material for antennas The Roger (ULTRALAM 3850) and DuPont (Pyralux AP9161R) materials were chosen for production. They are copper laminates with two layers of copper and a special (proprietary) substrate in between. The laminates are thin and light, hence do not add much material to the detector. Furthermore they are ﬂexible and can easily be bent, which can be of importance for placing the antennas in the detector. Their electrical properties are good in terms of small dielectric constants (εr = 2.9 at 10 GHz for Rogers, εr = 3.4at1MHz for DuPont), hence the materials suffer small energy losses when radiating at high frequency. The materials are expected to be radiation hard, which is important for working in the conditions of a particle detector.

6.3 Radiation damage to antenna substrate In particle detectors, the radiation from collision products [145]isextremely high, which requires electronics and materials to be very radiation hard. This is also required from antennas to be used in trackers. The effect of radiation damage on the antenna material must be studied. For patch antennas, it is crucial to understand how the electric properties of the PCB substrate changes, when radiated with high doses. Changes to the dielectric constant of the material will shift the resonance frequency of the antenna, which in the worst case can stop a wireless link from working. If several thousands of wireless links are placed in a detector system, a change in frequency could have tremendous effects and could break down the whole system.

6.3.1 Effect of changes in the dielectric constant Studies were performed using the ANSYS HFSS (High Frequency Structure Simulation) program [146] in order to simulate the effect of dielectric changes. A designed single patch antenna, which was optimized for the Rogers PCB substrate, was used for this study. The antenna is resonant at 60 GHz. The dielectric constant was changed from its nominal value 2.9 in the simulation 2 from 2.5 to 3.3. In ﬁgure 6.4 the effect on the S-parameter S11 is shown. For smaller values of the dielectric constant, the resonant frequency of the antenna moves to higher values, and vice versa. From the plot, a change of approximately 0.1 in the dielectric constant leads to a 1 GHz frequency shift.

2Scattering parameter, described in section 7.2 in detail.

63 0 -5 S11 [dB] -10 -15 -20 -25

ε=2.9 Nominal ε=2.5 -30 ε=2.6 ε=2.7 -35 ε=2.8 ε=3.0 ε=3.1 -40 ε=3.2 ε=3.3 -45 54 56 58 60 62 64 f [GHz]

Figure 6.4. The effect of a change in the dielectric constant on the resonant frequency of a single patch antenna optimized for 60 GHz on Rogers PCB substrate.

6.3.2 Radiation damage studies In order to study the effect of radiation in the two different PCB substrates, two studies were performed. In the ﬁrst study, small capacitors were produced on both substrates used for antennas. These capacitors were measured for different frequencies ranging from 100 kHz to 1 MHz with an LCR meter. The frequency range is limited by the measurement device. The capacitors were radiated with electrons and re-measured after irradiation. A second study was done with single patch antennas produced on the two substrates, which were measured before and after radiation with the Vector Network Analyser (VNA) at 60 GHz. Radiation with electrons was done at the university hospital in Uppsala reaching a dose of 100 kRad (with a few % precision), which is a dose relevant for space applications but only a small fraction of what is required for LHC. The two studies showed no measurable effect on capacitance and resonance frequency, hence no effect was observed on the dielectric constant for these substrates up to the delivered dose. In order to increase the radiation dose, the test structures were radiated at CERN with orders of magnitude higher doses. Unfortunately the test structures have not been returned for post-radiation measurements and no results are available at the time of writing.

64 6.4 Outlook The next step in this project is to demonstrate the transfer of data at 60 GHz with the required data bandwidth. This project is performed in collaboration with the University of Heidelberg in Germany. There, a 60 GHz transmitter- receiver chip is being designed [147, 148]. This chip will be connected with the antennas designed in Uppsala, and feasibility studies of data transfer will be performed. Possible disturbances from the surrounding detector system will be studied as well. A future possible development would be the integration of the antenna on the transceiver chip. This would have the beneﬁt of a smaller antenna on top of the chip, saving space and making the coupling from the chip to the antenna shorter, possibly resulting in smaller losses. Disadvantages are of course the loss of ﬂexibility in terms of antenna choice, but also in terms of operation at different frequencies of the 60 GHz band.

65 7. Wireless technology

7.1 Electromagnetic waves In radio communications, the propagation of electromagnetic waves in free space is the basis for sending and receiving information between two points which are not connected physically with each other [149]. Inside the receiving and transmitting components, the radio signals exists in form of alternating currents. Outside these conductors, radio signals exist as electromagnetic waves. On the transmitter side, the alternating current in the antenna generates an electromagnetic ﬁeld and the energy coming from the transmitter is converted into real electromagnetic waves. The antenna on the receiver side captures the electromagnetic waves, and the ﬁelds are converted back into alternating currents. The concept of electromagnetic waves can be described by Maxwell’s equations [150]:

ρ ∇ · E = (7.1) ε0 ∇ · B = 0 (7.2) ∂B ∇ × E = − (7.3) ∂t ∂E ∇ × B = μ J + ε (7.4) 0 0 ∂t where ε0 is the permittivity of free space, μ0 is the permeability of free space, ρ is the electric charge density, J is the electric current density, B is the magnetic field and E is the electric field. From these equations it can be seen that whenever an electric current flows, a magnetic field is induced in the surrounding space. Any variation of this magnetic field results in the creation of an electric field. With an oscillating current an oscillating magnetic field is created as well as an oscillating electric field. In turn, an oscillating electric field creates a magnetic field again. Oscillating magnetic and electric fields cannot exist alone. Therefore, the expression “electromagnetic field“ is used. Electromagnetic waves are periodic, oscillating, i.e. with a sinusoidal form and can be characterized by a frequency ( f ). The frequency is expressed in Hertz (Hz). The wavelength λ is in turn defined by: ν λ = (7.5) f

66 where ν is the wave velocity, which can have different values depending on the medium in which the wave propagates. In vacuum ν is equal to the speed of light c = 3 × 108 m/s. Plane waves can in general be expressed as: π ( , )= π − 2 z + Φ , Ex z t E0 sin 2 ft λ (7.6) π ( , )= π − 2 z + Φ Hy z t H0 sin 2 ft λ (7.7) where E0 is the amplitude of the electric field, H0 is the amplitude of the magnetic field and Φ is a phase. The propagation is along the z direction, see figure 7.1. A nomenclature was established for different frequency bands, see table 7.1.

Figure 7.1. A plane electromagnetic wave in free space.

7.2 The scattering parameter An electrical network can be seen as a black box containing basic electrical elements, which are connected to each other and behave linearly. The inputs to the black box are called ports and they are interacting with other electrical circuits.

67 Table 7.1. Radio frequency portion of the electromagnetic spectrum [151]. Frequency designation Frequency range Ultra low frequency (ULF) < 3 Hz Extremely low frequency (ELF) 3 Hz to 3 kHz Very low frequency (VLF) 3-30 kHz Low frequency (LF) 30-300 kHz Medium frequency (MF) 300 kHz to 3 MHz High frequency (HF) 3-30 MHz Very high frequency (VHF) 30-300 MHz Ultra high frequency (UHF) 300 MHz to 3 GHz Super high frequency (SHF) 3-30 GHz Extremely high frequency (EHF) 30-300 GHz Submillimeter 300 GHz to 3 THz

The scattering matrix describes the relation between the voltage wave applied on the ports to the voltage waves reflected from or transmitted to the ports in an electrical network. The electrical circuit in the black box can be characterized by a square matrix of dimension N,foraN-port circuit, having N2 elements. Each element of the matrix is a complex number, the S-parameter. These elements can be used to calculate the response to a signal which is applied to a port. For a multi- port electrical network, the port numbering goes from 1 to the total number of ports N. The S-parameter√ is defined in terms of the normalized complex√ + = in/ − = re f / incoming Vn Vn Z0 and normalized complex reflected Vn Vn Z0 wave voltage1 [152]. The relation between normalized incoming and reflected waves in matrix form is given by: ⎛ ⎞ ⎛ ⎞⎛ ⎞ − + S11 S12 ... S1N V1 V1 ⎜ − ⎟ ⎜ . ⎟⎜ + ⎟ ⎜ V2 ⎟ ⎜ S21 ...... ⎟⎜ V2 ⎟ ⎜ . ⎟ = ⎜ ⎟⎜ . ⎟ (7.8) ⎝ . ⎠ ⎝ . . . . ⎠⎝ . ⎠ − . . . . + VN SN1 ...... SNN VN S-parameters are defined under certain conditions: • The characteristic impedance of the circuit, Z0; • The applied frequency, f of the voltage wave; • The port numbers, n. Figure 7.2 shows the analogy between an incident light-wave and a RF-wave, which is partly reflected and transmitted. What an optic lens is for a light wave, is ”the device under test“ for the RF wave. The left side of the schematic can be interpretet as port one and the right side as port two.

1 ± Vn are deﬁned in terms of the terminal voltage Vn, the terminal current In, and the characteristic in re f + Vn+√InZ0 √Vn − Vn−√InZ0 V√n impedance Z0: V = = and V = = . n 2 Z0 Z0 n 2 Z0 Z0

68 Figure 7.2. Analogy between an incident light-wave and a RF-wave, which is partly reﬂected and transmitted.

The two port network For an electric circuit with only two ports, the equation (7.8) simpliﬁes to: − + V S11 S12 V 1− = 1+ (7.9) V2 S21 S22 V2 + An incoming wave V1 in port one will result in an exiting wave in port one V − and port two V −. Assuming that port two is terminated by a load identical 1 2 − to the characteristic impedance Z0, all reﬂected power on this port V will be + 2 absorbed and V2 will be zero. In such a two port system the S-parameters simplify to: − − V1 V2 S11 = + and S21 = + (7.10) V += V += 1 V2 0 1 V2 0

S11 is the reflected power on port one and S21 is the power transferred from port one to port two. A similar relation can be found in the case where port one is terminated + = with a load identical to the characteristic impedance Z0,i.e.whenV1 0: − − V2 V1 S22 = + and S12 = + (7.11) V += V += 2 V1 0 2 V1 0 69 It should be noted that the parameter S11 also can be expressed as S11 = Z1−Z0 where Z1 is the input impedance of port one. In the case of an antenna, Z1+Z0 the electrical input of the antenna is defined as port one and the radiating part of the antenna as port two. In this case, the S11 parameter describes how much power is reflected by the antenna back to the transmitter, often called “reflection coefficient” Γ. It is used to characterize the input impedance of the antenna, i.e. the matching. The antenna is designed to be resonant at a certain frequency at which also a good matching is achieved. If the antenna is resonant, it will radiate power and only a smaller fraction will be reflected. In case of no resonance, the input power will mostly be reflected. The S- parameters are commonly given in deciBels2 (dB). The S-parameters can be converted into dB by: ( )= | | Sxx dB 20log10 Sxx dB (7.12) when the two measurement ports use the same reference impedance. The S-parameters can be measured with a Vector Network Analyser (VNA). Figure 7.3 shows the simulated S11 parameter of a patch antenna resonant at 58 GHz. In the non resonant region, where almost all power is reflected, S11 is close to 0 dB. In the region around 58 GHz, the antenna reflects almost no power and transmits most of it as radio waves, the S11 drops to very small dB values: .

S11 [dB] 0

-10

-20

-30

-40

-50 54 56 58 60 62 64 66 f [GHz]

Figure 7.3. The S11 parameter of a simulated antenna resonant at 58 GHz.

2L = 10log Pb where P and P are power values. dB 10 Pa a b

70 7.3 Antenna characteristics Different parameters are used to characterize antennas [151].

Radiation pattern: The radiation pattern is one of the most fundamental properties of an antenna. This property describes the relative strength of the radiated ﬁeld in different directions at a constant far-ﬁeld distance. Radiation patterns show how focussing an antenna is and its preferred direction of radiation.

Directivity: Directivity is a measure of the ability of an antenna to concen- trate energy in a certain direction. The directivity of an antenna is deﬁned as the ratio of “radiation intensity in a given direction” divided by the “average radiation density in all directions” [136]. The average radiation intensity of the antenna is the same as the total radiated power divided by 4π. The directivity D can be expressed as: 4πU D = (7.13) Prad where U is the radiation intensity (W/unit of solid angle) and Prad is the total radiated power (W).

Gain: The gain of an antenna is a combined measure of the antenna’s directivity and its electrical efficiency. For a receiving antenna, the gain gives the ability to convert radio waves from a certain direction into electrical power. For transmitting antennas it is the opposite. If the gain is specified without a direction, it refers to the main loop of the antenna, which is the direction in which most power is transmitted or received. The gain is defined as the power received from a source at far-field distance, divided by the received power of an isotropic antenna at the same distance. An isotropic antenna is an antenna equally sensitive in all directions. The gain is specified in dB. When referring to a ratio with an isotropic antenna, it is specified in decibels-isotropic dBi.

Bandwidth: The bandwidth is the frequency range under which the antenna works satisfactory in terms of that it radiates or receives electric power. It is often quoted in terms of Voltage Standing Wave Ratio (VSWR) 1 + |Γ| VSWR= (7.14) 1 −|Γ| or in terms of the reﬂection S-parameter S11. For example, the antenna in ﬁg- ure 7.3, operates with a VSWR< 1.5orS11 < −13.98 dB in a frequency range 57.4-58.6 GHz and has a bandwidth of 1.2 GHz.

71 Input impedance: Usually, a transmission line of characteristic impedance Z0 is connected to an antenna in order to deliver radio frequency power to the antenna. At the connection point between the antenna and a transmission line, the later sees the complex load impedance ZL of the antenna. If this load impedance differes from the impedance of the transmission line Z0,an impedance mismatch occurs. This leads to losses in the power transfer to the antenna and standing waves in the transmission line. The impedance also determines the voltage level needed in order to generate radio frequency current in the antenna and in turn to radiate a certain amount of power.

7.4 The transmission line 7.4.1 Transmission line types A transmission line is a specialized cable or other structure designed to carry signals at high frequencies. Transmission lines are used for connecting antennas to transmitter and receiver, distribution of radio frequency (RF) signals such as telecommunication lines, but also high speed data buses used on PCBs. Different types of transmission lines exist, among the most common ones are:

(a) Twin-lead line (b) Coax line

• The twin-lead line, shown in ﬁgure 7.4(a), is a two-conductor ﬂat cable used as a balanced, symmetric transmission line. Its construction is made from two wires placed parallel and which are spaced at a precise

72 distance apart by a plastic (usually polyethylene) ribbon. The uniform spacing gives this line its characteristic impedance Z0. The 300 Ω type, is the most common twin-lead line (for historical reason), used for example in television. • The coaxial line, shown in figure 7.4(b), is an unbalanced type of transmission line. It is built from an inner conductor (signal line) surrounded by a tubular insulating layer, which is surrounded by a tubular conducting shield. The spacing between signal conductor and shielding is constant to provide the characteristic impedance of the coaxial line. In ideal coaxial lines the electromagnetic field of the signal exists only in the space between the inner and the conducting shield. This allows to put this line close to metal objects without getting problems of power loss. The line is also protected against external electromagnetic interferences. This is a big advantage compared to other transmission line types. • The microstrip line, shown in figure 7.4(c), is an unbalanced type of transmission line produced by PCB technology. It consists of a conducting strip, which is separated from a ground plane by the dielectric PCB substrate. Microstrips are often used on high speed PCBs, where fast signals need to be transferred with minimal distortion. • The coplanar strip line, shown in figure 7.4(d), is a balanced type of strip line similar to the microstrip line. The main difference is that two differential pairs of microstrip are routed parallel to each other under constant spacing. The most important parameters of a transmission line are the inductance L and capacitance C [153]. A schematic of an equivalent circuit for a lossless transmission line is shown in figure 7.5.

Figure 7.5. Equvivalent circuit of a lossless transmission line.

The characteristic impedance Z0 of a transmission line is independent of the line length and load, it is only a function of the line parameters (i.e. size and spacing of the conductors and type of insulation used).

7.4.2 Characteristic impedance of a transmission line For a lossless line (containing only L and C) the characteristic impedance is real and equals [153]: jωL L √ Z = = , j = −1 (7.15) 0 jωC C

73 For a lossy line, as shown in ﬁgure 7.6, Z0 becomes complex and starts to depend on the conductor and dielectric losses (R and G) R + jωL Z = (7.16) 0 G + jωC where G is the shunt conductance3 and R is the resistance.

Figure 7.6. Equivalent circuit of a lossy transmission line, with additional resistance R and shunt conductance G compared to the lossless transmission line.

7.4.3 Matched and unmatched transmission line The incident current in a transmission line is related to the incident voltage V + by: V + i+ = (7.17) Z0 The reflected current is expressed in terms of the reflected voltage V −: V − i− = − (7.18) Z0 in this definition the convention, that the positive current travels in the direction of the load is used. If a transmission line is terminated with a load impedance equal to the characteristic impedance Z0 of the transmission line (ZL = Z0), the wave will not notice any difference in impedance until it reaches the termination. No reflection occurs in such a matched line and Ohm’s law is valid. + VL + = Z0 = ZL (7.19) iL L denotes the current, voltage and impedance at the receiving end (load). If however, the load impedance is unequal Z0, then Ohm’s law can only be fulfilled, if there is another wave. Assuming: + VL + = Z0 = ZL (7.20) iL

3Shunt conductance is the conductance between two wires which are separated by an isolator. Shunt conductance can produce losses that are caused by the voltage existing between the two wires. These losses include losses due to leakage currents, dielectric hysteresis losses, etc.

74 in that case a reflection occurs. Such a reflection can cause problems on the transmission line and with the connected components. At the termination the following equation must be fulfilled:

Vtotal = ZL, (7.21) itotal + − with V = V + +V − and i = i+ + i− = VL − VL . total L L total L L Z0 Z0 Equation (7.21) can be rewritten as: V V + +V − total = Z = Z L L (7.22) L 0 + − − itotal VL VL From this, the relation for the voltage reflection coefficient Γ can be found: − − VL = ZL Z0 = Γ + + (7.23) VL ZL Z0 It can be seen that for Z0 = ZL the voltage reflection coefficient becomes zero. The input impedance Zin, that a generator sees at the beginning of the transmission line, for a mismatched transmission line can be calculated by [153]:

ZL cos(βl)+ jZ0 sin(βl) ZL + jZ0 tan(βl) Zin = Z0 = Z0 (7.24) Z0 cos(βl)+ jZL sin(βl) Z0 + jZL tan(βl) where ZL is the load impedance, l is the length of the line and parameter β is β = 2π = 2π f frequency dependent and is deﬁned as λ v with v the speed of light in the medium. A schematic of such a mismatched line is given in ﬁgure 7.7. If the load impedance ZL is equal to the characteristic impedance Z0 then the input impedance Zin is also equal to Z0. For the design of the 60 GHz antennas it is important that the generator impedance, the transmission line impedance and the load impedance of the antenna are in agreemnet.

Figure 7.7. Mismatched transmission line, the generator sees the input impedance Zin. Mismatching ZL = Z0, produces reﬂections.

7.4.4 The Smith chart A Smith chart [154, 155] can be used, in order to determine the characteristics of a transmission line in a graphical representation. It is a chart, giving a graphical presentation of the impedance moving along the transmission line.

75 The Smith chart is usually a normalized chart where all impedances are normalized to the characteristic impedance Z0.Asanexamplea50Ω transmission line which is terminated by a load impedance of 40 + j50 Ω will be plotted as 0.8 + j1 on the Smith chart. Furthermore, information about the reflection coefficient Γ can be derived from the chart. A Smith chart normalized to Z0 = 50 Ω is shown in figure 7.8 with the point ZL = 40 + j50 Ω as an example. The standing wave ratio is determined as well as the phase angle at the termination point. Smith charts are often used as a tool in vector network analyser to get a quick display of how good an impedance match is.

Figure 7.8. Smith chart for the load impedance 40 + j50 Ω, the characteristic ◦ impedance Z0 is 50 Ω. The phase angle of 72 as well as the VSWR of 3 can be directly found in the chart.

7.4.5 Impedance matching To eliminate reflections occurring on not properly terminated transmission lines, impedance matching can be applied. Advantages are that the input impedance of the transmission line stays at Z0 when the frequency changes, no power is reflected into the generators output circuitry and the power is transferred in a more efficient way down the line. Most impedance matching problems occur at the load side. For high frequencies, as for example relevant for 60 GHz, the following matching methods can be used.

76 • A quarter-wave transformer is built from a λ/4 long transmission line as shown in ﬁgure 7.9.

Figure 7.9. Quarter-wave transformer, matching the input impedance Zin to the load impedance Z0.

Using equation (7.24) the input impedance of a lossless quarter-wave transmission line terminated with ZL can be found: + 2 0 jZ0 Z0 Zin = Z0 = (7.25) 0 + jZL ZL

Two different impedance, Zin and ZL, can be matched by√ a quarter-wave transmission line with characteristic impedance Z0 = ZLZin.Asan example a 100 Ω impedance should be matched to a 50 Ω√line, here a quarter-wave transformer with characteristic impedance of 50 × 100 = 70.711 Ω is needed. This technique was used in order to impedance match the patch antenna array presented in Paper V, see ﬁgure 7.10.

Figure 7.10. Photo of a patch antenna array. At every line split, a quarter-wave transformer matches the line back to 50 Ω.

• A single stub tuner consists of an open- or short-circuited section of transmission line, shunted across the main line at some distance l1 away from the load. The length of the line l2, and the point of attachment, both need to be calculated from the load impedance. An example of a single stub is shown in ﬁgure 7.11. A open stub was used in the feed construction of the 60 GHz patch antenna design, described in section 7.6.3.

77 Figure 7.11. Single stub tuner, for matching the load impedance ZL to the transmission line.

• The double stub tuner consists of two adjustable stubs placed at certain positions on the transmission line as shown in ﬁgure 7.12.Thisisause- ful matching when the load impedance ZL can change. A single stub tuner is very difﬁcult to match when the impedance ZL changes, since l1 the position of the stub and the length of the stub have to be adjusted. With a double stub tuner, the two stubs can be permanently connected. For the matching only their length has to be adjusted. Usually the distance between the two stubs is λ/8[153].

Figure 7.12. Double stub tuner, with the advantage, that for changing loads only the length of the two stubs have to be adjusted but not their position. This is an advantage compared to the single stub tuner.

• The exponential taper is a transmission line with exponentially variat- ing characteristic impedance along the length. The advantage is that if the taper per wavelength is small, such a transmission line can provide impedance matching insensitive to the frequency. An exponential taper is shown in ﬁgure 7.13. δ is the taper rate.

7.5 Signal modulation To transmit analogue or digital data over radio, the information needs to be packed on a carrier signal, which is able to transport this information. Such a

78 Figure 7.13. Exponential taper, for impedance matching. Such a transmission line can provide impedance matching insensitive to the frequency, if the taper rate δ is small. process is called modulation. In this modulation process, one or more properties of the periodic carrier wave are changed, in order to code the information, for example the phase, the frequency or the amplitude of the carrier wave. Different examples of modulation methods exist, like frequency modulation (FM) or amplitude modulation (AM) known from analogue radio broadcast. For digital modulation, different types are phase shift keying (PSK), frequency shift keying (FSK), or quadrature amplitude modulation (QAM), among others [156, 157]. In amplitude modulation the transmitted wave has the following form:

ysend(t)=I(t)cos(2π fct) (7.26) where I(t) is the information in terms of amplitude variations, ysend(t) is the transmitted wave and fc is the carrier frequency. If additionally the phase should be changed, as for example done in quadrature amplitude modulation, a second signal can be used, which has the same carrier frequency but comes with a 90◦ phase shift:

ysend(t)=I(t)cos(2π fct) − Q(t)sin(2π fct) (7.27) This method is also called quadrature modulation [156]. I(t) is the in-phase signal and Q(t) is the quadrature signal. Demodulation on the receiver side is done using a coherent demodulator. To demodulate the I(t) part, the signal is multiplied with cos(2π fct).

yreceived(t)=ysend(t) · cos(2π fct) = I(t)cos(2π fct)cos(2π fct) − Q(t)sin(2π fct)cos(2π fct) (7.28) With the trigonometric identities:

sin(2x)=2sin(x)cos(x) and (7.29) cos(2x)=2cos2(x) − 1 (7.30)

79 the equation (7.28) simpliﬁes to:

1 y (t)=I(t) · [1 + cos(4π f t)]− Q(t) · sin(4π f t) received 2 c c 1 1 1 = I(t)+ I(x)cos(4π f t) − Q(t)sin(4π f t) (7.31) 2 2 c 2 c which gives the required I(t) after low-pass ﬁltering, since the terms with higher frequencies are removed. In the same way Q(t) can be extracted by multiplying with −sin(2π fct):

yreceived(t)=ysend(t) · [−sin(2π fct)] 1 1 1 = − I(t)sin(4π f t)+ Q(t) − Q(t)cos(4π f t) (7.32) 2 c 2 2 c The trigonometric identities cos(2x)=1−2sin2(x) and sin(2x)=2sin(x)cos(x) were used. After low pass ﬁltering Q(t) is left. A sketch of the modulation using a 60 GHz carrier is given in ﬁgure 7.14. For high frequencies the mixing is usualy done in hardware, with e.g. a Gilbert cell. For lower frequencies mixing can also be done in a FPGA using digital multiplication or CORDIC [158] (COordinate Rotation DIgital Computer).

(a) modulation

(b) demodulation Figure 7.14. Modulation (a) and demodulation (b) scheme at 60 GHz.

80 Quadrature amplitude modulation Quadrature amplitude modulation (QAM) can be used as an analogue and a digital modulation scheme. QAM can carry two data streams at the same time, one in I(t) and one in Q(t). In digital modulation, the amount of different amplitudes and phases used in the signal determines the amount of bits, which can be transferred per symbol. Table 7.2 shows some of the lower QAM modulation schemes with the corresponding spectral efﬁciency (bits/s/Hz).

Table 7.2. Spectral efﬁciency for different QAM modulation modes. Type of modulation Spectral efﬁciency (bits/s/Hz) 2-QAM / BPSK 1 4-QAM / QPSK 2 16-QAM 4 64-QAM 6

It should be noted that, with using more bits per symbol, the requirements on the signal quality and the electronics increase. The signal to noise ratio (SNR) is an important factor that influences the spectral efficiency. It can be expressed as the carrier to noise power ratio (CNR) which is measured as a bit error rate (BER). This is the percentage of errors that occur in a given number of transmitted bits. As the noise becomes larger compared to the signal level, more errors occur. Having more amplitude levels requires an analogue to digital converter (ADC) to distinguish with higher accuracy between levels. Also the digital to analogue converter (DAC) needs to produce more levels. The requirements on the signal quality and ADC/DAC usually increase the power requirements and price of these devices. Figure 7.15 shows the constellation diagram for a QPSK signal and a 16-QAM signal. Using QPSK requires only to discriminate between two amplitude levels. Also the BER is lower compared to higher modulation schemes [159, 160], which is good for the power budget and simplicity of a circuit. Having simpler modulation schemes comes with the cost of lower spectral efficiency and more bandwidth is required in order to transfer the same amount of data compared to an advanced modulation scheme. In the 60 GHz band, this is not an issue due to the large amount of bandwidth available. A simulation of QPSK modulation simulated with MATLAB/Simulink is shown in figure 7.16.

81 (a) QPSK (b) 16 QAM Figure 7.15. Amplitude levels of the I(t) and Q(t) signal for QPSK modulation (a) and 16 QAM (b).

7.6 The patch antenna Patch antennas were studied in this thesis, since they are low profile, simple and inexpensive to produce with printed-circuit technology. Rectangular patch antennas usually have a length λ/3 < L < λ/2[137]. The patch and the ground are separated by a dielectric substrate as shown in figure 7.17. Sub- 4 strates can be bought with different dielectric constant εr ranging from 2.2 to 12. The best performance is achieved using a thick substrate with a low dielectric constant, which gives better efficiency and larger bandwidth than a high dielectric constant, at the cost of a larger element size [161].

7.6.1 Design steps for a patch antenna This section describes the design steps for a single patch antenna. Start- ing from the substrate Rogers ULTRALAM 3850 with a dielectric constant εr = 2.9 and a substrate thickness h = 100 μm, a patch antenna for a resonance frequency fr = 60 GHz is designed.

The ﬁrst step in the design is the calculation of the width of the patch W. This can be done by using the following equation: c 2 W = · = 1790.3 μm (7.33) 2 fr εr + 1

The second step is to calculate the effective dielectric constant.Someof

4Also called relative permittivity.

82 ie n fe iciiain(ledse line). (blue/dashed discrimination after and line) n nlythe ﬁnally and ouae ntecrir hntemdltdadcombined and modulated the then carrier, the on modulated obto:tedgtlsga,wihi ouae to modulated is which signal, digital the bottom: to 7.16. Figure

iuaino h PKmdlto ihMTA/iuik rmtop From MATLAB/Simulink. with modulation QPSK the of Simulation 0.5

I 0 ( Amplitude t

) −0.5 inlatrdmdlto n o asﬁtrn (red/continues ﬁltering pass low and demodulation after signal −1

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 Time (secs)

0.5

0 Amplitude −0.5

−1

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 Time (secs) 1.5

0.5

0 Amplitude I −0.5 (

t −1 )

and −1.5

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 Time (secs) Q 1 ( I t ( )

t 0.5 ) inl eoebeing before signal,

and 0 Amplitude −0.5 Q −1 ( t

) 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 Offset=0 Time (secs) channel, 83 Figure 7.17. The patch and the ground, separated by a dielectric substrate of thickness h and with a dielectric constant εr. the waves travel through the substrate and some through the surrounding air (fringing), this is illustrated in ﬁgure 7.18. For a patch antenna with L/h 1, fringing effects are reduced but must be taken into account, since they inﬂu- ence the resonant frequency. Fringing effects make the patch antenna appear electrically wider compared to its physical dimensions. Therefore, an effective dielectric constant εef f has to be introduced in order to take this mixture of dielectric substrate and air into account. The effective dielectric constant εef f for a patch antenna on a substrate with εr covered by air is in the range 1 < εef f < εr. For substrates with εr 1, the effective dielectric constant is close to εr.

Figure 7.18. Physical and electric length of a microstrip patch antenna. The fringing effect makes the patch antenna electrically longer, due to the discontinuity of the dielectric constant of the substrate in air.

An approximation of the effective dielectric constant is given by [162]:

− 1 ε + 1 ε − 1 h 2 ε = r + r 1 + 12 = 2.6851 for W /h 1 (7.34) ef f 2 2 W

84 Because of the fringing effect the patch antenna looks electrically longer compared to its physical dimensions. The enlargement on each side of the patch ΔL can be approximated [163]:

W (εre f + 0.3)( + 0.264) ΔL = 0.412 h · h = 0.4922 μm (7.35) (ε − . )(W + . ) re f 0 258 h 0 8 The last step is to calculate the physical length of the antenna:

c L = √ − 2ΔL = 1427.2 μm (7.36) 2 fr εef f

7.6.2 Impedance matching The input impedance of the patch antenna described in the previous section needs to be matched to the 50 Ω of a feeding line. The impedance of the patch antenna can be changed by using an inset feed, creating an opening of adistancey0 from slot #1 as shown in ﬁgure 7.19. With this technique, the patch can be matched to the feeding microstrip for example.

Figure 7.19. Microstrip patch antenna with an inset feed of length y0 for matching the patch antenna to the feeding impedance.

In order to calculate the impedance of the patch antenna, the conductance G1 has to be calculated ﬁrst:

k0W ( ) ( ) = 1 − + ( )+ sin y + sin k0W G1 2 2 cos k0W k0W dy (7.37) 120π 0 y k0W = . μ [ = 1 ] 3108 4 S S Ω (7.38)

85 where λ is the wavelength λ = c = 5mm,k is the phase constant for free fr 0 2π √λ space given by k0 = , λg = and W is the width of the patch antenna. λg εeff Next, the mutual conductance G12 [164] between slot #1 and slot #2 is needed: 2 π sin( k0W cosθ) = 1 2 ( θ) 3 θ θ G12 2 J0 k0Lsin sin d (7.39) 120π 0 cosθ = −79.9 μS (7.40) where J0 is the Bessel function of zeroth order. Furthermore detailed information about these variables can be found in [137]. Using the conductances G1 and G12, the impedance of the patch antenna can be calculated [165], 1 Zin = = 165.1 Ω (7.41) 2(G1 + G12)

Zin is the impedance of the patch with no inset feed (y0 = 0). In order to match the patch antenna to Zin(y = y0)=50 Ω, the length y0 of the inset feed is calculated as follows:

π 2 Zin(y = y0)=Zin(y = 0)cos ( y0) (7.42) L ( = ) L −1 Zin y y0 y0 = cos = 448.9 μm (7.43) π Zin(y = 0)

The width of the microstrip to feed the patch antenna can be calculated by using standard transmission line calculator design tools like ANSYS Designer [166], Agilent Technologies AppCAD [167] and AWR TX-line [168]. The width of the inset feed was chosen as 1/2 of the width of the microstrip.

7.6.3 Design of the feeding-line In order to measure the patch antennas properties it has to be connected to a Vector Network Analyser. The antennas were tested with an Agilent Tech- nology vector network analyser (PNA 8364B). The connection to the antenna is with a microwave probe. The probe has three contacts GND − SIGNAL − GND in a row with a pitch of 100 μm, contacting the signal line and ground contact of the antenna. For this contact, a coplanar wave-guide feed was designed, as shown in figure 7.20. + a The distance (b 2 ) in the figure is defined by the pitch of the microwave probe used for the measurement. The width a of the signal line can be calculated by standard transmission line calculator design tools. The length d of

86 Figure 7.20. Feed of the feeding line for the patch antenna. The feed is contacted by a microwave probe to connect the VNA with the patch antenna. the coplanar wave-guide is arbitrary and was chosen to be long enough to ﬁt the requirements of the probe. The length e of the signal line in the coplanar wave-guide is a bit longer compared to the ground of the wave-guide in order to make a smooth transition from coplanar wave-guide to the microstrip. Its length was optimized using HFSS. The feed was designed to match the 50 Ω impedance of the VNA and the patch antenna. The ground connection of the coplanar wave-guide acts as an open λ/4 stub, see section 7.4.5. Its length G was calculated according to the following equation: c 2 G = = 895.14 μm (7.44) 2 fr εr + 1

7.6.4 Antenna simulation The antenna based on the theoretical calculations detailed previously is then simulatedinHFSSandtheS11 parameter is determined and compared with an optimized design. The various parameters from theory and their optimized values are shown in table 7.3. The theoretical designed antenna shows already good values for S11 and is very close to resonance at 60 GHz in the HFSS simulation. In order to improve the design, the different design parameters are tuned to find an optimum. Since the inset feed is crucial for the impedance matching of the patch antenna, its length and width have been chosen for optimization. The effect of such width and length variations on the S11 parameter is shown in figure 7.21. Furthermore, in order to get the desired resonant frequency of 60 GHz, the length of the patch is slightly changed. The S11 parameter of the non- optimized and the optimized design are shown in figure 7.22(a). With the optimization of just three parameters, a 60 GHz resonance was achieved. The

87 Table 7.3. Parameters of the designed and optimized antenna. theoretical [μm] optimized [μm] Length Patch (L) 1427.2 1421 Width Patch (W) 1790.3 1790.3 Inset feed (y0) 448.9 460 Inset feed width 120 125 Width microstrip 240 240 Length microstrip 2500 2500 Feed (a) 118.9 118.9 Feed (b)2828 Feed (G) 895.14 895.14 Feed (d) 125 125 Feed (e) 200 200

max(S11) -20.5 db -33.6 dB

0 0 -5 S11 [dB] S11 [dB] -5 -10 -15 -10

-20 -15

-25 μ Ins. Feed Length 450 m -20 Width MS/2 -30 Ins. Feed Length 460 μm Width MS/3 μ Ins. Feed Length 470 m -25 Width MS/4 -35 Ins. Feed Length 480 μm Width MS/5 -40 -30 54 56 58 60 62 64 54 56 58 60 62 64 f [GHz] f [GHz]

(a) Length optimization (b) Width optimization

Figure 7.21. Effect of length and width change of the inset feed on the S11 spectrum. The simulation was performed using the High Frequency Structure Simulation (HFSS).

88 radiation pattern of the optimized antenna is shown in ﬁgure 7.22(b).The antenna has a gain of 6 dBi in the simulation.

135 45

S11 [dB] -5

-10 180 0 051015 -15

-20

-25 theoretical

-30 optimized 225 315 -35 54 56 58 60 62 64 f [GHz] 270

(a) S11 spectrum, theoretical vs. optimized (b) Radiation pattern

Figure 7.22. a) Comparison of S11 spectra for the design antenna and after optimization. The simulation was performed using the High Frequency Structure Simulation (HFSS). b) Radiation pattern of the optimized patch antenna. The polar plot is produced at φ = 90◦.Theθ coordinate is shown from 0 to 360◦,whereθ = 0◦ is the axis perpendicular to the patch. The radial distance represents the transmitted energy.

89 7.7 Fabrication of the antennas The first set of patch antennas were produced in industry with a wet etching process on Roger material. This is a cheap method to produce antennas. The antennas showed reasonably good agreement with the HFSS simulation and results were presented in Paper IV. Unfortunately the outsourced production took long time from the design submission until the final antennas were received. The turnaround was too slow in order to have fast studies of new materials and designs. Therefore, several alternative production methods were investigated to produce antennas in-house. Several options were considered. One approach was to use a laser cutter to remove the copper on one side of the substrate and to cut out the patch antenna. This approach failed, since it was not possible to precisely control how deep the laser was cutting into the laminate. With the machine at the labratory in Uppsala the laser cut through all layers, leaving holes on both sides of the substrate. Not all copper was removed from the signal side for other substrates or the dielectric substrate was burned. No functional antenna could be produced by this process. Due to the high fabrication precision needed for good antennas, investigated in Paper IV, further experiments were made with a milling machine available in the workshop. With this machine, the passive repeaters were produced, presented in Paper V, as well as single patch antennas. Even though the passive repeaters were successfully produced, it turned out during the measurement of the single patch antennas that large resonance frequency fluctuations were observed. The main reason was the milling into the substrate when removing the copper on one side. This effect could not be controlled due to the length expansion of the drill during milling. Also, the placement of the substrate in the milling machine was not perfect, since it was done with tape, which does not have precise thickness. The substrate was bent when removed from the tape, whereas the antenna is supposed to be flat. A vacuum table could possibly solve some of these problems but was not available in the workshop. Pictures of an etched and milled antenna are shown in figure 7.23. Therefore in-house wet etching was investigated. A first test with FR4 substrate was done in the bathroom of the author. An etching machine was bought and further tests with improved equipment were performed. A light board was bought and Roger and DuPont materials were sent to Bungard Elektronik GmbH & Co.KG in Germany for photo-resist coating. The photo-resist coated material was then used to produce the first antennas by etching in house, see figure 7.24. Measurements of the antennas with the VNA are shown in figure 7.25. The antennas are measured close to the target frequency of 60 GHz. The produced antennas were used in the radiation hardness study. Also a passive repeater was produced and its functionality demonstrated. An accurate control of etching time, Na2S2O8 concentration and temperature is required to avoid over- or under-etching.

90 (a) Etched antenna in industry (b) Milled antenna Figure 7.23. Antenna produced in industry with etching, and in-house produced with milling. On the left, the patch antenna on Rogers material produced in industry is shown. On the right, a milled patch antenna produced on DuPont substrate is dis- played. Scratches can be seen where the milling has gone into the substrate .

A combined fabrication process with both milling and etching was also considered. The idea was to use the high precision in xy-direction of the milling together with the etching to remove the last micrometers of copper, to protect the substrate from milling. This could be a good method as soon as the substrate can be held on the milling machine without tape. Otherwise the antennas are bent during removal from the milling machine and the photo-coating can be destroyed, leading to subsequent problems during etching.

(a) UV light board (b) Etching machine (c) Inhouse produced antenna Figure 7.24. a) Professional UV light board. b) Etching machine with air bubbles, and heating. c) Finished etched patch antenna on Rogers substrate.

91 0 S11 [dB]

-5

-10

-15 Rogers -20 DuPont 50 52 54 56 58 60 62 64 f [GHz]

Figure 7.25. Measured S11 of an in-house etched antenna on DuPont material (red) and Rogers material (black). The antennas have a resonance frequency close to the design frequency of 60 GHz. Small variations could come from the fact that the dielectric constant is not known exactly at 60 GHz and from small over and under etching. Such an agreement proves that antenna production in-house with etching is possible and results in reasonably good antennas.

7.8 Test setup for passive repeater antennas For testing the passive antenna repeater structure, that was developed to demonstrate radial wireless data transfer, as presented in Paper V, it is important to be able to penetrate the antenna with a narrow 60 GHz signal. The experimental setup is shown in ﬁgure 7.26. For simple tests to verify if a 60 GHz signal is transferred, a combination of signal generator, power-splitter/combiner, two 60 GHz mixers and an oscilloscope can be used, as shown in ﬁgure 7.27. This is an easier way to test the function of the antenna repeater structure, since the signal generation and detection is at baseband frequency, compared to the measure of 60 GHz directly. Measurements at 60 GHz need very ex- pensive and accurate calibrations. This method modulates a sine or cosine wave (baseband) onto the 60 GHz carrier signal. Using a simple mixer, where a 60 GHz carrier fc is mixed with a sine wave at baseband frequency fb, two frequencies occur after mixing fc ± fb. Here equation (7.26) is used and the amplitude I(t) is modulated by a sine wave:

ysend(t)=sin(2π fbt)sin(2π fct) (7.45) 1 = [cos(2π( f − f )t) − cos(2π( f + f )t)] (7.46) 2 c b c b

92 Figure 7.26. Schematic layout of the test setup for testing the passive antenna repeater structure. A signal at the baseband frequency is modulated on a carrier of 60 GHz, transferred through the passive repeater antenna and is down modulated to the baseband frequency.

Figure 7.27. Schematic layout of a setup for testing if an antenna is working at 60 GHz or not. The test setup consists of a signal generator, power-splitter, 60 GHz up-converter, 60 GHz down-converter, power combiner and an oscilloscope. Such a setup was used to test the passive repeater antennas presented in Paper V.

93 These two frequencies are separated by two times the baseband frequency, with the carrier frequency in the centre. This is not an optimal condition for antenna testing since the antenna is always penetrated by two different frequencies at the same time. A better approach is to use an I/Q mixer as used for quadrature modulation. If this mixer is fed with a sine and a cosine wave at the baseband frequency, only one frequency is left after mixing, as shown in the following. This technique is also called single-sideband modulation (SSB). Starting with:

I(t)=cos(2π fbt) (7.47) Q(t)=−sin(2π fbt) (7.48) the mixed and combined signal gets the following form:

ysend(t)=cos(2π fbt) · cos(2π fct)+sin(2π fbt) · sin(2π fct) = cos(2π( fc − fb)t). (7.49) Here the trigonometric identity cos(x ± y)=cos(x)cos(y) ∓ sin(x)sin(y) is used, resulting in a single frequency of fc − fb. If using

I(t)=cos(2π fbt) (7.50) Q(t)=sin(2π fbt) (7.51) the resulting frequency is fc + fb.

94 8. Summary of papers

Paper I This paper was the combination of three important decay channels for light −1 charged√ Higgs boson searches. It uses the full ATLAS 2011 dataset of 4.6fb at s = 7 TeV. The limits set in the paper were a signiﬁcant improvement compared to all charged Higgs boson searches performed before. The author of this thesis was involved in the τ+lepton channel where he did the code development for the event selection, produced control plots in order to compare data and simulation, and helped developing the Matrix Method for estimating the background with misidentiﬁed leptons.

Paper II This paper improved the limits from Paper I by using the same dataset, but applying a ratio based method in the τ+lepton channel, which has the advantage of decreasing the amount of systematic uncertainties since some of them cancel out. A higher sensitivity and better limits in the low H+ mass range was achieved. By combining the ratio based limits with these derived in the τ+jets analysis of Paper I an even higher exclusion was reached. The author of this thesis was involved in the development of the event selection, control plots in order to compare data and simulation, and the integration of the Matrix Method into the analysis.

Paper III This study describes two methods of data driven estimates for non-prompt and misidentiﬁed lepton backgrounds√ in the context of top quark related analyses. The full 2012 ATLAS dataset at s = 8 TeV was used. Final states with one or two leptons (and jets) are considered. The Matrix Method and the Fitting Method are described and compared with each other in the single lepton channel. Systematic errors are determined and results are consistent between the two methods. The author of this thesis was working on the development of the Matrix Method and was responsible for the knowledge transfer from the H+ analysis team to the top working group in ATLAS. The author of this thesis was also part of the team editing the supporting document for this publication.

95 Paper IV This paper presents a feasibility study of 60 GHz antenna production for future detector concepts. The antennas were designed using the High Frequency Structure Simulation program HFSS, and produced with etching and milling techniques. The etched antennas were measured with a Vector Network Anal- yser (VNA) and compared with results from simulation. The agreement is sufﬁciently good and a production using etching is possible. Studies were performed to understand the effect of over-sizing and under-sizing as well as substrate removal in the production process occurring during milling. The simulation studies, as well as the analysis of the results, were performed by the author of this thesis. He wrote the paper and was contact editor during the publication process.

Paper V This paper is a concept proof of a passive repeater. This repeater is a combination of two patch antenna arrays which are connected by a micro strip. One antenna array acts as a receiver and converts incoming electromagnetic waves into alternating currents, which are then transported to the second antenna array via a micro-strip. The second antenna arrays converts the current back into an electromagnetic wave. With such a concept, transmission through detector layers is possible without the need of visibility for the active sender and receiver. Such a passive repeater was designed and produced on PCB material with a milling process and tested in the lab. It was demonstrated that a transfer through at least two detector layers can be achieved. The author of this thesis did the design of the repeater, all studies in this paper and was contact editor during the publication process.

96 9. Conclusion

The main topics of this thesis are the search for charged Higgs bosons in ATLAS and the development of low mass high bandwidth data transfer for future tracking detectors. So far only particles contained in the Standard Model have been discovered and no particles predicted by theories beyond the Stan- dard Model have been observed. There are a lot of unanswered questions in particle physics, which can not be answered by the Standard Model and that require extensions to the Standard Model. Questions about gravity, unification of fundamental forces and the origin of dark matter and energy are some of these. One possible extension for physics beyond the Standard Model is supersymmetry. Introducing this would at least double the particle spectrum and would lead to five Higgs bosons, of which three are neutral and two are charged. With the discovery of a neutral Higgs boson in 2012, the last particle of the Standard Model has been found. The remaining question is of course if it is really the neutral Higgs boson of the Standard Model or maybe a Higgs boson in a model beyond the Standard Model. The answer may be found through future precision measurements of this particle. On the other hand, the discovery of a charged Higgs boson would be a clear proof of physics beyond the Standard Model, since it is not part of the Stan- dard Model. Searches for such a new charged scalar particle were part of the physics program from the beginning, in ATLAS. The new incoming collision data was analysed in many different channels to search for new physics. So far, no evidence for a charged Higgs boson was found. Limits were set and regions in the parameter space were excluded, narrowing down the regions where a charged Higgs boson could hide. Paper I is an ATLAS publication√ on charged Higgs boson searches based on the full 2011 dataset at s = 7TeV. In this paper, three different channels τhad+lepton, τhad+jets and lepton+jets were combined to search for light charged Higgs bosons, produced in the decay of a top quark. The existing limits could be significantly improved. Lepton in this context means electron and muon. This paper was setting the world’s best limits on charged Higgs boson searches at the time. The same dataset was re-analysed with a ratio based method, having the advantage of cancelling several systematics uncertainties. This analysis is described in Paper II and even better exclusion limits could be set especially in the lower mass range 90 − 130 GeV. One important background when searching for charged Higgs bosons, with a lepton in the final state, is misidentified leptons arising from the semileptonic decay of hadrons with b or c-quarks, from the decay-in-flight of π± or K mesons and in the case of electrons, from π0 mesons, photon

97 conversions or shower fluctuations. This kind of events are very difficult to account for with simulation. Therefore, data driven methods are used to estimate their contribution. The Matrix Method was developed and used for this purpose. This method was continuously developed and optimized to cope with the changing conditions of the incoming ATLAS data. Paper III was published in 2014, summarizing all the efforts done on misidentified lepton background estimations in top quark related analysis. The second main topic of this thesis is the development of future detector technology. The LHC is expected to run in the next 15 to 20 years with increasing collision energy and luminosity. There are plans to upgrade the LHC to a high luminosity LHC (HL-LHC) able to deliver 250 fb−1 of data per year. In comparison the total amount of luminosity collected 2011 and 2012 was around 27 fb−1. The increase of luminosity will produce more collisions per time unit but also more pile-up events, which in turn leads to an increase of data to be read out from the detector. This makes it very challenging to ex- tract signal from background. Future detectors will have higher granularity in order to reconstruct all the particle tracks from a collision. To read out the full detector system under these extreme conditions is putting a high demand on the available bandwidth for data transfer. Of course bandwidth could be increased by more cables, but this would also increase the amount of non sensitive material in the detector system and deteriorate its performance. One possible technology to increase the capacity of data transfer is wireless technology. The 60 GHz frequency band has shown to be promising for the use in a tracker. The wavelength of the order of mm is optimal for components, using little space and power. Small, highly directive antennas can easily be fabricated as demonstrated in Paper IV. The technology could reduce the amount of cables in a detector system. The whole detector volume could be used for data transfer compared to actual designs where cables are brought out in dedicated regions, which have a significantly lower detector performance in those regions. It was shown in Paper V that it is possible to get electromagnetic waves pass boundaries with passive antenna repeater structures. A possible scenario for the use of wireless technology is that the data is brought out of the detector using wireless and is collected on the outside for further processing. An other scenario using wireless technology is the communication inside the detector. In this scenario, different detector layers and elements could communicate with each other and could already inside the detector make pre- decisions on the interest of every event. Only if the event is of interest, the full detector system is read out. This could be used to realize track triggers which are pre-analysing the track informations already inside the detector. Wireless technology is a clear candidate for future detector systems and is likely to open up a lot of new possibilities in future HEP detectors.

98 10. Summary in Swedish - Sammanfattning på svenska

Frågan "Var kommer vi ifrån?" har männskligheten begrundat i årtusenden. Vetenskapen försöker besvara denna fråga på olika sätt. Inom biologi blir svaret evolution och inom fysik big-bang, med många perspektiv därtill. Om man tittar utifrån fysikerns perspektiv så kan frågan "Var kommer vi ifrån?" väldigt snabbt brytas ner till frågan "Vad består vi av?". Detta är exakt vad partikelfysik handlar om: Materiens minsta kända beståndsdelar.

Standardmodellen Standardmodellen är en modell som försöker beskriva de mest elementära partiklarna och hur de växelverkar med varandra. Redan i grundskolan lär vi oss att vår värld är uppbyggd av molekyler, att molekyler består av atomer och att atomer byggs upp av protoner och neutroner i atomkärnor och elektroner som omger atomkärnorna. Baserat på vad vi vet idag är elektroner elementarpartiklar, men protoner och neutroner är det inte. Protoner och neutroner består av kvarkar och gluoner. De ﬁnns tre kvarkar i protonen och neutronen som heter upp- och nerkvarkar. En uppkvark har en elektrisk laddning som är 2/3 av elektronens elementarladdning (e) och en nerkvark har en elektrisk laddning av -e/3. Protonen har en elektrisk laddning av +e och är uppbyggd av två uppkvarkar och en nerkvark. Neutronen är elektriskt neutral och består av en uppkvark och två nerkvarkar. Elektronen samt upp- och nerkvarkarna bildar den första familjen i standardmodellen och är de elementarpartiklar som är stabila. Varje familj har en neutrino som fjärde elementarpartikel. Den är elektriskt neutral och väx- elverkar bara genom dem svaga kraften. Totalt existerar ytterligare två familjer. Dessa två har liknande kvarkar som den första familjen men kvarkarna är tyngre och sönderfaller till lättare kvarkar i familjer som ligger under den ursprungliga familjen. Liknande är det för de laddade leptoner som också är tyngre än elektronen beroende på vilken familj de tillhör. Tabellen visar stan- dardmodellens kvarkar och leptoner:

Familj I Familj II Familj III uppkvark (u) charmkvark (c) toppkvark (t) nerkvark (d) särkvark (s) bottenkvark (b) elektron (e) myon (μ) taulepton (τ) elektronneutrino (νe) myonneutrino (νμ ) tauneutrino (ντ )

99 Standardmodellen förklarar också växelverkningar mellan olika kvarkar och leptoner. Det ﬁnns fyra kraftbärande partiklar i standardmodellen: Fotonen som förmedlar den elektromagnetiska kraften, gluoner som förmedlar den starka kraften och W -ochZ-bosoner för den svaga kraften. En sista partikel i standardmodellen ger massa till samtliga massiva partiklar. Partikeln kallas Higgspartikeln och blev upptäckt 2012 av ATLAS- och CMS-experimenten på CERN. Nobelpriset 2013 tilldelades Peter Higgs och François Englert för deras teoretiska forskning som förutsåg att en sådan partikel måste ﬁnnas.

Fysik bortom standardmodellen Tyvärr är standardmodellen ingen universalteori som förklarar allt och det finns många fysikaliska problem som inte kan förklaras med standardmodellen. Några exempel är mörk materia, beskrivningen av gravitation saknas och standardmodellen kan inte koppla samman alla krafter till en kraft vid en högre energi. Därför är fysikerna säkra på att det måste finnas en teori som innehåller standardmodellen men även innebär “mer fysik”. En möjlig utvidgning av fysiken bortom standardmodellen är supersymmetri. Supersymmetri löser några problem som standardmodellen inte kan lösa. Supersymmetri har minst dubbelt så många partiklar som standardmodellen. Den lättaste partikeln är en kandidat för mörk materia. Dessutom in- nehåller supersymmetri gravitation och kan sammankoppla alla krafter till en kraft vid högre energi. Om supersymmetri finns, borde det finnas minst fem Higgspartiklar istället för en som i standardmodellen. Två av dessa Higgspar- tiklar skulle vara elektriskt laddade, de övriga neutrala. Den upptäckta Hig- gspartikeln skulle kunna vara en av de neutrala Higgspartiklarna i supersymmetri. Den här avhandlingen handlar om letandet efter de laddade Higgspartik- larna. Att upptäcka dessa skulle vara ett direkt bevis för att det finns fysik bortom standardmodellen. Artikel I och II beskriver sökningar efter de laddade Higgspartiklarna och exkluderar olika parameterområden där partiklarna inte har hittats. Artikel III beskriver en databaserad metod som kallas matris- metoden (Matrix Metod) som beräknar hur många bakgrundsreaktioner det finns i de utvalda händelserna man använder för en sökning efter till exempel en laddad Higgspartikel. Än så länge har vi inte hittat några tecken på ny fysik i våra analyser. När LHC startar igen i år så kommer letandet att fortsätta.

Framtidens detektorteknologi För att kunna forska vidare och leta efter ny fysik, men också för att undersöka den nyupptäckta Higgspartikeln, behöver man ännu fler och renare händelser att analysera. För att kunna producera fler händelser per tidsenhet behöver man uppgradera de befintliga detektorsystemen, eller bygga helt nya experiment. En del av forskningen inom partikelfysik är därför att utveckla nya teknologier som kan användas i framtidens detektorer. En av de nya teknologier som utvecklas i denna avhandling är kommunikation inom ett detektorsystem som

100 baseras på elektromagnetiska vågor med frekvensen 60 GHz som används för trådlös kommunikation. I de befintliga detektorerna läser man ut alla sensorer med kablar som förs ut på olika ställen till utsidan av detektorn. För att kunna detektera fler kollisioner per tidsenhet med en högre precision behövs fler sensorer som producerar mer data. Det innebär att man också behöver mer kablar för att få ut all data till utsidan. Ett problem med kablar är att de inte är en del av detektorns akiva volym, utan bara är i “vägen för signalerna“, vilket man vill undvika. Man kan jämföra dessa med en kabel som hänger framför en digitalkamera och ger en svart streck genom bilden. Många kablar ger ett stort svart streck genom bilden, färre kablar leder till ett mindre streck. Därför är det nödvändigt att trots att man använder fler sensorer hålla kabelmängden konstant eller ännu hellre reducera antalet kablar. En möjlighet att göra det är att använda trådlösa datalänkar istället för kablar för dataöverföring. Trådlösa länkar kräver lite plats och lite energi. Genom att använda trådlös 60 GHz teknik för dataöverföring får man även en stor bandbredd som kan användas för att få ut all detektordata till utsidan. Hela detektorvolymen kan användas för att placera ut länkarna, för att undvika att några kablar hamnar i vägen. Artikel IV presenterar möjligheten att designa antenner för dataöverföring och om det är möjligt att producera dessa antenner med enklare metoder. Det går att tänka sig olika användning- sområden för dessa. Den första är att all data skickas ut från detektorernas system och samlas på utsidan för att sedan transporteras vidare via kabel för vidare bearbetning. I ett sådant scenario skulle det vara bra om 60 GHz- vågorna kunde passera icke-transparent detektormaterial. Därför utvecklades passiva repeterar (motsvarande en mobilmast som koppa ihop två mobiltele- foner, förutom att en sådan mast är aktivt) för signalen och deras funktion demonstrerades i artikel V. En annan möjlighet är att man har olika sensorer inom själva detektorn som kommunicerar med varandra trådlöst, för att redan innan man läser ut all information bestämma om informationen är viktigt eller inte. Bara ifall informationen är viktig och händelsen är intressant sparar man hela händelsen. Detta skulle spara mycket digital bandbredd och reducera mängden kablar. Nästa steg i detta projektet är att bygga och testköra en pro- totyp.

101 11. Acknowledgements

First of all, I would like to thank my supervisors Richard, Enzo (Arnaud) and Elin for your support with this PhD studies and the thesis writing. I would like to thank you, Enzo and Sevinc, for your hospitality when I first arrived in Uppsala on the 29th of December, 2010. Enzo, you offered me your sofa for the first week and Sevinc you rented me your newly renovated apartment for the first months of my time in Uppsala. This made the transition very comfortable. Enzo, as a supervisor, you were always available for me when I had questions or needed help. After my peak time in charged Higgs boson searches, with the start of the 60 GHz project, Richard took over in guiding me though my PhD studies, especially the hardware part. I would like to thank you for all the good advice and freedom in this project. I have learned many new things and felt like a real experimentalist in the laboratory. It took a while to get a light board and to convince you that etching of antennas in our laboratory was the right way to go, but you bought a light board. I can clearly say that this project changed my life in a good way. Talking about the 60 GHz project, a very big thank you goes to Leif. You were a great mentor for me and always available for discussion. You gave me the passion for electronics and taught me a lot about FPGA and radio communication technology. Furthermore, you encouraged me to take more courses in electronic related topics. I would also like to thank Nils and Lars- Erik for your support and your advice in the 60 GHz project. Thanks also to Dragos. I met you for the first time in the forest picking mushrooms, but we became colleagues and friends when working together on the 60 GHz project. I learned a lot from you about antenna design and the usage of measurement equipment for high frequencies. Elin joined our group in the last year of my PhD and we had very nice discussions about life as a physicist. It was a pleasure to talk to you about doing a PhD and to get understanding and support in return. Camila became our post-doc in my last year of PhD studies. It was nice to have you around as another young scientist in our group. It was interesting to hear how education works on the other side of the world. Thanks also go to Mattias, with whom I shared an office during the first weeks. You probably got all the questions from me, which a new person at the office asks. You were always there when GRID problems needed to be solved, and especially when deep technical knowledge about the GRID, and in particular NorduGRID, was needed.

102 Alexander, you started your master thesis around the same time as I started my PhD and we started to work together on charged Higgs bosons analysis. It was nice to work and discuss charged Higgs boson analysis with you, and to get your advice on all kinds of things. Good luck with your own PhD thesis! I would also like to thank Oskar Stål. Without you I would never have come to Uppsala. We met for the ﬁrst time at the PLHC conference in Ham- burg 2010, when you were doing a post-doc at DESY. When I told you about my love for Sweden, you suggested me to apply for a PhD position in Upp- sala. Quicker than I could imagine, Tord and Richard were interviewing me at CERN, giving me 10 days to consider moving to Sweden. Therefore many thanks to Tord and Richard for having me enrolled as a PhD student. A big thank you goes to Volker, you were my ofﬁce neighbour for some years and we shared the way home to Flogsta a couple of times. It was funny to hear your point of view about the Flogsta roof parties, after having been there the previous weekend. You introduced me to microprocessor programming and we had a lot of discussions about having electronics as a hobby. Your article in TheMagPi magazine encouraged me to publish my own. Furthermore, I would like to thank Inger, Annica and the other administra- tive staff for all your support in university related issues. I would also like to thank Li, Lena, Aila, Carla, Stefan, Charlie, Dominic, Karin, Patrik, Mathias, Richard S., Henrik Ö, Joakim, Henrik T., Jim and all the others not mentioned here and with whom I had lunch on a daily basis, Maja for your education in mushroom picking and for being a very friendly lab assistant colleague, Glenn for discussing the theory about charged Higgs bosons with me and for proof reading my thesis. Thanks also to Harvey for helping me correct the English in this thesis. Richard E., I would like to thank you for lending me your bible, “The Higgs Hunter’s Guide”, which helped me write the theory chapter of this thesis. A great thanks goes to Carla and Joakim who I already knew from Germany, but with whom I became even closer friends in Uppsala. A special big thank you goes to Josephina, we were good friends in Giessen and fought through our physics studies by supporting each other. This tradition continued in Uppsala when you started your PhD. You are one of my closest friends and I really appreciate your support in all ways. You helped me in all kinds of situations. Also thank you for proof reading this thesis, which helped me a lot. Jan, Enno, Dominik, Pascal and Katrin should not be forgotten since without them I would not look back on 10 years of physics. Thanks also goes to Liron. We were hunting the charged Higgs boson together, and shared our frustration about event challenges. It was so much fun to work and talk with you. An even bigger thank you goes to Tove, my partner. Thanks for all the support you gave me during my PhD and for accepting my nerdy hobbies and the chaos on my desk at home. You did not complain when work got late and

103 served me food during the ATLAS tb-meetings, which quite often went far beyond dinner time. Also thanks for proof reading my thesis, even if this is not your topic at all. You were the best Swedish teacher I could get and helped me improve my mechanics lab-lectures. I’m very happy to be with you. Last, but not least, I would like to thank my parents. "Danke für all die Unterstützung!". You supported me through all these years and without your support I would have not come so far.

104 List of Acronyms √ s Centre of mass energy 2HDM Two Higgs Doublet Model 4FS Four-flavour scheme 5FS Five-flavour scheme ADC Analogue to Digital Converter ALICE A Large Ion Collider Experiment AM Amplitude Modulation ATLAS A Toroidal LHC ApparatuS BCO Beam Cross Over BR Branching Ratio BER Bit Error Rate CERN Conseil Européen pour la Recherche Nucléaire CKM Cabibbo-Kobayashi-Maskawa CL Confidence Level CMS Compact Muon Solenoid CMSSM Constrained Minimal SuperSymmetric Model CNGS CERN Neutrinos to Gran Sasso CNR Carrier to Noise power Ratio CP Charge Parity CSC Cathode Strip Chambers DAC Digital to Analogue Converter dB deciBels dBi deciBels-isotropic EF Event Filter EM ElectroMagnetic EMEC ElectroMagnetic Endcap Calorimeter miss ET Missing transverse energy eV electron Volt fb femto barn FCal Forward Calorimeter FM Frequency Modulation FSK Frequency Shift Keying GUT Grand Unification Theory HEC Hadronic Endcap Calorimeter HEP High Energy Physics HFSS High Frequency Structure Simulator HL-LHC High Luminosity Large Hadron Collider Hz Hertz L1 Level 1 L2 Level 2 LAr Liquid Argon LEIR The Low Energy Ion Ring LEP Large Electron Positron collider LHC Large Hadron Collider LHCb Large Hadron Collider beauty

105 Linac Linear accelerator LTE Long-Term Evolution MDT Monitored Drift Tubes MS MicroStrip MSSM Minimal SuperSymmetric Model NMSSM Next to Minimal SuperSymmetric Model PCB Printed Circuit Board PS Proton Synchrotron PSB Proton Synchrotron Booster PSK Phase Shift Keying QAM Quadrature Amplitude Modulation QFT Quantum Field Theory RPC Resistive-Plate Chambers SCT SemiConductor Tracker SM Standard Model SNR Signal to Noise Ratio SPS Super Proton Synchrotron SSB Single-SideBand modulation SUSY SUperSYmmetry RF Radio Frequency ROI Region Of Interest TGC Thin-Gap Chambers TRT Transition Radiation Tracker UMTS Universal Mobile Telecommunications System VNA Vector Network Analyser VSWR Voltage Standing Wave Ratio WLAN Wireless Local Area Network

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119 Acta Universitatis Upsaliensis Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1222 Editor: The Dean of the Faculty of Science and Technology

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