Search for a Singly Produced Excited Bottom Quark Decaying to a Top √ Quark and W Boson at S =13 Tev with the CMS Experiment

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Master-Thesis University of Hamburg

Search for a Singly Produced Excited Bottom Quark Decaying to a Top √ Quark and W Boson at s =13 TeV with the CMS Experiment

Alexander Fröhlich Geboren am 15.02.1991 in Hamburg

08.11.2017 1. Gutachter: Prof. Dr. Johannes Haller 2. Gutachter: Dr. Roman Kogler Abstract

A search for a singly produced excited bottom quark b∗ decaying to a top quark and a √ W boson in the muon+jets decay channel in proton-proton collisions at s = 13 TeV is presented. The analyzed dataset has been recorded by the CMS experiment in 2016 and corresponds to an integrated luminosity of 35.87 fb−1.

This is the ﬁrst search for new physics to use the HOTVR top tagger. The capabilities of the HOTVR top tagger are demonstrated and a comparison to another top tagging algorithm is given.

No signiﬁcant excess of data over the Standard Model prediction is observed. Upper limits on the b∗ production cross section at 95 % conﬁdence-level are set. These limits are used to exclude b∗ quarks for purely left-handed, purely right-handed and vector-like benchmark couplings up to masses of 2050 GeV/c2, 2150 GeV/c2 and 2350 GeV/c2, respectively.

Furthermore, the sensitivity of this search to a singly produced vector-like B0 quark decaying to a top quark and a W boson in the muon+jets decay channel is demonstrated and upper cross section limits are set.

Zusammenfassung

Eine Suche nach einem einzelnd produzierten, angeregten bottom Quark b∗, das in ein top Quark und ein W Boson im Muon+Jets Zerfallskanal zerfällt, ist präsentiert. Die √ Suche wurde in Proton-Proton Kollisionen bei s = 13 TeV durchgeführt, die vom CMS Experiment in 2016 aufgezeichnet wurden. Der analysierte Datensatz entspricht einer integrierten Luminosität von 35.87 fb−1.

Dies ist die erste Suche nach neuer Physik, die den HOTVR Algorithmus zur Identiﬁkation von top-Jets verwendet. Die Einsatzmöglichkeiten von HOTVR werden demonstriert und ein Vergleich mit einem anderen Algorithmus zur top-Jet Identiﬁkation wird aufgezeigt.

Es wurde kein signiﬁkanter Datenüberschuss über der Standard Modell Vorhersage be- obachtet. Obere Grenzen für den b∗ Produktionswirkungsquerschnitt bei einem 95 % Konﬁdenzintervall wurden gesetzt. Diese Grenzen wurden dann benutzt, um b∗ Quarks für reine linkshändige, reine rechtshändige und vektorartige Benchmark-Kopplungen bis hin zu Massen von 2050 GeV/c2, 2150 GeV/c2 und 2350 GeV/c2, in dieser Reihenfolge, auszuschließen.

Desweiteren wird die Sensitivität dieser Suche auf ein einzelnd produziertes vektorartiges B0 Quark, das in ein top Quark und ein W Boson im Muon+Jets Zerfallskanal zerfällt, demonstriert und obere Grenzen für den Produktionswirkungsquerschnitt werden gesetzt. Contents

1 Introduction 1

2 Theory 3 2.1 The Standard Model ...... 3 2.2 Shortcomings of the Standard Model ...... 7 2.3 Beyond the Standard Model ...... 7 2.4 Heavy Bottom Quarks ...... 9 2.4.1 Excited Bottom Quarks ...... 9 2.4.2 Vector-Like B Quarks ...... 10 2.5 Standard Model Backgrounds ...... 11 2.6 Proton-Proton Collisions ...... 12

3 Jet Clustering and Top Tagging 15 3.1 Jet Clustering Algorithms ...... 15 3.1.1 Heavy Object Tagger with Variable R ...... 17 3.2 Top Tagging ...... 18 3.2.1 Jet Substructure ...... 18 3.2.2 b Tagging ...... 20 3.2.3 CMS Top Tagger ...... 20 3.2.4 HOTVR Top Tagger ...... 20

4 Experimental Setup 22 4.1 The Large Hadron Collider ...... 22 4.2 The Compact Muon Solenoid Experiment ...... 24 4.2.1 Coordinate System ...... 25 4.2.2 Inner Tracking System ...... 26 4.2.3 Electromagnetic Calorimeter ...... 27 4.2.4 Hadronic Calorimeter ...... 28 4.2.5 Solenoid Magnet ...... 30 4.2.6 Muon System ...... 30 4.2.7 Trigger ...... 31

5 Object Reconstruction and Identiﬁcation 32 5.1 Particle Flow Algorithm ...... 32 5.2 Primary Vertex ...... 34 5.3 Muons ...... 35 5.4 Jets ...... 36 5.4.1 Jet Energy Corrections ...... 37 5.5 Other Variables ...... 37

5.5.1 E T ...... 37

5.5.2 ST ...... 37

6 Studies on the HOTVR Algorithm 38 6.1 Jet Energy Corrections for HOTVR Jets ...... 38 6.2 Top Tagging Performance ...... 43

7 Analysis 47 7.1 Dataset and Simulated Events ...... 48 7.2 Event Selection ...... 49 7.2.1 Pre-Selection ...... 50 7.2.2 Top Jet Selection using HOTVR ...... 55 7.2.3 Top Jet Selection using the CMS top tagger ...... 59 7.3 Reconstruction of the Invariant tW Mass ...... 59 7.3.1 Neutrino Reconstruction ...... 61 7.3.2 Reconstruction of the tW System ...... 61 7.3.3 Determining the Goodness of the Hypothesis ...... 62 7.3.4 Comparison of the Diﬀerent Top Tagging Methods in the Recon- struction ...... 65 7.4 Systematic Uncertainties ...... 67

8 Results 71 8.1 Statistical Interpretation ...... 71 8.2 Further improvements of the Analysis ...... 73

9 Summary 77 1 Introduction

The Standard Model of elementary particle physics is a theory describing the fundamental building blocks of our universe – the elementary particles – and their interactions. It is extremely successful in providing precise predictions of experimental results. With the discovery of the Higgs boson in 2012 [1,2], the last missing piece of the Standard Model is found. There are, however, still some questions left unanswered by the Standard Model. For example the question of naturalness, arising from the hierarchy problem and the large number of free parameters in the Standard Model. In order to approach those open questions, many possible extensions to the Standard Model have been proposed. Many of these extensions predict the existence of new, heavy quarks. With the discovery of the Higgs, a fourth generation of chiral quarks is ruled out [3]. There are, however, other possibilities to introduce new heavy quarks, either as vector-like quarks, or as excited states of the already existing quarks.

The analysis presented in this thesis focuses on the search for excited bottom quarks b∗ decaying to a top quark and a W boson in the final state with one muon and jets. Due to the similarity of their signatures, the search is also sensitive to heavy vector-like B0 quarks in the same final state. The analysis is performed using data from proton-proton collisions at a center-of-mass energy of 13 TeV, recorded by the Compact Muon Solenoid (CMS) experiment at the Large Hadron Collider (LHC). The dataset used was recorded in 2016 and corresponds to an integrated luminosity of 35.87 fb−1. Events with a highly energetic muon and missing transverse energy are selected to reconstruct the leptonically decaying W. Then, top tagging is used to identify the jet originating from the hadronically decaying top quark. The tW system is reconstructed using a χ2-method, where the back-to-back signature of the signal process is exploited to discriminate signal from the dominant t¯t background. The invariant mass of the tW system is used to search for excited bottom quarks and heavy vector-like B0 quarks over a wide range of possible masses, reaching from 700 GeV/c2 to 3000 GeV/c2. The reliable identification of top quarks over such a wide kinematic range is important to maintain sensitivity over the whole mass spectrum. In this search, top tagging is performed with the Heavy Object Tagger with Variable R (HOTVR) [4]. By adapting the jet size to its transverse momentum pT, HOTVR achieves a stable top tagging efficiency over a wide pT spectrum. This is the first search for new physics to implement this new top tagging algorithm. A performance comparison of the HOTVR top tagger with the soft drop top tagger is presented.

This thesis is structured as follows. The theoretical background for this thesis is given in chapter 2, where the Standard Model and possible extensions are discussed. Furthermore, an introduction to excited bottom quarks, as well as heavy vector-like quarks is given. In chapter 3, the jet clustering algorithms and top tagging methods used in this analysis are described. A brief description of the LHC and the CMS detector is given in chapter 4. The reconstruction and identiﬁcation of physics objects from detector data is described in chapter 5. In chapter 6, the performance of the HOTVR algorithm is demonstrated and a comparison with the CMS top tagger is shown. The analysis is presented in chapter 7 and the results are discussed in chapter 8. Finally, a summary is given in chapter 9.

2 2 Theory

2.1 The Standard Model

The Standard Model of particle physics (SM) is a quantum ﬁeld theory describing all known elementary particles and their interactions via three fundamental forces, the strong force, the weak force, and the electromagnetic force, see for example [5, 6]. According to the SM, all observed matter is fundamentally made up of fermions. Fermions are particles carrying half-integer spin. There are twelve diﬀerent fermions and their respective antifermions contained in the SM. They are further categorized into quarks and leptons. The interactions between the fermions are mediated by the exchange of spin 1 particles called gauge bosons.

The SM is formulated as a gauge theory with internal symmetry of the

SU(3)C × SU(2)L × U(1)Y symmetry group. That means the SM Lagrangian is gauge invariant under local gauge transformations of this group. This invariance eventually gives rise to the three fundamental interactions and their respective gauge bosons.

The electromagnetic interaction is described by the theory of quantum electrodynamics (QED). It postulates a local gauge symmetry of the Lagrangian under phase transformations of the U(1)Q group. QED introduces a massless gauge boson, the photon, that mediates the electromagnetic interaction between particles carrying electromagnetic charge Q.

The theory of the strong interaction, quantum chromodynamics (QCD), is formulated similarly to QED. It postulates local gauge invariance under transformations of the non- abelian SU(3)C symmetry group and describes the interaction between particles carrying color charge C. Color charge can have three states called red, green and blue. The only fermions in the SM that carry color are quarks. Their interaction via the strong force is mediated by the exchange of massless gauge bosons called gluons. In total, QCD introduces eight gluons, which also have color charge, since they arise from the generators of a non-abelian symmetry group. This leads to a property of the strong force called color confinement. As a result of the interaction between gluons, the potential between quarks increases with the distance between them. If the distance becomes large enough, new quark-antiquark pairs are formed from the potential energy stored in the gluon field. Due to this process, called hadronization, the quarks can only appear in bound, colorless states called hadrons. Because of the hadronization, quarks and gluons can not be observed directly. When these particles decay, their final states consist of cascades of many charged and neutral hadrons, called jets. The top quark is the only exception to this. It is the only quark that decays before the hadronization takes place. This is due to the high mass of the top quark of 2 mtop = 172.44 ± 0.13(stat.) ± 0.47(syst.) GeV/c [7], and the resulting large phase space for the decay.

On the other hand, the strong interaction becomes insigniﬁcant at short distances, so that the quarks inside of hadrons can be considered free particles. This eﬀect is called asymptotic freedom. It is an important feature of QCD, because it allows the calculation of processes of the strong interaction at high energies in perturbation theory. This further allows the factorization ansatz in the calculation of deep inelastic proton-proton scattering cross sections described later in this chapter.

The weak interaction arises from the invariance under SU(2)L transformations. However, for a consistent description of the weak interaction as a gauge theory, it has to be uniﬁed with the electromagnetic interaction to the electroweak interaction [8, 9]. Above the electroweak uniﬁcation energy, the electromagnetic interaction and the weak interaction are combined into a single interaction. Below this energy, the electroweak symmetry is broken, and the two separate interactions are obtained. The underlying gauge symmetry of the electroweak theory is of the SU(2)L × U(1)Y symmetry group. The U(1)Y sector gives rise to the B gauge boson. Instead of the electromagnetic charge Q, the hypercharge Y , given by

Y = 2(Q − T3) , (2.1) is conserved. Here, T3 is the third component of the weak isospin. The SU(2)L sector gives ± rise to three gauge bosons W1, W2 and W3. The W bosons of the weak interaction are obtained by the superposition of W1 and W2:

± 1 W = √ (W1 ∓ iW2). (2.2) 2

4 0 The Z boson and the photon (γ) are mixed states of the W3 and B bosons. The mixing is represented by a rotation

      γ cos θW sin θW B  0 =     , (2.3) Z − sin θW cos θW W3 where θW is the Weinberg angle.

The W± bosons couple only to particles with weak isospin. Special about the weak interaction is, that in the SM only fermions with left-handed chirality and anti-fermions with right-handed chirality carry weak isospin. This property of the weak interaction is called parity violation. Left-handed fermions form isospin doublets, while right-handed fermions are isospin singlets. Leptons can thus be arranged as shown here:

      νe νµ ντ   ,   ,   , eR, µR, τR. (2.4) e µ τ L L L

In the lower row the charged leptons, electrons (e), muons (µ) and tauons (τ) are shown. They carry electric charge of Q = −e, where e is the elementary charge, and weak isospin 1 of T3 = − 2 . In the upper row of the doublets are the electron-, muon-, and tauon-neutrinos 1 (νe, νµ and ντ). They have weak isospin of T3 = 2 and do not carry electric charge, this means neutrinos are only weakly interacting, which makes them diﬃcult to detect. Since neutrinos are assumed to be massless in the SM, there are no right-handed neutrinos.

Quarks can be arranged similar to the leptons:

      u c t   ,   ,   , uR, dR, cR, sR, tR, bR. (2.5) d s b L L L

In the upper row the so called up-type quarks, up-, charm- and top-quark are shown. They 1 2 have weak isospin of T3 = 2 and electric charge of Q = 3 e. The down-type quarks, shown in the lower row, are the down-, strange-, and bottom-quark, which have weak isospin of 1 1 T3 = − 2 and electric charge of Q = − 3 e.

The diﬀerent isospin doublets are referred to as generations. The charged gauge bosons of the weak interaction, W±, mediate the transition within one generation. It is, however, observed in experiments, that the W± also mediate transitions between diﬀerent generations of quarks. These transitions happen, because the mass eigenstates of the quarks are not

5 the same as their weak eigenstates. The mixing of the weak eigenstates is implemented by rotating the down-type quark mass eigenstates with a unitary matrix called Cabbibo-

Kobayashi-Maskawa matrix (CKM matrix) VCKM,

 0       d d Vud Vus Vub d          0        s  = VCKM s = Vcd Vcs Vcb s , (2.6)  0       b b Vtd Vts Vtb b with [10]

  |Vud| |Vus| |Vub|     |VCKM| = |Vcd| |Vcs| |Vcb| (2.7)   |Vtd| |Vts| |Vtb|  +0.00011  0.97434−0.00012 0.22506 ± 0.0005 0.00357 ± 0.00015     = 0.22492 ± 0.0005 0.97351 ± 0.00013 0.0411 ± 0.0013  .  +0.00032  0.00875−0.00033 0.0403 ± 0.0013 0.99915 ± 0.00005

The squares of the matrix elements give the probability of a certain transition.

All SM particles would have to be massless, since explicit mass terms would violate gauge invariance of the Lagrangian. This is in contradiction to experimental results. Fortunately, this problem can be solved by introducing the mechanism of spontaneous symmetry breaking, developed by Brout, Englert and Higgs independently [11–13]. They introduced a new complex scalar field φ. Gauge invariance of this new field introduces a new potential, called Higgs potential. The form of this potential leads to a non-zero vacuum expectation value of the scalar field, which spontaneously breaks the electroweak symmetry. Excitations of the Higgs potential around the minimum are interpreted as a new boson with spin 0, the Higgs boson. The mechanism of spontaneous symmetry breaking introduces new terms to the SM Lagrangian, giving mass to the Higgs boson and the W± and Z0 bosons and describing their interactions with the Higgs boson. Furhtermore, fermions obtain their masses via the interaction with the Higgs field. In the SM, the fermion masses are free parameters.

The Higgs boson was discovered in 2012 at the LHC [1,2] with a mass of mH = 125.09 ± 0.21(stat.) ± 0.11(syst.) GeV/c2 [14], completing the SM.

6 2.2 Shortcomings of the Standard Model

The SM is very successful at giving precise predictions of experimental measurements. There are however some phenomena observed in nature, that cannot be explained with the SM. This section gives a brief description of some of these shortcomings.

Gravity is the only known fundamental interaction that is not described by the SM. This is due to the fact that there is to this point no consistent formulation of the theory of general relativity as a quantum ﬁeld theory. The gravitational interaction is many orders of magnitude weaker than the other fundamental interactions. It is therefore negligible in current elementary particle physics experiments. Nevertheless, for a complete and consistent description of the fundamental interactions in the universe, gravity has to be included.

Another problem concerning the scale of gravity is the hierarchy problem. It considers the large difference of the energy scale of the electroweak interaction (O(103 GeV)) and the energy scale of gravity, which is the Planck scale (O(1019 GeV)). All particles in the SM receive quantum corrections to their masses. For the Higgs boson, these corrections can become huge, since they depend on the scale up to which the SM is valid, e.g. the Planck scale. In order to explain the light Higgs boson in terms of the SM, the corrections would have to be fine-tuned to cancel out in a way that they result in the observed Higgs mass. Furthermore, since all fermions obtain their masses by the coupling to the Higgs field, the fermion masses can not be derived from the SM, but are free parameters. The large number of free SM parameters, as well as the fine-tuning of these parameters, are considered unnatural.

2.3 Beyond the Standard Model

Various possible extensions to the SM have been proposed to address the shortcomings discussed above. All extensions postulate the existence of new particles. A selection of possible extensions is introduced in this section.

7 Supersymmetry A famous type of extension to the SM is Supersymmetry (SUSY) [15]. It assumes a fundamental symmetry between fermions and bosons. In SUSY models, each elementary particle has a supersymmetric partner with the same quantum numbers, but with diﬀerent spin. The partner particles of fermions are bosons and vice versa. The contributions of the new particles to the loop corrections cancel out with the contributions of their SM partners thus solving the hierarchy problem. To this point, there is no evidence for SUSY at low energies, indicating that SUSY particles would have higher masses than their SM partners. As a consequence, the loop corrections would not cancel completely, resulting in a smaller version of the hierarchy problem.

Warped Extra Dimensions The physics described in the SM takes place in four dimensions, three in space and one in time. However, there is no reason to limit the physics to these four dimensions. The Randall-Sundrum (RS) model [16] proposes a five-dimensional universe, where the fifth dimension is warped and spans between two (3+1)-dimensional branes. All SM particles are localized on one of the branes, while gravitons, the mediators of gravity, are localized on the other brane. Gravitons can propagate through the fifth dimension towards the SM brane. Traveling along the warped dimension reduces their energy, explaining the weakness of gravity and thus explaining the hierarchy problem.

Compositeness In compositeness models [17,18], the SM fermions are assumed to be not elementary particles, but composed of new, more fundamental particles. This drastically reduces the number of free parameters in the SM, since the fermion masses are no longer fundamental quantities. Compositeness would also give an explanation for the seeming symmetry between leptons and quarks.

Composite Higgs Another type of compositeness models, the composite Higgs models (CHM) [19], address the hierarchy problem by assuming that the Higgs boson is not elementary, but composed of new, undiscovered particles. CHMs predict new particles with masses around O(1 TeV), which are excited states of the composite Higgs boson. This avoids the problem of unnaturalness by introducing a new physics scale and explains the small mass of the Higgs boson.

8 2.4 Heavy Bottom Quarks

Many of the above described extensions to the SM predict the existence of excited quark states or heavy vector-like quarks. This analysis focuses on the search for excited bottom quarks (b∗), but due to the similarity of the processes, it is expected to be also sensitive to heavy vector-like B0 quarks. This section focuses on the description of the b∗, while the B0 is brieﬂy introduced in the end.

2.4.1 Excited Bottom Quarks

∗ 1 The b is an excited state of the b quark, assuming a composite b quark. It is a spin 2 1 particle and has, like the b quark, a charge of − 3 q and forms a color triplet. Its interactions are described by an eﬀective Lagrangian [20]. As described above, the W bosons couple only to SM fermions with left-handed chirality, but this must not hold for new particles. Instead, the coupling of the b∗ to the W boson is a free parameter. Three diﬀerent benchmark models are considered. In the purely left-handed and purely right-handed models, only the left-handed or right-handed chiral projections of the b∗ couple to the W boson, respectively. The vector-like model assumes the left-handed and right-handed couplings to be equally strong. The predicted cross-sections from these three models are compared to experimentally observed cross-sections. The main production process of b∗ at the LHC would be single production via the interaction of a b quark and a gluon. Pair production of b∗ is also possible, but it is highly suppressed due to the high mass of the b∗. Possible decay modes of the b∗ are gb, bZ, bH and tW. The branching ratios of these decay modes are shown in Fig. 2.1 as a function of the b∗ mass. It can be seen, that the decay to tW is the dominant process at high b∗ masses, reaching a plateau of almost 40 %. The presented search for b∗ in this thesis is therefore performed in the tW decay channel. The corresponding leading order feynman diagram is shown in Fig. 2.2.

Searches for b∗ decaying to tW have already been performed by CMS [22] and ATLAS [23]. √ The latest analysis was done by CMS at s = 8 TeV. They were able to set mass exclusion limits for the three diﬀerent benchmark models. The current limits exclude b∗ masses up to 1390 GeV/c2, 1430 GeV/c2 and 1530 GeV/c2 for the left-handed, right-handed and vector-like benchmark models, respectively.

9 Figure 2.1: Branching ratio of the heavy bottom quark (B0) decay modes as a function of B0 mass [21].

b t b∗

g W

Figure 2.2: Leading order feynman diagram of the process bg → b∗ → tW.

2.4.2 Vector-Like B Quarks

Other than the b∗, the B0 is a completely new kind of quark [24,25], rather than an excited 1 1 state. It is a spin 2 particle, has a charge of − 3 e and forms a color triplet. It is called vector-like, because the left-handed and right-handed components both transform in the same way under transformations of the electroweak symmetry group.

Vector-like B0s are singly produced at the LHC via the weak interaction as seen in Fig. 2.3. The possible decay modes of the B0 include gb, bZ, bH and tW. The branching fractions to the diﬀerent decay modes depend on the speciﬁc model. For this analysis, a benchmark

10 q q0

t Z/W B0

g b/t

Figure 2.3: Leading order Feynman diagram of the considered production and decay process of the vector-like B0. model with BR(B0 → bZ) = BR(B0 → tW) = 0.5 is assumed. The ﬁnal states of the B0 decay all contain an additional quark and either a top or a b, due to the production process. In this analysis only the production with an associated b quark is considered.

2.5 Standard Model Backgrounds

The presented search focuses on the muon+jets final state of the b∗ decay into tW. The leading order Feynman diagram for this decay is shown in Fig. 2.4. In this specific final state, the W from the top quark decays hadronically, while the W from the b∗ decays into a muon and a muon neutrino. There are various SM processes, that can result in the same or in a similar final state. Processes with the same signature are called irreducible backgrounds, while all other processes are called reducible backgrounds. The considered SM processes contributing to the expected background are discussed in the following. t¯t + jets The production of top-antitop (t¯t) pairs in association with jets constitutes the main background in this analysis. If one of the top quarks decays leptonically, this decay mode is hard to distinguish from signal events. Only constraints on the extra b jet and on the event topology can reduce this background.

W + jets The production of a W boson and extra jets can have a similar signature as the signal, when the W boson decays leptonically. The requirement for heavy ﬂavor jets

11 q0

W q t b W µ

Figure 2.4: Feynman diagram of the b∗ decay into tW in the muon+jets ﬁnal state.

(top-jets and b-jets) reduces this background.

Single top The production of a single top quark in association with a W boson has the same signature as the signal. This makes it an irreducible background.

Other backgrounds The other considered SM backgrounds are the production of a Z boson with additional jets (Z+jets), diboson production (WW, ZZ, WZ) and the production of multiple jets via the strong interaction (QCD). All of these backgrounds are reducible and make only small contributions to the total expected background.

There are of course more background processes, but their contribution is negligible due to their small cross-sections.

2.6 Proton-Proton Collisions

The dynamics of elementary particles are studied in scattering experiments. The presented search analyzes data from proton-proton (pp) collisions. This section gives a brief description of the physics of pp collisions and the inner structure of the proton.

The proton structure was studied in deep inelastic electron-proton scattering experiments. These experiments found, that the proton is not an elementary particle, but a complex formation quarks and gluons. Every proton consists of three valence-quarks (u, u, d).

12 Arising from the strong interaction between the valence quarks, the proton additionally contains several gluons and short-lived quark-antiquark pairs, the so-called sea-quarks.

In this context, all proton constituents are generally referred to as partons. High energy scattering of protons is hence described as the scattering of partons. The partons each carry only a fraction x of the protons momentum. At leading order, this fraction is described by the Bjorken x, Q2 x = . (2.8) 2P q Here, Q2 = −q2 is the transferred momentum squared and P is the proton’s four- momentum. Consequently, the center-of-mass energy of a scattering event in pp collisions is reduced by the value of x of both participating partons. The eﬀective center-of-mass √ energy sˆ is given by √ √ sˆ = x1x2s. (2.9)

In general, the value of x of the two interacting partons are not equal, resulting in a boost of the event in z direction, where z is the direction of the beam axis (see section 4.2.1). As a result, the z component of the total momentum vector of a simple interaction is unknown. Instead, the transverse momentum pT, given by

q 2 2 pT = px + py , (2.10) is used in pp collision experiments, because it is invariant under Lorentz transformations in z direction.

The cross section σ of a certain process in pp collisions is given by the cross section of the parton interaction σˆ, convoluted with the parton density functions (PDFs) fi and fj,

ZZ X 2 2 2 σpp = dx1dx2fi(xi,Q )fj(xj,Q )ˆσi,j(x1, x2,Q ). (2.11) i,j

The PDFs give the probability to encounter a certain parton as a function of x and Q2.A measurement of the PDFs can be seen in Fig. 2.5. At low values of x, the pp scattering is dominated by gluon interactions, while the valence quark interaction becomes more likely in the high x region.

13 MSTW 2008 NLO PDFs (68% C.L.)

) 1.2 ) 1.2 2 2

Q2 = 10 GeV2 Q2 = 104 GeV2

xf(x,Q 1 xf(x,Q 1 g/10 g/10 0.8 0.8

0.6 u 0.6 b,b u

d 0.4 d 0.4 c,c

c,c s,s 0.2 s,s d 0.2 d u u

0 0 -3 -3 10-4 10 10-2 10-1 1 10-4 10 10-2 10-1 1 x x

Figure 2.5: PDFs for quarks, antiquarks and gluons as a function of x at Q2 = 10 GeV2/c2 and Q2 = 104 GeV2/c2 [26].

14 3 Jet Clustering and Top Tagging

Quarks and gluons can not be observed directly due to color confinement. At high energies, they result in final states of many charged and neutral hadrons. These hadrons can be clustered into jets to simplify the final state of a process. Since the investigated final state in this analysis features a top quark, the identification of jets originating from top quark decays plays an important role. This chapter gives a description of the jet clustering algorithms and the top tagging methods used in this analysis.

3.1 Jet Clustering Algorithms

In general there are two types of jet clustering algorithms, cone algorithms and sequential recombination algorithms. The focus of this section will be on sequential recombination algorithms, since the algorithms used are of this type.

Sequential recombination algorithms build jet candidates by pairing four-momenta, also referred to as pseudojets, using the distance parameters dij and diB, deﬁned as

2 2k 2k ∆Rij dij = min(p , p ) , (3.1a) Ti Tj R2 2k diB = pTi . (3.1b)

Here, dij describes the distance between two pseudojets i and j and diB describes the distance between a pseudojet and the beam, pTi is the transverse momentum of the q 2 2 pseudojet i, ∆Rij = (yi − yj) + (φi − φj) is the distance between the pseudojets i and j y φ R y 1 E+pz in the - -plane, and is the cone size parameter. In this case = 2 ln E−pz denotes the rapidity. For each combination of pseudojets i and j, the values of dij and diB are calculated. If one of the dij is the smallest, the pseudojets i and j are paired, i.e. their four-momenta are added. Otherwise, if the smallest value is one of the diB, the pseudojet i is added to the jet collection and removed from the list of pseudojets. Figure 3.1: A simulated event clustered with diﬀerent jet algorithms. The found jets and their respective area are shown [27].

In Eq. (3.1), k is a free parameter. The choice of k changes the behavior of the clustering algorithm with respect to the pT of the pseudojets. Three prominent algorithms, which are defined by their choice of k, are briefly introduced. The kT algorithm [28,29] chooses k = 1, meaning softer pseudojets are paired preferably. The resulting jets have a more irregular shape, see Fig. 3.1. The Cambridge/Aachen algorithm (CA) [30,31] uses k = 0, i.e. jets are combined according solely to their geometrical distance. This approach makes it most suitable for many substructure algorithms. For the anti-kT algorithm [27] k = −1 is chosen. In this case, hard pseudojets are combined first, resulting in more uniformly shaped jets.

All jet algorithms have to be infrared and collinear (IRC) safe. That means the calculated observables should not change for ﬁnal states with or without inﬁnitely soft (infra red) radiation of gluons or collinear splittings. The clustering algorithms used in this search

16 fulﬁll these requirements.

3.1.1 Heavy Object Tagger with Variable R

The HOTVR algorithm [4] is a sequential clustering algorithm specialized in the iden- tiﬁcation of boosted, hadronically decaying, heavy particles. Other than the sequential clustering algorithms described above, HOTVR does not use a ﬁxed cone radius, but adapts the cone size to the jet’s pT. HOTVR also introduces a mass jump criterion to identify subjets within the jet.

HOTVR uses distance parameters dij and diB as defined in Eq. (3.1), but instead of having a fixed cone radius R an effective radius Reff,

 R ρ/p < R  min for T min,  Reff = Rmax for ρ/pT > Rmax, , (3.2)   ρ/pT else. is used, where ρ is a parameter describing the slope of Reff. Like the CA algorithm, HOTVR uses n = 0 for the clustering. Before combining two pseudojets, HOTVR requires them to fulfill a mass jump criterion,

θ · mij > max (mi, mj) , (3.3)

if their combined mass mij is above a certain mass threshold µ. Otherwise, the lighter pseudojet is removed from the list of pseudojets. Additionally, if the mass jump criterion is fulﬁlled, the pseduojets have to have pT ≥ pT,sub in order to be combined, where pT,sub is a parameter of the algorithm, else they are removed. Finally, if the pseudojets are combined, they are stored as subjets of the combined pseudojet.

HOTVR is used in the default top tagging mode [4], the parameter settings are shown in table 3.1.

17 Parameter Default Description

Rmin 0.1 Minimum value of Reff. Rmax 1.5 Maximum value of Reff. ρ 600 GeV/c Slope of Reff. µ 30 GeV/c2 Mass jump threshold. θ 0.7 Mass jump strength. pT,sub 30 GeV/c Minimum pT of subjets.

Table 3.1: Parameters of the HOTVR algorithm in default top-tagging mode [4].

3.2 Top Tagging

An important discriminator against many SM backgrounds in this analysis is the presence of a jet originating from a boosted top quark. In order to identify this top-jet, a method called top tagging is used. There are various top tagging algorithms, which identify top-jets based on diﬀerent variables, like the jet mass and the number of subjets. This analysis features a new top tagging method called the HOTVR top tagger. The performance of the new algorithm is studied and compared to the standard top tagging method in CMS.

3.2.1 Jet Substructure

√ At the high center of mass energy of s = 13 TeV even heavy objects like top quarks can be created with high transverse momentum pT. The decay products of those boosted objects are therefore collimated, such that they are likely to be clustered into a single big jet. It is useful to resolve the substructure of those big jets in order to discriminate jets originating from diﬀerent initial particles. In this analysis two sophisticated substructure algorithms are used to obtain top tagging variables. They are described below.

Soft Drop

The soft drop algorithm [32] is used to remove soft, wide-angle radiation from jets (grooming), leading to a better mass resolution and therefore improving the top tagging performance. Information on the jet substructure is obtained by reverting the last clustering iteration. In this step, called declustering, the jet is divided into two subjets with a distance

18 of ∆R1,2. The algorithm then checks the soft drop criterion

!β min (pT,1, pT,2) ∆R1,2 > zcut , (3.4) pT,1 + pT,2 R0 where R0 is the cone size of the jet, and zcut and β are free parameters to control the behavior of the algorithm. If the criterion is not fulﬁlled, the softer subjet is removed. The procedure is repeated, until the soft drop criterion is fulﬁlled.

For optimal performance of the soft drop algorithm, jets clustered with the CA algorithm are required. The so-called soft drop mass is obtained for anti-kT jets by clustering the jet constituents again with the CA algorithm and taking the invariant mass of the groomed CA jet.

N-subjettiness

N-subjettiness [33] is a jet substructure variable that measures the compatibility of the jet with having up to N subjets. It is deﬁned as

1 X τN = pT,k min (∆R1,k, ∆R2,k,..., ∆RN,k), (3.5) d0 k where ∆Ri,k is the distance between a hypothetical subjet axis i and the jet constituent k. A normalization factor X d0 = pT,kR0 (3.6) k is used to restrict τN to values between 0 and 1. A jet with τN close to 0 denotes a good compatibility with having up to N subjets. Having a value close to 1 means that the jet is likely to have more than N subjets.

The ratio τ3/2 = τ3/τ2 is often used as a discriminating variable for identifying jets originating from top quarks. Jets from top quarks are expected to have three subjets, i.e.

τ3 is expected to be close to 0 while τ2 is expected to be close to 1, resulting in a τ3/2 < 1. Jets from light quarks, gluons or vector bosons on the other hand are expected to have less then three subjets. The variables τ2 and τ3 are both expected to be of similar size, resulting in τ3/2 ≈ 1.

19 3.2.2 b Tagging

The top quark decays almost exclusively into a b quark and a W boson. It is therefore useful to be able to distinguish between b-jets and jets originating from light quarks or gluons.

The b-jet identiﬁcation exploits the longevity of B mesons. Due to their long lifetime, the B mesons travel an average distance of 1 mm in the detector before they decay. This results in a secondary vertex, measurable with the pixel detector. In this analysis the optimized Combined Secondary Vertex (CSVv2) algorithm [34, 35] is used for b tagging. CSVv2 uses a multivariate approach to combine information from jet tracks and reconstructed secondary vertices to a single variable. The CSVv2 variable ranges from 0 to 1, where a value close to 1 means the jet is likely to be originating from a b quark.

In this analysis a jet is considered to be originating from a b quark if the CSVv2 variable is > 0.935. This corresponds to the tight identification working point. The misidentification rate at this working point is 0.1 %, while the efficiency of the tagger is 49 % [35].

3.2.3 CMS Top Tagger

The top tagging method recommended by CMS uses the soft drop mass as the discriminating variable. It requires groomed AK8 jets with pT > 400 GeV/c. Four different working points are provided for the CMS top tagger [36]. Top-jet candidates are required to have 2 2 a soft drop mass of 105 GeV/c < mjet < 220 GeV/c . The different working points are obtained by varying the threshold on the N-subjettiness variable τ3/2. The top tagging performance can be further improved by requiring one of the subjets to fulfill the loose working point of the CSVv2 b-tagger.

3.2.4 HOTVR Top Tagger

The HOTVR algorithm oﬀers its own set of substructure variables, which can be calculated from the HOTVR subjets. The following criteria are used for the standard HOTVR top tagging working point [4]:

• The number of subjets has to be Nsubjet ≥ 3.

20 2 2 • The jet mass is required to be within 140 GeV/c < Mjet < 220 GeV/c .

• The fraction of the leading subjets pT with respect to the jet pT is fpT = pT,1/pT < 0.8.

2 • The lowest combined mass of two of the ﬁrst three subjets has to fulﬁll Mpair > 50 GeV/c .

This selection on itself should be suﬃcient to achieve a good top tagging performance. However, for a better comparison to the CMS top tagger, an additional requirement on the N-subjettiness variable τ3/2 is imposed.

21 4 Experimental Setup

The data used in this thesis was recorded with the CMS experiment at the LHC. This chapter gives a brief description of the LHC and the components of the CMS detector.

4.1 The Large Hadron Collider

The LHC is a superconducting synchrotron and storage ring with a circumference of 27 km. √ It was designed for proton-proton collisions at a center-of-mass energy of s = 14 TeV with an instantaneous luminosity of 1034 cm−2s−1 [37]. Collisions with heavy ions (e.g. Pb-Pb) are also possible. It is located at the European Organization for Nuclear Research ("Conseil Européen pour la Recherche Nucléaire" - CERN) near Geneva, Switzerland. The purpose of the LHC is to perform precision measurements on the SM including the search for the Higgs boson and to search for new phenomena beyond the SM to solve questions left open by the SM.

Before the protons are injected into the LHC they are prepared and accelerated in a chain of pre-accelerators. Those are the Linac 2, the Proton Synchrotron Booster (PSB), the Proton Synchrotron (PS) and the Super Proton Synchrotron (SPS). In the SPS the protons reach the required energy of 450 GeV to be injected into the two beampipes of the LHC. The protons are then accelerated to the ﬁnal collision energy using superconducting radio-frequency (RF) cavities. The proton beam is divided into bunches due to the RF used.

The protons travel in the two beam pipes in opposite directions around the ring. They are bent on their circular path by 1232 superconducting dipole magnets. The beam pipes intersect at four points along the ring, where the experiments are located. These experiments are ALICE (A Large Ion Collider Experiment) [38], ATLAS (A Toroidal LHC Aparatus) [39], CMS (Compact Muon Solenoid) [40] and LHCb (LHC-beauty) [41]. ATLAS and CMS are multi-purpose detectors used for proton-proton collision experiments. CMS Integrated Luminosity, pp, 2016, s = 13 TeV p Data included from 2016-04-22 22:48 to 2016-10-27 14:12 UTC 45 45

) 1

1 LHC Delivered: 40.82 fb¡ ¡ 1 b 40 40

f CMS Recorded: 37.76 fb¡ (

t 35 35 i s o

n 30 30 i m

u 25 25 L

d 20 20 e t a

r 15 15 g e t

n 10 10 I

l a

t 5 5 o T 0 0

1 Jul 1 May 1 Jun 1 Aug 1 Sep 1 Oct Date (UTC) √ Figure 4.1: Integrated luminosity of proton-proton collisions at s = 13 TeV delivered by LHC (blue), and recorded by CMS (orange) in 2016 as a function of time [42].

LHCb is a detector focused on B meson physics and ALICE is a detector used for heavy ion collision experiments. The dataset analyzed in this thesis was recorded with the CMS experiment. It is described in more detail in section 4.2.

One of the main goals of the LHC is the discovery of new physics. The expected number of events N of a certain process occurring in a collider experiment is given by,

N = Lintσ , (4.1)

where σ is the cross-section of the process and Lint is the integrated luminosity. Since the cross-section of new physics processes is expected to be small compared to SM processes, according to Eq. (4.1), a high integrated luminosity is required to produce a suﬃcient number of events, i.e. a lot of proton-proton collisions have to be recorded. The integrated luminosity is given by Z Lint = Ldt , (4.2) where L is the instantaneous luminosity. The instantaneous luminosity is a measure for

23 the number of events per cross section and time. It is given by

n1n2 L = Nbfrev . (4.3) 4πσxσy

Here, Nb is the number of bunches, frev is the revolution frequency, n1 and n2 are the numbers of protons in the colliding bunches, and σx and σy are the beam diameters in x- and y-directions respectively. At the design luminosity of L = 1034 cm−2s−1 the LHC is 11 operated with Nb = 2808 bunches per beam, n1 = n2 = 1.15 × 10 protons per bunch, and a revolution frequency of frev = 11.25 kHz [37]. The beam proﬁle is measured in special runs with Van der Meer scans [43]. In these runs, the proton beams are scanned through each and the event rate is measured as a function of the displacement, to calculate the beam diameter. The luminosity measurement in CMS is described in detail in [44]. √ The integrated luminosity in proton-proton collisions at s = 13 TeV delivered by the LHC and recorded by CMS in 2016 can be seen in Fig. 4.1. The LHC delivered an integrated luminosity of 40.82 fb−1 of which 37.76 fb−1 were recorded by CMS.

4.2 The Compact Muon Solenoid Experiment

The CMS experiment is a multi-purpose detector to record particles produced in proton- proton collisions in the LHC. The CMS detector is located at one of the four interaction points of the LHC. It is 14.6 m long and has a diameter of 21.6 m. The detector is divided into the central barrel part and the endcaps at each side of the barrel, as shown in Fig. 4.2.

The CMS detector consists of several diﬀerent sub-detector layers that each serve a special purpose for measuring and identifying particles produced in proton-proton collisions. Listing from the inside out, these layers are the tracking system, the electromagnetic and the hadronic calorimeters (ECAL and HCAL), the superconducting solenoid, and several alternating layers of the return yoke and the muon chambers. The following sections describe these sub-systems based on information from [40,45].

24 Superconducting Solenoid Silicon Tracker Very-forward Pixel Detector Calorimeter

Preshower

Hadronic Calorimeter Electromagnetic Calorimeter Muon Detectors C ompact Muon S olenoid

Figure 4.2: Schematic overview of the CMS detector [45]

4.2.1 Coordinate System

The coordinate system used by CMS to describe a position within the detector is centered at the nominal interaction point of the proton beams. The y-axis points upwards, the x-axis points inwards toward the center of the LHC, and the z-axis points in counterclockwise direction along the beam axis. It is convenient to use spherical coordinates when referring to the position of particles within the detector. The azimutal angle φ is measured in the x-y-plane starting from the x-axis, the polar angle θ is measured starting from the z-axis and r is measured as the radial distance to the beam axis. Another coordinate η is introduced, because, unlike in θ, diﬀerences in η are invariant under Lorentz transformations in z direction. The relation between η and θ is given by

" θ !# η = − ln tan . (4.4) 2

25 Figure 4.3: Schematic cross section view of the CMS tracking system [40].

Using these coordinates, a Lorentz invariant distance measure in the φ-η-plane can be expressed as q ∆R = (∆φ)2 + (∆η)2 . (4.5)

4.2.2 Inner Tracking System

The inner tracking system is located in the heart of the CMS detector. Its purpose is the measurement of the trajectories of charged particles in order to reconstruct their charge and momentum. It is also used to reconstruct secondary vertices. The tracking system is 5.8 m long and 2.5 m in diameter. Its ﬁrst layer is only 4.4 cm away from the proton beam. The high particle ﬂux and the fast rate of bunch crossing require a high granularity, a quick response and radiation hardness of the detector components. On the other hand the material budget should be kept as low as possible to minimize the energy loss in the tracking system. Therefore the layout of the inner tracking system features an inner part consisting of a silicon pixel detector with 66 million pixels, and an outer part consisting of silicon strip detectors with a total number of 9.6 million strips. The layout is shown in Fig. 4.3.

The pixel detector (PIXEL) is composed of three cylindrical layers in the barrel part and two endcap discs on each side. Each pixel has a size of 100 µm × 150 µm. The strip

26 detector is divided into three subsystems. The tracker inner barrel (TIB) and tracker inner disc (TID) make the ﬁrst subsystem. They consist of four layers in the TIB and three discs at each end in the TID. The strips in TIB and TID have a pitch of 320 µm. Around the TIB and TID the tracker outer barrel (TOB) is located. The TOB is made up of six layers with 500 µm pitch. At each end of the TOB are the tracker endcaps (TEC+ and TEC-, where the sign indicates the orientation on the z-axis). The TECs are each composed of 9 discs with up to seven rings of silicon strips with a pitch of 320 µm in the inner four rings and 500 µm in the outer three rings.

The inner tracking system has an overall acceptance of up to |η| = 2.5.

4.2.3 Electromagnetic Calorimeter

The ECAL is built directly around the inner tracking system. It is used to measure the energy of particles that interact mostly via the electromagnetic interaction, i.e. electrons and photons. This is done by stopping those particles within the ECAL volume, such that they deposit all their energy in the calorimeter. When high-energy particles interact with the ECAL they cause cascades of secondary particles, so called electromagnetic showers. The amount of material needed to contain the electromagnetic shower is dictated by two material properties, the radiation length X0 and the Molière radius. The radiation length is deﬁned as the mean distance an electron has to traverse in the material until its energy 1 is reduced by a factor of e . The Molière radius is the radius of the cylinder containing 90 % of the energy of the electromagnetic shower. Distances in a calorimeter are usually given in units of X0.

The ECAL used in the CMS detector is a homogenous calorimeter made of lead tungstate crystals. Lead tungstate has a radiation length X0 = 0.89 cm and a Molière radius of 2.2 cm. The energy deposited in the calorimeter is measured by exploiting the scintillation process. When particles interact with the ECAL, they excite the lead tungstate molecules, which re-emit the energy as photons that can be detected using photo detectors. The amount of photons produced is proportional to the deposited energy. In lead tungstate, 80 % of the scintillation light is emitted within 25 ns. These properties allow a compact construction design of the ECAL with a ﬁne granularity.

The barrel section of the ECAL (EB) is composed of crystals with a front face cross section of 22 mm × 22 mm and a length of 230 mm (25.8 X0). It has an inner radius of 1.29 m

27 Barrel ECAL (EB)

y = 1.653 = 1.479 Preshower (ES) = 2.6 = 3.0 Endcap z ECAL (EE) Figure 4.4: Schematic overview of the ECAL layout [40]. and covers a pseudorapidity interval of 0 < |η| < 1.479. The ECAL endcaps (EE) consist of crystals with a front face cross section of 28.6 mm × 28.6 mm and a length of 220 mm

(24.7 X0). They are located at a distance of 3.14 m in z from the nominal interaction point and cover a pseudorapidity interval of 1.479 < |η| < 3.0. An overview of the ECAL layout is shown in Fig. 4.4.

The ECAL has a relative energy resolution of [40]

σE 2.8 % 12 % = q ⊕ ⊕ 0.3 % . (4.6) E E/GeV E/GeV

There are three different contributions to the energy resolution, as shown in Eq. (4.6). The first term is the stochastic term, describing statistical fluctuations in the shower development. The second term is called noise term and describes the contribution of electronic noise. The last term describes constant contributions to the relative energy resolution, such as calibration errors and non-linearity in the readout elements.

4.2.4 Hadronic Calorimeter

Hadrons lose only a fraction of their energy in the ECAL, since the hadronic interaction length λI is much longer than X0. The HCAL is build around the ECAL to stop the

28 Figure 4.5: Schematic overview of the HCAL layout [45]. hadrons and measure their energy. It is also a crucial component in the measurement of missing transverse energy E T . Other than the ECAL, the HCAL is a sampling calorimeter. It consists of alternating layers of active medium and passive absorber material. This choice was made to ﬁt most of the HCAL into the solenoid. The HCAL uses plastic scintillator tiles as the active medium. They are embedded between layers of brass, which acts as the absorber material. The absorber material has a short interaction length, for brass that is λI = 16.42 cm. Hadrons interacting with the absorber material develop a shower of secondary particles. These particle showers can then be measured in the scintillators. Sampling calorimeters decrease the energy resolution because they only measure a fraction of the deposited energy. On the other hand they allow the measurement of the longitudinal shower proﬁle. The overall energy resolution is [46]

σE 115.3 % = q ⊕ 5.5 % . (4.7) E E/GeV

The HCAL features four diﬀerent parts, shown in Fig. 4.5. In the barrel region the hadron barrel (HB) and the hadron outer barrel (HO) calorimeters are located. The HB is placed directly above the EB and covers a region of 0 < |η| < 1.3. The HO is placed

29 outside the solenoid. It is used to improve the shower containment in the central region of 0 < |η| < 1.26. The endcaps consist of the hadron endcap (HE) and the hadron forward (HF) calorimeters. HE covers a region of 1.3 < |η| < 3.0, while HF covers a region of 2.9 < |η| < 5.0.

4.2.5 Solenoid Magnet

The superconducting solenoid is used to produce a homogeneous magnetic ﬁeld of B = 4 T in z-direction on its inside. It is 12.9 m long and has an inner diameter of 5.9 m. Contained in this volume are the inner tracking system, as well as the ECAL and HCAL. This is done to maximize the magnetic ﬁeld in the inner tracking system, while ensuring that most of the energy is absorbed in the calorimeters and not in the solenoid.

The magnetic ﬁeld bends the trajectories of charged particles via the Lorentz force. The curvature of the trajectories is used to determine the momentum and the charge of those particles. The magnetic ﬁeld is returned through the iron yokes on the outside of the solenoid. Embedded between the iron yoke layers is the muon system. This improves the measurement of muon momenta.

4.2.6 Muon System

Muons can traverse the ECAL, HCAL and even the solenoid without considerable loss of energy. Nearly all other particles are absorbed before they reach the muon system. It therefore makes up the outermost part of the CMS detector. The detectors of the muon system are placed inside the return yoke of the solenoid. The muon trajectories are bent due to the magnetic ﬁeld, which allows a momentum measurement like in the tracking system. This additional measurement improves the resolution of the muon momenta.

Three diﬀerent kinds of gaseous detectors are used in the muon system: drift tubes (DT), resistance plate chambers (RPC) and cathode strip chambers (CSC). The layout of the muon system can be seen in Fig. 4.6. It consists of two parts, the muon barrel (MB) and the muon endcaps (ME). The MB uses DTs and RPCs. It covers a region of 0 < |η| < 1.2. The MEs use CSCs and RPCs and they cover a region of up to |η| < 2.4

30 ) 800 m c ( DT eta = 0.8 1.04 MB 4

R RPC 1.2 700

MB 3 600

MB 2 500 MB 1 1.6

400

300 2.1

2.4 200

ME 4 100 ME 2 ME 3 ME 1 CSC 0 0 200 400 600 800 1000 1200 Z (cm)

Figure 4.6: Schematic overview of the muon system [40].

4.2.7 Trigger

Operating at design luminosity the LHC provides an event rate of 40 MHz. Considering the average disc space needed to store an event, which is O(MB), the rate of events written to disk has to be reduced. The trigger system is used for this purpose and to save only potentially interesting events. The trigger system works in two levels. The first level (L1) is a hardware based trigger that reduces the event rate to about 100 kHz. The events can be saved in a buffer for 3.2 µs. In this time the L1 trigger decides whether to keep an event based on information from the muon system and the calorimeters. Events that fulfill the L1 trigger criteria are then passed to the software based high level trigger (HLT). The HLT reconstructs the whole event with full detector granularity and resolution. It further reduces the rate to about 100 Hz based on that information. The events passing the HLT are then stored for offline analysis.

31 5 Object Reconstruction and Identiﬁcation

The physical objects used by physics analyses have to be reconstructed from signals in the detector and interpreted as particles. In CMS stable particles are reconstructed and identiﬁed using the particle ﬂow (PF) algorithm [47]. Quarks and gluons appear as cascades of neutral and charged hadrons, so called jets, due to the hadronization process. Jets can be used to identify the initial particles. Sophisticated jet clustering algorithms are used to identify jets using the objects from the PF algorithm.

This chapter gives a description of the PF algorithm and the jet algorithms used. Additional identiﬁcation criteria for the physical objects used in this analysis are also given.

5.1 Particle Flow Algorithm

The particle flow algorithm is used to reconstruct all stable particles of a proton proton collision using the signals (hits) of the full detector. The different particles can be identified by their characteristic interaction with the detector, as shown in Fig. 5.1. Charged particles produce signals in the tracking system while neutral particles pass it undetected. Photons and electrons lose all their energy in the ECAL and cause electromagnetic showers in the process. Charged and neutral hadrons are stopped in the HCAL and deposit their energy in the form of hadron showers. Muons and neutrinos are the only particles that can pass through the detector. While neutrinos leave the detector undetected, the muons produce hits in the muon detectors.

The reconstruction of an event with the PF algorithm is done in three steps. First it analyzes all sub detectors independently by combining hits to particle trajectories (tracks) or clusters. In the second step the tracks and clusters are linked to each other. Finally the PF algorithm identiﬁes these objects as particles by their characteristic behavior in the detector. Key: Muon Electron Charged Hadron (e.g. Pion) Neutral Hadron (e.g. Neutron) Photon

3.8T Transverse slice through CMS

Silicon Tracker

Electromagnetic Calorimeter

Hadron Calorimeter Superconducting Solenoid Iron return yoke interspersed with Muon chambers

0m 1m 2m 3m 4m 5m 6m 7m

Figure 5.1: Sketch of signatures of diﬀerent particles in a cross-section of the CMS detector [47].

Hits in the tracking system and muon detectors are combined to tracks using an iterative approach. First a seed for the track is generated using a few consecutive hits. Then, a track is built using hits in all tracker layers that are compatible with the seed track. Finally, the trajectory is fitted using a χ2-method to determine the transverse momentum, charge, and origin of the charged particle. If the track then fulfills the reconstruction criteria, it is kept for further analysis and the associated hits are removed. This procedure is repeated in several iterations to increase the efficiency of this method while keeping the misreconstruction rate low. The reconstruction criteria are loosened after every iteration.

Hits in the calorimeter cells are combined to clusters using a clustering algorithm. Like in the track reconstruction the ﬁrst step is to generate a seed. Local energy maxima with respect to either four or eight calorimeter cells are selected as cluster seeds if they are above a certain energy threshold. Topological clusters are grown from the cluster seeds by adding neighboring cells to the cluster if their energy is above a given threshold. Finally

33 the energy and position of the clusters are determined using a Gaussian mixture model with N Gaussian distributions, where N is the number of cluster seeds in the topological cluster.

After the subsystems are analyzed separately, the PF algorithm links them together to so called PF blocks. Tracks in the inner tracking system and calorimeter clusters are linked by extrapolating the tracks into the calorimeters up to a certain depth. If the track ends in a cluster, the two are linked. Additionally, at each layer of the tracking system, tangents to the track are extrapolated to the ECAL and linked to clusters to collect photons from bremsstrahlung. Tracks in the muon detector are linked to tracks in the inner tracking system if the extrapolated trajectories match. The combined track is used in a χ2-ﬁt to reconstruct a so-called global muon.

The final step in the PF algorithm is to identify the PF blocks as specific particles. The first particles to be identified are muons, followed by electrons and photons and finally charged and neutral hadrons. The specific identification criteria are described in detail in [47]. In this step, the PF algorithm also decides which sub detector measurements are used to achieve the most precise reconstruction. For example, if a muon has a transverse momentum of pT < 200 GeV/c, the measurement from the inner tracking system is used. Otherwise, the momentum is determined from the track fit with the smallest χ2 value.

5.2 Primary Vertex

The primary interaction vertices are reconstructed as a part of the track reconstruction. The primary vertex reconstruction algorithm [48] uses the tracks reconstructed by the PF algorithm. The primary vertex reconstruction works in three steps. First, the algorithm selects tracks that fulﬁll certain quality criteria. The selected tracks are then clustered to primary vertex candidates according to their z-coordinate at their closest approach to the center of the beam spot. In the last step, the tracks in each cluster are use in a ﬁt to determine the position of the primary vertex.

In this analysis only primary vertices fulﬁlling the following criteria are considered:

• The primary vertex has to be in the center of the interaction region, i.e. √ x2 + y2 < 2 cm and |z| < 24 cm.

34 • The number of degrees of freedom of the ﬁt must be ≥ 4.

It is likely that there are more then one primary vertices in an event, due to the high number of protons in the colliding bunches. In this case, the vertex with the largest value of the sum of all transverse momenta squared of the associated track-level physics objects is considered the main interaction vertex. All other primary vertices are pile-up vertices.

5.3 Muons

Muons identified and reconstructed from the PF algorithm have to fulfill additional criteria to be considered as muons in this analysis. CMS provides different working points for identification of muons depending on the efficiency and misidentification rate. The tight working point was chosen for this analysis. It has the following requirements on muon candidates [49]:

• It must be reconstructed as a global muon.

• The global track ﬁt must have χ2/d.o.f. < 10.

• At least one hit in the muon chamber must be included in the ﬁt.

• The track in the inner tracking system must be matched to at least two muon stations.

• It must have at least 10 hits in the inner tracking system, including at least one hit in the pixel detector.

• It must have a transverse impact parameter of |dxy| < 2 mm with respect to the primary vertex.

The muon candidate is also required to have a minimum transverse momentum of pT > 50 GeV/c and to be within a pseudorapidity range of |η| < 2.4. Furthermore, the muon candidate has to be isolated, i.e. its relative isolation

P h± P γ P h0 P h±,PU pT + max pT + pT − 0.5 pT Irel = µ,cand , (5.1) pT

35 considering particles within a cone of ∆R < 0.4 around the muon candidate, must be γ h± h0 Irel < 0.15. Here, pT is the photon transverse momentum and pT and pT are the charged and neutral hadron transverse momenta, respectively. The transverse momentum of h±,PU charged hadrons originating from a diﬀerent primary vertex is denoted by pT . It is used to approximate the contribution of neutral hadrons from diﬀerent primary vertices.

5.4 Jets

The PF candidates are passed to jet clustering algorithms, which combine them into jets. This analysis uses three different jet definitions. So-called AK4 jets and AK8 jets are clustered using the anti-kT algorithm [27] with a cone radius of R = 0.4 and R = 0.8, respectively. HOTVR jets are clustered using the Heavy Object Tagger with Variable R (HOTVR) algorithm [4]. After clustering, jets have to fulfill certain criteria to be kept for further analysis.

HOTVR jets and AK8 jets are required to have pT > 200 GeV/c and |η| < 2.5. AK4 jets have to have pT > 30 GeV/c and |η| < 2.4. The |η| requirement is recommended for b tagging [35]. Additionally, the AK4 jets have to fulﬁll the requirements of the loose identiﬁcation working point [50]:

• The neutral hadron energy fraction has to be < 0.99.

• The neutral electromagnetic energy fraction hast to be < 0.99.

• The jet has to have at least two constituents.

• The charged hadron energy fraction has to be > 0.

• The charged electromagnetic energy fraction hast to be < 0.99.

• The charged multiplicity has to be > 0.

36 5.4.1 Jet Energy Corrections

Pile-up and non-linear response of the calorimeter aﬀect the measurement of the jet four-momentum. In order to account for those eﬀects the jets have to be corrected. The

CMS collaboration provides several different jet energy corrections (JEC) [51] for anti-kT jets that each account for a specific effect. The first corrections (L1 corrections) account for particles from pile-up events that are clustered into the jets. The next corrections (L2L3 corrections) account for non-linear response of the detector. The final corrections (L2L3Res corrections) account for residual differences between simulated events and data.

5.5 Other Variables

5.5.1 E T

Neutrinos and hypothetical particles that can not be detected with the CMS detector appear as missing transverse energy ( E T). It is deﬁned as

~ X E T = E T = − ~pT,i . (5.2)

All particle ﬂow objects are considered in this sum. This variable is used to reconstruct neutrinos from a leptonically decaying W boson in this analysis and as a discriminating variable to reduce background events without neutrinos.

5.5.2 ST

The transverse activity in an event ST is deﬁned as the sum of the transverse momenta of all electrons, muons and AK4-jets plus the missing transverse energy:

X ST = pT + E T. (5.3) e,µ,jets

It is a good indicator for heavy particles in an event, because they result in ﬁnal states with high pT objects. The ST of such an event is expected to have a value around the mass of the heavy particle. It is used as a discriminating variable to select potential signal events.

37 6 Studies on the HOTVR Algorithm

In the presented analysis, the HOTVR algorithm is implemented for the ﬁrst time in a search for new physics. A method to calibrate the HOTVR jets is developed. Afterwards the performance of the HOTVR algorithm is demonstrated and compared to the CMS top tagger.

6.1 Jet Energy Corrections for HOTVR Jets

Up to now there are no JEC provided for jets clustered with HOTVR. The following approach is used to calibrate the jets. The effect of pile-up is expected to be dominant for HOTVR jets in the low and intermediate pT region, since these jets can become very large. It is studied in data and in simulated events of SM processes. A description of the event simulation using Monte-Carlo generators can be found in section 7.1. Simulations of all SM processes discussed in section 2.5 were used to get a reasonable prediction that can be compared to the observed data. A baseline selection, as described in section 7.2.1, is applied. The selection requires the presence of exactly one highly energetic isolated muon, E T > 50 GeV/c and ST > 400 GeV/c. Afterwards, at least one HOTVR jet with pT > 200 GeV/c and |η| < 2.5 is required. The effect of pile-up on the HOTVR jets can be seen by measuring the selection efficiency of the pT > 200 GeV/c requirement as a function of the number of primary vertices NPV. The selection efficiency is given by the ratio between the number of events before and after the selection. In Fig. 6.1a, the selection efficiency as a function of NPV is shown. The red markers correspond to the selection efficiency in data, while the blue markers correspond to the selection efficiency in simulated SM events. In the lower part, the ratio between data and simulation is shown. The error bars depict the statistical uncertainties. A trend towards higher selection efficiency with higher NPV, i.e. more pile-up, is clearly visible. The pile-up dependency is described well by the simulation, as only small deviations between data and simulation are observed. 1 1 0.9 Data 0.9 Data 0.8 0.8 MC MC Efficiency 0.7 Efficiency 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1

1.2 0 20 40 1.2 0 20 40 1 1 0.8 0.8 DATA/MC DATA/MC 0 20 40 0 20 40

NPV NPV (a) (b)

Figure 6.1: Eﬃciency of the selection of HOTVR jets with pT > 200 GeV/c as a function of the number of primary vertices NPV in data (red) and simulated SM events (blue) for (a) uncorrected HOTVR jets and (b) HOTVR jets with pile-up correction.

In order to account for the pile-up, an offset method is used. Under the assumption that the activity of the pile-up is distributed uniformly over the whole detector, a correction factor apile-up is derived with ρ · Ajet apile-up = 1 − raw , (6.1) pT raw where ρ is the mean pT per unit area arising from pile-up, Ajet is the jet area, and pT is the uncorrected jet pT. Control distributions of ρ and the subjet area after the event selection are shown in Fig. 6.2. Data is shown as black markers and the different simulated processes are shown as colored areas. The simulated events are stacked, to allow a comparison between data and simulation. In the lower parts the ratio between data and simulation is shown. The error bars correspond to the statistical uncertainties. The calculated corrections are applied to the subjets of each HOTVR jet. As shown in Fig. 6.1b, the pile-up dependency is removed almost completely using this offset method.

It is shown in [51], that the response is similar for anti-kT jets with distance parameter R in the range of R = 0.3 − 1.0, after they were corrected for pile-up. To get an approximation for the L2L3 and L2L3res corrections for HOTVR, the L2L3 and L2L3Res corrections provided for anti-kT jets are used for the HOTVR subjets as well. Finally, to account for

39 35.9 fb•1 (13 TeV) 35.9 fb•1 (13 TeV) 6 Data 10 5 TTbar 10 5 Events WJets Events 10 4 DYJets 10 104 SingleTop 103 3 DiBoson 10 QCD 102 102 10 10 1 1

1.50 20 40 60 1.50 1 2 3 4 5 1 1 0.5 0.5 DATA / BG DATA / BG 0 20 40 60 0 1 2 3 4 5 subjet ρ [GeV/c] A [a.u.] (a) (b)

Figure 6.2: Control distributions of (a) ρ and (b) the subjet area.

diﬀerences in the response between anti-kT jets and HOTVR jets, an additional correction factor r is derived by calculating rec pT r = gen (6.2) pT rec from simulated t¯t events. Here pT is the pT of the subjet with full detector simulation gen and pile-up, and pT is the pT of the corresponding subjet on particle level, i.e. without detector simulation and pile-up. This ratio is calculated for several bins in η and pT.A correction factor ares is then derived using

1 ares = , (6.3) hri where hri denotes the mean value of r in one (η,pT) bin. Finally, a correction function fη(pT) is obtained via a ﬁt to the correction factors for a ﬁxed η, using the ansatz

b·pT+c fη(pT) = a + e . (6.4)

The corresponding correction function is then used for the ﬁnal correction of the HOTVR subjets. The ﬁts can be seen in Figs. 6.3 and 6.4 for all considered η regions.

40 1.2 1.2 •4.0< η < •1.5 •1.5< η < •1.0 correction factor correction factor

correction factor fit correction factor fit 1.1 1.1

1 1