Constraints of Leptoquark Models with CMS Data

Masterarbeit

vorgelegt von Henrik Jabusch

November 2019

Eingereicht am 27. November 2019

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

Abstract

Recently observed deviations from the Standard Model prediction in B meson decays could be explained by existence of leptoquarks (LQs). LQs are new hypothetical bosons mediating transitions between leptons and quarks, and are predicted by several different theories beyond the Standard Model. Many direct searches for LQs have been performed at the Large Hadron Collider at CERN, but no evidence for their existence was found so far. In this master’s thesis, a remodeling of the CMS search for the pair production of scalar leptoquarks decaying exclusively into top quarks and muons is presented using a parameterized description of the CMS detector. The results are validated against those obtained with a full detector simulation. Good agreement is found. A reinterpretation of CMS data is performed to test a novel LQ flavor model motivated by recent hints towards lepton flavor universality violation. It includes sophisticated production processes of scalar leptoquarks beyond those of pair production only, which depend on the strength of the Yukawa coupling λ between the LQs and the quarks and leptons. The impact on the LQ production cross section and the kinematics of such decays is studied. For the scalar leptoquark S3, different couplings to third-generation quarks and second-generation leptons are studied and limits on the mass and the production cross section are derived. The LQ coupling to a b quark and a muon is constrained for the first time and found to yield the most stringent exclusion limits on the lower mass of the S3. For λ = 1, it is MLQ = 1520 GeV.

Kurzfassung

Kürzlich beobachtete Abweichungen von der Standardmodellvorhersage in Zerfällen von B- Mesonen könnten durch die Existenz von Leptoquarks (LQs) erklärt werden. LQs sind neue hypothetische Bosonen, die Lepton-Quark-Übergänge vermitteln und von mehreren verschie- denen Theorien jenseits des Standardmodells vorhergesagt werden. Viele direkte Suchen nach LQs wurden am Large Hadron Collider am CERN durchgeführt, ohne dass derzeit Beweise für deren Existenz gefunden wurden. In dieser Masterarbeit wird eine Neumodellierung einer CMS-Analyse mithilfe einer para- metrisierten Beschreibung des CMS-Detektors präsentiert. In der CMS-Analyse wurde nach Paarproduktion von skalaren Leptoquarks gesucht, welche ausschließlich in Top-Quarks und Myonen zerfallen. Die Ergebnisse der Neumodellierung werden mit den Ergebnissen der voll- ständigen Detektorsimulation verglichen. Eine gute Übereinstimmung wird gefunden. Eine Neuinterpretation von CMS-Daten wird durchgeführt, um ein neuartiges LQ-Flavor- Modell zu testen, welches durch jüngste Hinweise bezüglich einer Verletzung der Leptonﬂavor- universalität motiviert ist. Dieses beinhaltet erweiterte Produktionsprozesse von skalaren LQs jenseits der Paarproduktion, welche von der Stärke der Yukawa-Kopplung λ zwischen den LQs und den Leptonen und Quarks abhängen. Die Auswirkungen auf die Produktionswirkungsquer- schnitte der LQs und auf die Kinematik solcher Zerfälle wird untersucht. Für das skalare Lep- toquark S3 werden verschiedene Kopplungen an Quarks der zweiten Generation und Leptonen der dritten Generation untersucht und Grenzen auf die Masse sowie den Produktionswirkungs- querschnitt abgeleitet. Zum ersten Mal wird die LQ-Kopplung zu einem Bottom-Quark und einem Muon eingeschränkt. Diese stellen zudem die stärksten unteren Ausschlussgrenzen der

Masse des S3 dar. Für λ = 1 beträgt diese MLQ = 1520 GeV. Contents

1. Introduction1

2. The Standard Model and Leptoquarks in BSM Physics3 2.1. The Standard Model of Particle Physics...... 3 2.1.1. Quantum Chromodynamics: The Strong Interaction...... 5 2.1.2. The Proton: Structure and Collisions...... 6 2.1.3. Electroweak Symmetry Breaking and the Higgs Mechanism...... 7 2.2. Shortcomings of the SM...... 12 2.3. Beyond the Standard Model...... 13

3. Leptoquark Phenomenology 16 3.1. Experimental Motivation...... 16 3.2. Production of Leptoquarks in pp Collisions...... 19 3.3. Current Status of Leptoquark Searches at the LHC...... 20 3.4. Indirect Constraints on Leptoquarks...... 21 3.5. Flavorful Leptoquark Model...... 21

4. Experimental Setup 27 4.1. The Large Hadron Collider...... 27 4.2. The Compact Muon Solenoid Experiment...... 30 4.2.1. The Coordinate System...... 30 4.2.2. Detector Components...... 32

iv 5. Leptoquark Analysis by CMS 37 5.1. Data Set and Event Generation...... 37 5.2. Event Selection...... 38 5.3. Leptoquark Mass Reconstruction...... 39 5.3.1. Reconstruction of the Neutrino...... 40 5.3.2. Reconstruction of the Top Quarks...... 41 5.3.3. Reconstruction of the Leptoquarks...... 41 5.4. Results...... 42

6. Remodeling the CMS Analysis 45 6.1. Signal Event Generation...... 45 6.2. Detector Simulation with DELPHES ...... 46 6.2.1. Tuning DELPHES ...... 48 6.3. Results...... 54

7. Search for Scalar Leptoquarks 60 7.1. Signal Event Generation...... 60 7.2. Results...... 61 −1/3 − 7.2.1. Decay Scenario: S3 → tµ ...... 61 −1/3 − 7.2.2. Decay Scenario: S3 → tµ , bν ...... 65 −4/3 − 7.2.3. Decay Scenario: S3 → bµ ...... 68 +2/3 7.2.4. Decay Scenario: S3 → tν ...... 71

8. Conclusion and Outlook 74

A. Additional Tables 76

Bibliography 81

1. Introduction

In particle physics, the Standard Model (SM) is a theory that describes three of the four known fundamental forces (the electromagnetic, weak and strong interactions) and classifies all known elementary particles. Formulated in the 1970’s as a gauge quantum field theory, the SM is extremely successful to date, tested in numerous experiments with unimagined precision. Al- though the SM is renormalizable and mathematically self-consistent, it leaves some questions unanswered. Neither does it contain gravity, explain neutrino masses, have a candidate for (cold) dark matter, nor allows for a unification of gauge couplings. In fact, the SM at the latest breaks down at energy scales where gravitation comes into play. This energy scale, called Planck scale, is of order 1019 GeV. Compared to the electroweak scale of about 100 GeV, this gives rise to the hierarchy problem that asks for a reason of this huge discrepancy. Conse- quently, the mass of the Higgs boson is unstable with respect to large quantum corrections, as quadratically divergent terms are added to the Higgs mass in higher order corrections. Many different theories were developed addressing the shortcomings of the SM, e.g. Grand Unified Theories (GUTs), Supersymmetry (SUSY) and compositeness models. In such beyond the Standard Model (BSM) approaches, often new particles such as leptoquarks (LQs) appear. Leptoquarks are hypothetical bosons that simultaneously couple to leptons and quarks. There- fore, they carry lepton and baryon number, and could violate the SM property of lepton flavor universality (LFU). Hints for such BSM effects have recently been observed in the decay of B mesons. Since LQs could explain all observed deviations simultaneously, they are promising candidates for new physics. Searches for LQs have been performed in many experiments, where many decay modes have been investigated, but no evidence for their existence was found so far. Hence, constraints on the LQ parameter space were provided. These constraints were generally obtained by simplified models considering leading-order diagrams for LQ pair production cross section only. A deeper investigation with more sophisticated models is needed to identify the regions of the LQ parameter space that are already excluded by current measurements, and in particular those that are not ruled out yet. This thesis aims at an exploration of the LQ parameter space by performing a more physically complete reinterpretation of published measurements conducted at the Large Hadron Collider

1 1. Introduction

(LHC) at CERN. First, a search for pair-produced LQs coupled to third-generation quarks performed by the CMS collaboration [1] is remodeled using the fast simulation approach of the DELPHES framework [2] for the detector simulation. In addition, DELPHES is validated by com- paring this remodeling to the original analysis. The second step constitutes the transition to a more sophisticated LQ model that includes additional LQ production processes, which additionally depend on the Yukawa coupling λ between LQs and quarks and leptons. Using data collected from the Compact Muon Solenoid (CMS) detector, constraints on the LQ mass, the LQ production cross section and also the Yukawa coupling are set.

This thesis is organized as follows. Chapter2 discusses the theoretical foundations introduc- ing the SM and several BSM theories. The phenomenology of LQs is presented in Chapter3, including a novel LQ ﬂavor model. A brief introduction to the Large Hadron Collider (LHC) and the CMS experiment is given in Chapter4. Chapter5 summarizes the LQ analysis performed by the CMS collaboration, which is remodeled with DELPHES fast simulation in Chap- ter6. Results of the search testing the novel LQ ﬂavor model with the remodeled analysis are presented in Chapter7. The thesis is concluded and an outlook is given in Chapter8.

2 2. The Standard Model and Leptoquarks in BSM Physics

This chapter discusses the theoretical foundations relevant for this thesis based on Refs. [3–5]. Section 2.1 introduces the Standard Model of particle physics, the theory of elementary particles and their interactions with each other, except gravity. As the SM has open questions and cannot explain some observed phenomena, a selection of its most important shortcomings is presented in Section 2.2, whereas possible theories beyond the Standard Model are highlighted in Section 2.3.

2.1. The Standard Model of Particle Physics

The SM describes the fundamental components of matter consisting of fermions as well as the way they interact with each other via bosons. Each interaction has an underlying gauge group that determines its properties. For the strong interaction, which is described by quantum chromodynamics (QCD), the local symmetry group is SU(3)C. The weak and electromagnetic interactions can be uniﬁed to the electroweak interaction whose symmetry group is

SU(2)L ⊗ U(1)Y , such that in total the SM is formulated as a gauge quantum ﬁeld theory (QFT) containing the internal symmetries of the unitary product group

SU(3)C ⊗ SU(2)L ⊗ U(1)Y . (2.1)

Renormalization and regularization techniques [6] are applicable to the SM, such that divergencies from higher-order loop corrections cancel and observables remain finite. The fundamental objects of the SM are quantum fields, which are defined at all points in the four-dimensional spacetime (x,y,z,t). Particles are quantum excitations of such fields and are distinguished by 1 their spin s: fermions have half-integer spin s = 2 and follow the Fermi-Dirac statistics and Pauli’s exclusion principle, whereas bosons have integer spin s = 0,1 and follow the Bose- Einstein statistics.

3 2. The Standard Model and Leptoquarks in BSM Physics

Figure 2.1. Schematic depiction of elementary particles in the SM. The values in the upper left corner denote the mass, charge and spin of the respective particle. For the neutrinos νe,µ,τ upper mass limits are shown, although the SM assumes them to be massless1. Taken from Ref. [7].

In Fig. 2.1 a schematic depiction of all elementary particles is shown. The fermions f are grouped into six quarks (q) and six leptons, whereof three carry the electric charge Q = 1e— the electron e, the muon µ and the tau lepton τ—and three do not, the neutrinos νe, νµ and ντ. The six quarks consist of three up-type quarks—the up u, the charm c and the top t quark—with 2 the electric charge Q = + 3 e, and the three down-type quarks—the down d, the strange s and the 1 bottom b quark—with Q = − 3 e. For each of the twelve fermions there is an anti-fermion f with opposite electric charge and same properties otherwise. In contrast, spin-1 vector bosons—the W± bosons, the Z0 boson, the photon γ and the gluons g—mediate the fundamental gauge interactions between fermions. Thus, they are also called gauge bosons. With its discovery in 2012, the scalar Higgs boson (H) completes the set of elementary particles and plays a central role in the SM since it explains how the gauge bosons W± and Z0 and the fermions obtain mass (see Section 2.1.3).

4 2.1. The Standard Model of Particle Physics

2.1.1. Quantum Chromodynamics: The Strong Interaction

The strong interaction is described by QCD, a non-Abelian gauge theory based on the symmetry group SU(3)C, where the subscript C denotes the color charge, the QCD equivalent to the electric charge. The dynamics of the color-carrying quarks and gluons is determined by the La- grange density LQCD, which is obtained by requiring local invariance under SU(3)C. Therefore, the gauge-covariant derivative Dµ is introduced,

a a ∂µ → Dµ = ∂µ − igsT Aµ (2.2)

a where gs is a free, real parameter—the gauge coupling of the strong interaction, T are the eight a a generators of the SU(3)C group given by the Gell-Mann matrices λ /2, and Aµ are eight vector ﬁelds corresponding to the eight mediating gluons. The full QCD Lagrangian reads2

1 X L = − Ga Gµν,a + q¯ iγ µD q − m q¯ q . (2.3) QCD 4 µν f µ f f f f f

a The first term accounts for the gluon kinematics containing the gluon field strength tensor Gµν, which allows self-interaction between gluons. Quark kinematics are described by the second term involving the quark fields qf, the Dirac matrices γµ and the in covariant derivative Dµ stated in Eq. (2.2), which also yields quark-gluon interactions. The sum runs over all fermions f carrying color charge, i.e. the six quarks. The last term represents the mass term with the quark masses mf.

A unique feature of the strong interaction comes with the behavior of its coupling gs. Since gs is energy dependent, it is referred to as running coupling. It can be approximately described by g (Q2) 1 α (Q2) = s ∝ (2.4) s 4π log(Q2/Λ2) where Q is an energy scale and Λ is a parameter dividing Q into two regions: for Q > Λ, strong interactions can be described by pertubation theory, whereas in the Q < Λ region per- tubative methods fail to describe QCD. Below this threshold Λ = Λhadr ≈ 200 MeV, a process called hadronization sets in. It describes the phenomenon that quarks and gluons can neither be isolated nor directly observed due to color conﬁnement, but assemble to form bound color- neutral states referred to as hadrons. Since this low energy region corresponds to large spatial

2For consistency, the QCD theory requires additional gauge ﬁxing and ghost terms to maintain the consistency of the path integral formulation [8,9], which are not included here.

5 2. The Standard Model and Leptoquarks in BSM Physics

Figure 2.2. Next-to-leading order (NLO) proton PDFs for Q2 = 10 GeV2 (left) and Q2 = 104 GeV2 (right). Gluon PDFs are scaled down by a factor of ten for better visibility. Taken from Ref. [10]. separations, hadronization can be interpreted as follows: in order to spatially separate color- charged particles, ever-increasing amounts of energy are required until this potential becomes large enough to spontaneously produce a quark-antiquark pair. Color-neutral states with two or three quarks are formed, mesons or baryons, respectively. Prominent examples of baryons to be named here are the proton p = [uud] and the neutron n = [udd], which make up all atomic nu- clei. On the other hand, at small distances, the coupling αs decreases until the strong interaction strength between quarks and gluons almost vanishes: they reside in asymptotic freedom. Since this effect plays an important role for the proton and its structure, more details on this as well as consequences of hadronization for collider signatures are given in the following section.

2.1.2. The Proton: Structure and Collisions

Since the presented search uses data recorded by the CMS experiment at the LHC, a proton- proton collider, this subsection highlights the most important physical aspects of the proton. As already discussed in the previous section, the proton is a composite particle with a complex energy-dependent structure. This structure is typically investigated in deep-inelastic scattering (DIS) processes. An incoming electron e interacts with a constituent of the proton p, a so-called parton, via γ- or Z0-interaction. The parton carries the fraction x of the proton’s four-momentum P and the rest of the proton fragments into hadrons. An important quantity is

6 2.1. The Standard Model of Particle Physics the Bjorken scaling variable deﬁned as

Q2 x = , (2.5) 2qP where Q2 = −q2 is the negative squared momentum transfer in the scattering process. The internal structure of the proton is characterized by parton distribution functions (PDFs) f, which describe the probabilities for finding a given parton dependent on its momentum fraction x at the resolution scale Q2, see Fig. 2.2. For high values of x, it is likely that the three valence quarks u,u,d carry the predominant fraction of the proton momentum. The probabilities of contributions from gluons and sea quarks—virtual quarks produced by gluons as quark-antiquark pairs in higher order processes—arise with decreasing x. Sea quarks can have any flavor, but light quarks such as u,d,s and c are dominant. With higher energy scales Q2, finer structures become visible. Gluon and sea quark PDFs increase significantly and even b-flavored sea quarks appear. PDFs are well described in the experimental accessible region of x and Q2 by perturba- tive Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) evolution functions [11–13]. But also for the remaining phase space DGLAP equations allow extrapolations.

In proton-proton (pp) collisions, the matrix element of a given subprocess σˆij depends on 2 the energy scale Q and the momentum fractions x1,2 of the partons involved. One therefore √ √ √ introduces the effective center-of-mass energy sˆ = x1x2s, where s is the center-of-mass energy in the pp collision. According to the factorization theorem [14], the inclusive cross section of pp collisions is given by the convolution of σˆij and the PDFs,

ZZ X 2 2 2 σpp = dx1dx2 fi(x1,Q )fj(x2,Q )σ ˆij(x1,x2,Q ), (2.6) i,j in which the sum runs over all types of partons i and j.

2.1.3. Electroweak Symmetry Breaking and the Higgs Mechanism

The Weak Interaction

The weak interaction affects all SM fermions. Its local symmetry group is SU(2)L and according to Noether’s theorem [15], it therefore has a conserved quantity, the third component of the weak isospin T3. It is the weak equivalent to the electric charge in electromagnetism and the color charge in QCD. Thus, T3 serves as a quantum number and determines particle behavior in weak interactions. For a detailed understanding, the concept of chirality is introduced. For massless particles, chirality is the same as helicity which is the sign of the projection of a spin of a particle

7 2. The Standard Model and Leptoquarks in BSM Physics

S~ on its momentum ~p. Particles with positive (negative) helicity have right-handed (left-handed) chirality. In case of massive particles this no longer holds, as helicity is not Lorentz invariant. Hence, chirality is deﬁned more abstractly via the transformation under a representation of the Poincaré group. The Wu experiment [16] in the 1950s showed that parity is violated in weak interactions, i.e. its occurrence depends on chiral properties of the participating fermions: only left-handed fermions and right-handed anti-fermions take part in charged-current (CC) weak 1 1 interactions. They can be arranged in isospin doublets with T3 = + 2 in the upper and T3 = − 2 in the lower entry,

            u c t νe νµ ντ   ,   ,   and   ,   ,   . (2.7) 0 0 0 µ τ d L s L b L e L L L

Right-handed fermions and left-handed anti-fermions do not contribute to CC-weak interactions and form singlets with T3 = 0,

uR, dR, cR, sR, tR, bR and eR, µR, τR. (2.8)

Right-handed neutrinos (and left-handed anti-neutrinos) have not been observed so far. By ± exchanging W bosons (T3 = ±1) leptons can change their flavor within a doublet, whereas quarks can also change their flavor to the one of a different doublet. This phenomenon is called flavor mixing and is a consequence of the inequality of flavor and mass eigenstates3. Mass and flavor eigenstates are related via the complex unitary Cabibbo-Kobayashi-Maskawa (CKM) matrix VCKM,  0       d d Vud Vus Vub d          0       s  = VCKM s = Vcd Vcs Vcb s , (2.9)  0       b b Vtd Vts Vtb b where (d0,s0,b0) denotes the flavor eigenstates and (d,s,b) the mass eigenstates. The probability for a given quark transition is proportional to the absolute square of the respective matrix 2 element, |Vij| . These matrix elements are measured by different experiments individually. A combined global fit yields [17]

  0.97420 ± 0.00021 0.2243 ± 0.0005 (3.94 ± 0.36) × 10−3    −3  |Vij| =  0.218 ± 0.004 0.997 ± 0.017 (42.2 ± 0.8) × 10  . (2.10)   (8.1 ± 0.5) × 10−3 (39.4 ± 2.3) × 10−3 1.019 ± 0.025

3By convention, the representation of down-type quarks is used here. Other conventions, e.g. a deﬁnition in terms of mass eigenstates of up-type quarks (u0,c0,t0), are equally valid.

8 2.1. The Standard Model of Particle Physics

Electroweak Symmetry Breaking: The Higgs Mechanism

The electroweak theory (EWT) is a uniﬁed description of the weak and the electromagnetic interaction. Its symmetry group is the product SU(2)L ⊗ U(1)Y , wherein L indicates the parity violation of the weak interaction and Y = 2(Q − T3) denotes the weak hypercharge, a quantum number combining the electric charge Q and the weak isospin T3. Similar to the formulation of QCD, a gauge-covariant derivative Dµ is introduced,

i ∂ → D = ∂ + ig T a W a + g0 YB , (2.11) µ µ µ L µ 2 µ

1,2,3 to obtain local invariance under the symmetry group. Here, four vector ﬁelds Wµ ,Bµ and a a a the generators TL = σ /2 of SU(2)L, given by the Pauli matrices σ ,a ∈ {1,2,3}, appear.

The Lagrangian results in

1 µν,a a µν X ¯ LEW = − W Wµν + B Bµν + ψ iγµ Dµ ψ, (2.12) 4 ψ containing vector-boson kinematics and self-interaction terms, as well as kinematic terms of the fermion ﬁelds ψ and their interaction to the vector-bosons W 1,2,3,B. The two parameters g and 0 g in Eq. (2.11) are electroweak coupling constants related by the Weinberg angle θW, g tanθ = . (2.13) W g0

0 Since g and g are running constants, θW is also scale-dependent. At the Z mass scale, it is given 2 by sin θW(MZ) ≈ 0.231 [17]. Furthermore, the Weinberg angle θW describes a rotation related to the spontaneous symmetry breaking of the EWT. The fields of the four gauge bosons that are ± physically observed—the photon field Aµ and the weak boson fields Wµ ,Zµ—are mixtures of 1,2,3 the four vector fields Wµ ,Bµ:

      1 A cosθ sinθ B W ± = √ W 1 ∓ iW 2 , µ = W W µ . µ µ µ      3 (2.14) 2 Zµ −sinθW cosθW Wµ

Hence, θW is also called the weak mixing angle. However, neither fermion nor gauge boson mass terms are part of the electroweak Lagrangian as they would spoil local gauge invariance, instead they arise from the Higgs mechanism.

9 2. The Standard Model and Leptoquarks in BSM Physics

Figure 2.3. Depiction of the Higgs potential before and after spontaneous symmetry breaking. The location of the respective ground state is indicated by the blue ball. Taken from Ref. [18].

The Higgs mechanism postulates the existence of a new complex scalar ﬁeld, the Higgs ﬁeld φ:

    φ+ 1 φ + iφ φ = = √ 1 2 ,  0    (2.15) φ 2 φ3 + iφ4 where the upper index denotes the electric charge. It is a T3-doublet with Y = +1. Conse- quently, an additional term to the electroweak Lagrangian is proposed,

† µ LH = (Dµ φ) (D φ) − V (φ). (2.16)

Here, Dµ is the covariant derivative of the EWT from Eq. (2.11) and V (φ) is the so-called Higgs potential. Invariance under rotations of φ+ and φ0 as well as invariance under changes of a complex phase require the potential to show a dependence on |φ|2 only. Further constraints from renormalization and the demand of a stable minimum yield the maximum order of |φ|4 and no odd powers of |φ|. Thus, the ansatz for the Higgs potential is

V (φ) = µ2 |φ|2 + λ|φ|4, (2.17) in which µ2 and λ are two real paramters, where λ is required to be positive, λ > 0, because otherwise the vacuum would not be stable. If µ2 is also positive, µ2 > 0, the ground state remains at |φ| = 0. For µ2 < 0 however, the symmetry is spontaneously broken and the minimum of the potential changes to the vacuum expectation value

s −µ2 v = , (2.18) λ as depicted in Fig. 2.3. In four dimensions this is not a single minimum, but a continuum of

10 2.1. The Standard Model of Particle Physics

degenerate ground states. By choosing the neutral ground state φvacuum, ﬁeld excitations can then be interpreted as the physical Higgs particle H,

    1 0 1 0 φvacuum = √   → φ = √   . (2.19) 2 v 2 v + H

Inserting this back into the potential of Eq. (2.17) yields

1 V (φ) = −µ2H2 + λvH3 + λH4. (2.20) 4

q 2 3 The ﬁrst term has the form of a Higgs mass term with mH = −2µ , whereas the H - and H4-terms account for self-interaction via three- and four-Higgs vertices. It is notable that the Higgs mass is a free parameter in this theory. In 2012, the Higgs boson was discovered by the experiments ATLAS and CMS with the mass mH = 126.0 ± 0.8 GeV [19] and mH = 125.3 ± 0.9 GeV [20], respectively.

With this information about Dµ, φ and V (φ) in hand, the Lagrangian LH of Eq. (2.16) can be evaluated such that it contains all kinematic, (self-)interaction and mass terms of the Higgs 1,2,3 H and the gauge boson vector ﬁelds Wµ ,Bµ. It further provides the W and Z masses

1 1q M = gv and M = g2 + g02, (2.21) W 2 Z 2 which are related via the weak mixing angle, MW = MZ cosθW . The experimentally measured values are MW = (80.379±0.012) GeV and MZ = (91.1876±0.0021) GeV [17]. The mediator particles being massive is the main reason for the “weakness” of the weak interaction and its short range. Furthermore, the vacuum expectation value of the Higgs ﬁeld can be determined via the Fermi coupling constant GF,

1 2M v = = W ' 246.22GeV. (2.22) q√ g 2GF

It marks the uniﬁcation scale of the EWT. The Higgs as an isospin doublet allows a connection of fermion doublets and singlets such that their mass terms become gauge invariant. For a given fermion f, the corresponding La- grangian reads m L = −m ψ ψ − f H ψ ψ , (2.23) f f f v f f which further includes a chirality-changing process via the Higgs. The fermion mass mf is

11 2. The Standard Model and Leptoquarks in BSM Physics interpreted as v m = λ √ , (2.24) f f 2 where λf is a free parameter, the Yukawa coupling. It is evident that by coupling to the Higgs, fermions acquire mass. The Yukawa couplings, however, and thus also the fermion masses are neither predicted nor constrained by the Higgs mechanism.

2.2. Shortcomings of the SM

The Standard Model is an extremely successful theory. It predicted many particles and is con- ﬁrmed by numerous experiments with astonishing precision. And still, there are some open questions the SM cannot answer. In the following, selected shortcomings are brieﬂy discussed.

Gravity

As already mentioned, the fourth fundamental force, gravity, is not part of the SM. The current understanding of gravity is still based on the general theory of relativity that Einstein formulated over a hundred years ago. Modern approaches to describe gravity as a quantum ﬁeld theory have not been successful yet.

The Hierarchy Problem

The hierarchy problem addresses the large discrepancy between aspects of the three fundamental forces described by the SM and gravity, e.g. gravity is ∼ 1024 weaker than the weak interaction. Consequently, the Higgs mass mH is unstable with respect to large quantum corrections. Higher order contributions such as fermion-antifermion loops add quadratically divergent terms ∼ Λ2 to the Higgs mass, where Λ ∼ 1019 GeV denotes the Planck scale, up to which the SM would be valid in case of no new physics. Therefore, the Higgs mass is expected to be of the order ∼ 1014−17 GeV, at the Planck scale, which exceeds the measured value of mH = (125.18 ± 0.16) GeV [17] by many orders of magnitude. A hypothetical highly ﬁne- tuned mechanism that cancels out these large higher order corrections is not implemented in the SM.

Dark Matter & Dark Energy

The presence of dark matter is known by various astrophysical observations such as measurements from rotational curves of spiral galaxies, gravitational lensing effects and ﬂuctuations in

12 2.3. Beyond the Standard Model the cosmic microwave background. A dark matter particle is expected to be massive but neutral with respect to the strong and electromagnetic interaction. The SM does not provide a suitable candidate. Thus, the SM describes only ∼ 5% of the matter in the universe, whereas ∼ 23% are assigned to dark matter and the missing ∼ 72% to dark energy [21], a completely unknown form of energy responsible for the accelerated expansion of the universe.

Baryon Asymmetry

In the observable universe there is an imbalance in baryonic and antibaryonic matter. A natural assumption would be a balanced distribution. Although the SM includes a CP-violating phase in the weak interactions CKM matrix, this is not sufﬁcient to explain the matter-antimatter asymmetry.

Symmetry Between Leptons and Quarks

As fermions are arranged in three generations of matter, each containing two quarks and two leptons, there might be an underlying symmetry for the fermions of the SM. Also that the electric charges of quarks are exactly integer thirds of the leptons charge e may not be incidental. Quark-lepton symmetry models are motivated by these similarities.

Neutrino Masses

The SM assumes the neutrinos to be massless. Neutrino oscillations, however, the phenomena of neutrinos having ﬂavor and mass states that are not diagonalizable simultaneously (analo- gously to the CKM mixing in the quark sector, see Section 2.1.3), are nowadays experimentally established [22] and require neutrinos to have mass. First predicted by B. Pontecorvo in 1957 [23, 24], measuring neutrino masses is still a challenge in modern physics.

2.3. Beyond the Standard Model

As the previous section highlights shortcomings of the SM, this section presents theories beyond the Standard Model. Since there are many of them, only a brief summary is given in the following.

13 2. The Standard Model and Leptoquarks in BSM Physics

Grand Uniﬁed Theories

The aim of grand uniﬁed theories (GUTs) [25, 26] is to embed the SM gauge group

SU(3)C ⊗ SU(2)L ⊗ U(1)Y into a higher symmetry group GGUT. Consequently, also the three SM coupling constants are assumed to unify to a single coupling constant gGUT at the GUT- 15 scale MGUT ∼ 10 GeV. The SM fermions—along with possible new fermions—are grouped into multiplets relating the electric charges of leptons and quarks, which constitutes an elegant explanation to the symmetry of these particles. Furthermore, requiring gauge invariance under GGUT gives rise to new gauge bosons that mediate transitions between fermions within a multiplet. Some of them violate lepton and baryon number as they mediate lepton-quark transitions. Such new bosons are called leptoquarks. In some models, they are predicted along with a mechanism for neutrino masses. As LQs could also mediate proton decays, “simple” GUTs like SU(5) are strongly constrained by measurements of the lower bound on the proton lifetime.

Supersymmetry

Supersymmetry (SUSY) [27] hypothesizes a symmetry between fermions and bosons: for each SM particle it postulates a superpartner with same quantum numbers except the spin, which differs by 1/2. These new sparticles bring additional loop contributions to the Higgs mass such that divergencies (partially) cancel when the superpartner masses (nearly) equal the masses of the SM particles. In addition to that, many SUSY models provide an excellent dark matter candidate, the lightest supersymmetric particle (LSP), usually the neutralino χ0. However, no evidence for SUSY has been observed so far, ruling out the simplest models.

Large Extra Dimensions

The large extra dimensions (LED) or Arkani-Hamed-Dimopoulos-Dvali (ADD) model [28] also attempts to solve the hierarchy problem. Here, in addition to the four dimensions of spacetime, n extra dimensions are postulated, in which only gravity takes effect. Thus, gravity only seems to be weak in 4D, not because the fundamental scale is large but gravity acts in more than three dimensions of space. This solves the hierarchy problem if the real fundamental scale is

MD ∼ 1 TeV. However, no evidence for LED has been observed to date.

Compositeness Models

Compositeness models [29] assume the SM fermions to be no elementary particles but composite states of so-called preons. Such models provide a lepton-quark symmetry that explains the

14 2.3. Beyond the Standard Model fractional charge of quarks. Fermion masses, which are free parameters in the SM, could be re- placed by the preon mass. This is preferable since the SM has a large set of 19 free parameters. As for other BSM theories, no such model could be conﬁrmed yet.

15 3. Leptoquark Phenomenology

As presented in the previous chapter, leptoquarks appear in GUTs, where they mediate transitions between leptons and quarks. Furthermore, they can also arise in technicolor theories and composite Higgs models. In general, LQs could explain why there are three generations of matter and could also provide reasons for the apparent similarities between leptons and quarks. Assuming that the couplings of LQs to SM particles are dimensionless, invariant under the SM gauge group and conserve both lepton and baryon number L and B, several LQ states are considered by the Buchmüller-Rückl-Wyler model in Ref. [30]. However, LQs have not been observed yet, but constraints on their masses were set and searches at the TeV-scale are ongoing at the LHC. Besides theoretical motivation, there are also experimental hints for BSM physics in the (b-)flavor sector, which can be explained by the existence of LQs with large couplings to third- generation quarks in particular. They are discussed in Section 3.1. Furthermore, a brief introduction to the LQ production in pp collisions is given in Section 3.2, whereas Section 3.3 summarizes the current status of LQ searches. Section 3.4 briefly discusses indirect constrains on LQs. In Section 3.5, a LQ flavor model motivated by such observations is introduced.

3.1. Experimental Motivation

Deviations measured in ratios of branching fractions B in B meson decays with respect to SM predictions hint at BSM physics, as they seem to violate lepton ﬂavor universality (LFU). R R (∗) (∗) Such ratios are the D(∗) and K(∗) rates, referring to B meson decays to D or K mesons, respectively. They are deﬁned as

(∗) − (∗) − + B(B → D τ ν¯τ) B(B → K µ µ ) R (∗) = and R (∗) = (3.1) D (∗) − K (∗) − + B(B → D ` ν¯`) B(B → K e e ) with ` ∈ {e,µ}.

Fig. 3.1 shows a summary of results from RD∗ and RD measurements. It is noticeable that the measured RD∗ and RD values of all experiments tend to exceed the SM prediction. The

16 3.1. Experimental Motivation

2 HFLAV average ∆χ = 1.0 contours

R(D*) 0.4 LHCb15 BaBar12 0.35 3σ LHCb18 0.3 HFLAV

0.25 Belle19 Belle15 Winter 2019 Belle17 0.2 Average of SM predictions HFLAV R(D) = 0.299 ± 0.003 Spring 2019 R(D*) = 0.258 ± 0.005 P(χ2) = 27% 0.2 0.3 0.4 0.5 R(D)

Figure 3.1. Plot of RD∗ vs. RD. Latest results from various experiments (colored regions) are shown as well as the SM prediction (black cross). The combined result of all measurements is depicted as a red ellipse, where the dashed curve corresponds to the 3σ region. Taken from Ref. [31].

`+ `+ ν + W ν

b c b c LQ ( ) ( ) B D ∗ B D ∗ q q q q

Figure 3.2. Feynman diagrams for the B meson decay to a D(∗) meson. A SM process via W+-interaction (left) and a BSM process via a leptoquark (right) are shown.

17 3. Leptoquark Phenomenology

R Figure 3.3. Summary of K(∗) measurements performed by the BaBar (red), Belle (blue) and LHCb (black) collaborations. The vertical line (yellow) corresponds to the SM prediction. Taken from Ref. [32].

t γ µ µ µ µ LQ γ γ

Figure 3.4. Feynman diagrams for contributions to the muon anomalous magnetic dipole moment aµ. A SM process (left) and a BSM process via a leptoquark (right) are shown.

18 3.2. Production of Leptoquarks in pp Collisions combined result exceeds the SM prediction by ∼ 3.1σ. Fig. 3.2 left shows the SM process, where the ﬂavor change of the quark (b → c) is mediated by the weak interaction, i.e. W− 2 boson exchange with the CKM matrix element |Vcb| . BSM theories containing LQs, however, R allow additional processes contributing to D(∗) , see Fig. 3.2 right, and therefore could explain the higher values measured.

Fig. 3.3 summarizes measurements of the ratios RK and RK∗ performed by several experiments. The latest results from LHCb [33, 34] show that the experimentally measured values are lower than the SM predictions and deviate by ∼ 2.6σ and ∼ 2.1 − 2.5σ, respectively. Here, b → s quark transitions occur, which are ﬂavor-changing neutral current (FCNC) at tree-level in the SM and thus suppressed. Higher order FCNCs are realized via so-called box and penguin diagrams in the SM. In contrast, hypothetical LQ couplings at tree-level could even enhance the SM prediction such that loop-induced LQ couplings are a candidate to explain the measured suppression. Another discrepancy between experiments and the SM is the anomalous magnetic dipole moment of the muon aµ. In general, it is a measure for contributions of higher-order loop effects to the magnetic moment of a particle. While for the electron the experimental value ae agrees with the SM prediction at very high precision, the value aµ is higher than expected by ∼ 3.5σ [17]. Fig. 3.4 shows a SM process and a hypothetical contribution from LQs via loop a diagram. Since the results are not yet conclusive, it remains unclear whether these are hints towards lepton non-universal new physics or not. Either way, new results are awaited to clarify this matter.

3.2. Production of Leptoquarks in pp Collisions

At leading order (LO), there are two production mechanisms of LQs in pp collisions: single and pair production. Figs. 3.5 and 3.6 show dominant Feynman diagrams for both types. Note that only in case of singly produced LQs the production cross section is sensitive to the Yukawa coupling λq` between the LQ and the quark and the lepton. Thus, measuring such processes provides direct information about the Yukawa coupling matrix λ. For LQ pair production, the ﬂavor couplings come into play when the LQs decay. One part of this thesis aims at a remodeling of an analysis conducted by the CMS collaboration [1]. Therein, a search for scalar leptoquarks coupled to third-generation quarks is performed. In particular, LQs that couple to a top quark and a muon only are studied. As single production would require a top quark in the initial state, which is strongly suppressed by the

19 3. Leptoquark Phenomenology

Figure 3.5. Both LO Feynman diagrams for single LQ production in pp collisions: s-channel (left) and t-channel (right). The Yukawa coupling λ is marked in red. Adapted from Ref. [35].

Figure 3.6. Dominant LO Feynman diagrams for LQ pair production in pp collisions. Taken from Ref. [36]. proton PDFs (cf. Fig. 2.2), that analysis focuses on pair-produced on-shell LQs that decay exclusively into top quarks and muons, such that it is tailored to investigate the ﬁnal state of pp → LQLQ → tµ−tµ+. More details on the analysis procedure can be found in Chapter5.

3.3. Current Status of Leptoquark Searches at the LHC

Multiple searches for LQs have been performed thus far, yet no evidence for their existence was found to date. Therefore, lower limits on the mass of the leptoquark, MLQ, are set at the 95% conﬁdence level (C.L.). Table 3.1 summarizes the most stringent limits on pair-produced scalar LQs set by the ATLAS and CMS Experiments. In all of these searches the LO pair production processes shown in Fig. 3.6 are considered only and the narrow-width approximation (NWA) for the LQ mass is used. The only search for singly-produced LQs performed at the LHC [43] provides a mass limit of 740 GeV in the LQ → bτ decay mode for unit Yukawa coupling. Mass limits for vector LQs are higher in general due to higher production cross sections.

20 3.4. Indirect Constraints on Leptoquarks

lower mass limit [GeV] lower mass limit [GeV] decay mode by ATLAS by CMS qe qe 1400 1435 qe qν 1290 1270 qµ qµ 1560 1530 qµ qν 1230 1285 qν qν – 980 bν bν 970 1100 bν tτ 800 800 bτ bν 780 – bτ bτ 1030 1020 tν tν 1000 1020 tµ tµ – 1420 tτ tτ 930 900

Table 3.1. Lower mass limits at 95% C.L. by ATLAS [37, 38] and CMS [1, 36, 39–42] on pair-produced scalar LQs in the respective decay mode.

3.4. Indirect Constraints on Leptoquarks

In general, LQs could not only mediate transitions between quarks and leptons, but could couple to any combination of SM fermions. The above mentioned quark transition b → s, which occurs in B meson decays to K mesons, is an example for a FCNC at tree-level and is therefore suppressed in the SM. However, LQs could invoke such processes on tree-level, placing strong indirect constraints on LQ parameters. As certain quark-quark transitions could affect the proton stability, measurements of the proton lifetime strongly constrain corresponding couplings. For LQs coupling to more than one generation of leptons, lepton ﬂavor violating processes would arise. Examples are ` → `0γ and ` → 3`, mediated by LQ loops. The signatures of such decays would be observable in low-energy precision measurements. However, no evidence for their existence has yet been found, so that upper bounds on the branching fraction have been set. These in turn constrain the allowed LQ parameter space. A comprehensive review of physics effects provoked by LQs concerning precision experiments and particle colliders can be found in Ref. [44].

3.5. Flavorful Leptoquark Model

This thesis follows the approach of a leptoquark ﬂavor model by Hiller, Loose and Nišandžic´ [45], which is presented in this section. It is motivated by present hints of lepton non-universality

21 3. Leptoquark Phenomenology in B decay observables as described above.

Considered representations of leptoquarks are the scalar SU(2)L-triplet S3 and two vectors with spin-1, the singlet V1 and the triplet V3. Since the vector LQs V1 and V3 are expected to have higher production cross sections than the scalar S3, mass exclusion limits on S3 are then in general valid for all types. Hence, this thesis focuses on the scalar S3 leptoquark. Its quantum numbers with respect to the SM gauge group of Eq. (2.1) are (3¯,3,1/3) and the couplings to SM fermions are determined by the Yukawa Lagrangian

¯Cα 2 αβ βγ γ ¯Cα 2 αβ † βγ γ LYuk = λQL (iσ ) (S3) LL + Yκ QL (iσ ) (S3) QL + h.c., (3.2)

2 C where σ denotes the second Pauli matrix, α,β,γ are SU(2)L indices and ψ indicates the charge conjugated spinor. Since the second term describes quark-quark transitions, it is poten- tially dangerous regarding the proton decay and thus omitted. The ﬁrst term represents quark- lepton interactions mediated by the S3 with the 3×3 Yukawa coupling matrix λ. In terms of its isospin components, the S3 can be written as

 1/3 √ 4/3 S3 2S3 S3 = √ −2/3 1/3  , (3.3) 2S3 −S3 where the superscripts denote the electric charge in units of e. Expanding the quark-lepton term of Eq. (3.2) yields √ √ ¯C 4/3 ¯C 1/3 C −2/3 C 1/3 LQL = − 2λdL `LS3 − λdL νLS3 + 2λu¯L νLS3 − λu¯L `LS3 + h.c., (3.4) in which the same couplings λ for each representation of the S3 appear. The Yukawa matrices are given by   λde λdµ λdτ     ∗ λD = λse λsµ λsτ and λU = VCKMλU , (3.5)   λbe λbµ λbτ with U = u,c,t and D = d,s,b, and indicate the couplings to up- and down-type quarks, respectively. At this point, two assumptions are made: i) The SM hierarchy for the Yukawa couplings of the quarks also applies to those of the LQs, i.e. couplings to third generation quarks are dom- ii) R → µ+µ− inant, and since possible BSM effects of K(∗) predominantly depend on the b s 2 observables, the dominant couplings are λbµ ≡ λ0 and λsµ ∼ ε λ0. Here, ε ∼ 0.2 denotes a ﬂavor parameter of the size of the sine of the Cabibbo angle as it is, for instance, realized with

22 3.5. Flavorful Leptoquark Model

Figure 3.7. Parameter space λ0(MS3 ) of the S3 leptoquark. The red band corresponds to R Γ/M 5% the K(∗) data favored region of Eq. (3.7). Considering a narrow width, S3 . , yields λ0 . 1.1 which is depicted in yellow. Predictions from viable ﬂavor models on λbµ [48] are shown as a green horizontal band. Taken from Ref. [45]. a Froggatt-Nielsen-Mechanism [46]. This leads to a simpliﬁed coupling matrix

  O(ε3) O(ε3) O(ε3)    2  λD ∼ λ0  ∗ ε ∗  . (3.6)   ∗ 1 ∗

The upper entries are of higher order in ε and therefore negligible, whereas ∗-labeled entries R R are not needed to explain K(∗) data. With these assumptions, K(∗) data favors the region [47]

MS3 MS3 . λ0 . . (3.7) 11.6 TeV 3.9 TeV

−4/3 In Fig. 3.7 the relevant parameter space of the S3 LQ is displayed. The most important region is where all colored regions overlap, i.e. MLQ . 7 TeV and λ0 . 0.6.

In regard to collider signatures of the S3, its width and decay modes are important. Neglecting the masses of the decay products, the partial decay width is given by

2 |λ `| Γ(S → q`) = c q M , (3.8) 3 16π S3

4/3 −2/3 1/3 with c = 2 for S3 ,S3 and c = 1 for S3 , cf. Eq. (3.4). If λq` is the dominant coupling, Γ

23 3. Leptoquark Phenomenology

Figure 3.8. Additional LO Feynman diagrams with the ﬁnal state q`q`: single LQ production (left, center) as well as production via a LQ in the t-channel propagator (right). The Yukawa coupling λ is denoted in red. approximates the total width. Possible decays are constrained by the assumptions made and the electric charge. They are:

+2/3 −1/3 − −4/3 − S3 → tν,S3 → bν, tµ ,S3 → bµ . (3.9)

Although its representations have different electric charges and thus different decay modes, the

S3 leptoquark is a single particle with the mass MS3 . In contrast to traditional LQ searches that assume simple LQ pair production processes, this model includes additional production processes at LO. Fig. 3.8 shows Feynman diagrams of such inclusive production processes yielding the same final state q`q` as expected from LQ pair production. Since this model is not capable of NLO calculations, the obtained cross sections from the Monte Carlo (MC) generator MadGraph5_aMC@NLO are multiplied with a K-factor that accounts for NLO QCD corrections. Fig. 3.9 shows that the K-factor for scalar LQs is found to be approximately constant across the invariant LQ mass distribution with an average value of ∼ 1.5 [49]. Fig. 3.10 shows the production cross sections of LQ pair production and inclusive LQ production for different values of the Yukawa coupling λ considering a coupling to tµ only. It is observed that the cross sections for the inclusive LQ production are about one order of magnitude lower than those predicted for pair production. It is likely that this is caused by a narrow- width approximation used for the generated LQ mass in the simplified pair production model. Within the LQ flavor model considered, the cross sections show the expected behavior as the cross sections for inclusive LQ production are higher than those of pair production. The impact of λ is evident, leading to higher (lower) values of the production cross section for high (low) values of λ. In Fig. 3.11, the partial decay width of the LQ as a function of the coupling according to

24 3.5. Flavorful Leptoquark Model

Figure 3.9. NLO results for the production of a scalar LQ of mass MLQ = 750 GeV. The upper panel shows the differential cross section and the lower panel the K-factor as function of the invariant LQ mass. Taken from Ref. [49].

102 LQ → t µ [pb] 10 pair prod. (PYTHIA 8.205) σ incl. prod. (MadGraph5), λ = 0.5 λ 1 incl. prod. (MadGraph5), = 1.0 incl. prod. (MadGraph5), λ = 1.5 10−1

10−2

10−3

10−4

10−5

10−6

10−7 400 600 800 1000 1200 1400 1600 1800 2000

MLQ [GeV]

Figure 3.10. Inclusive production cross section σ for the LQ coupling to tµ (blue) as a function of MLQ for several values of λ compared to those of pair production from Ref. [50] (black). Values on σ obtained from MadGraph5_aMC@NLO are rescaled by a factor of 1.5 to account for NLO QCD corrections.

25 3. Leptoquark Phenomenology

0.7

MLQ = 0.7 TeV M = 1.0 TeV 0.6 LQ [TeV] M = 1.3 TeV

Γ LQ 0.5

0.4

0.3

0.2

0.1

0 1 2 3 4 5 λ

Figure 3.11. Partial decay width Γ of the S3 as a function of the coupling λ for several LQ masses.

−1/3 Eq. (3.8) is shown. The parameter c is set to unity, which corresponds to the S3 . The quadratic dependence of Γ on the strength of the Yukawa coupling λ is visible as well as the linear dependence on the LQ mass MLQ. These dependencies show that for models allowing more physically realistic LQ production processes, the NWA is no longer applicable.

26 4. Experimental Setup

The aim of this thesis is to remodel the search for leptoquarks coupled to third-generation quarks performed by the CMS collaboration [1] with the DELPHES framework for detector simulation and verify its validation. In a further step, the analysis is used for a reinterpretation of CMS data within a more sophisticated LQ model. In order to understand possible differences in the detector simulation between GEANT and DELPHES, the LHC is introduced in Section 4.1, followed by an overview of the CMS detector components in Section 4.2.

4.1. The Large Hadron Collider

The Large Hadron Collider at CERN1 (the European Organization for Nuclear Research) is the world’s largest and most powerful particle accelerator. Located underground near Geneva, Switzerland, it is able to accelerate and collide protons but also heavy ions. The purpose of the LHC was and is to answer fundamental open questions in particle physics, like the discovery of the Higgs boson in 2012, as well as testing the Standard Model to high precision. A schematic view of the CERN accelerator complex is shown in Fig. 4.1. Before the protons can be injected to the LHC tunnel of ∼ 27 km circumference, they need to pass several stages of pre-acceleration. Starting with electrons from a thermionic cathode ionizing gaseous hydrogen, the resulting protons are extracted with an energy of Ep = 90 keV. After the subsequent linear acceleration with Linear Accelerator 2 (LINAC2, Ep = 50 MeV), a set of circular colliders follows: Proton Synchrotron Booster (PSB, Ep = 1.4 GeV), Proton Synchrotron (PS, Ep = 26 GeV) and Super Proton Synchrotron (SPS, Ep = 450 GeV). Protons then leave the SPS and are injected into the LHC as two beams with opposite directions, where they are further accelerated to Ep = 6.5 TeV. Colliding protons therefore show a center-of-mass energy of √ √ s = 13 TeV. The design value of s = 14 TeV is expected to be reached with Run 3 starting in 2021. All values in this section are taken from Refs. [52, 53].

1from the french: Conseil européen pour la recherche nucléaire

27 4. Experimental Setup

Figure 4.1. Accelerator complex at CERN. Taken from Ref. [51].

28 4.1. The Large Hadron Collider

CMS Integrated Luminosity Delivered, pp

Data included from 2010-03-30 11:22 to 2018-10-26 08:23 UTC 100 1 100 ) 2010, 7 TeV, 45.0 pb¡ 1 1 ¡ 2011, 7 TeV, 6.1 fb¡

b 1 f 2012, 8 TeV, 23.3 fb¡ (

1 2015, 13 TeV, 4.2 fb¡ y 80 80

t 1

i 2016, 13 TeV, 41.0 fb¡

s 1 2017, 13 TeV, 49.8 fb¡ o 1 n 2018, 13 TeV, 67.9 fb¡ i 60 60 m u L

d e

t 40 40 a r g e t n

I 20 20

l a t o

T 50 0 £ 0

1 Jul 1 Apr 1 May 1 Jun 1 Aug 1 Sep 1 Oct 1 Nov 1 Dec Date (UTC)

Figure 4.2. Integrated luminosity of pp collisions delivered to CMS versus time of the respective period. Taken from Ref. [54].

An important quantity of a circular collider is its instantaneous luminosity L. It is a measure for the number of proton-proton collisions per cross section and time, given by

n1n2 L = Nbfrev . (4.1) 4πσxσy

Each beam consists of Nb = 2808 proton bunches uniformly separated in time by ∼ 25 ns with 11 a length of ∼ 30 cm. Every bunch contains ni ≈ 1.2×10 protons. The revolution frequency is frev = 11.245 kHz and 4πσxσy describes the spatial expansion of the bunches in the transverse plane perpendicular to the beam axis assuming Gaussian proﬁles. The designed peak luminosity of L = 1.0×1034 cm−2s−1 was already exceeded by 40% in the 2016 data-taking period of Run 2. The event rate of a given physical process with the cross section σ is

d N = σL. (4.2) dt

Integrating over time yields the expected number of events

Z N = σ Ldt = σLint, (4.3) where Lint is the integrated luminosity. The integrated luminosity as a function of time for several data-taking periods is displayed in Fig. 4.2. The LHC accommodates a total of four major experiments. ATLAS (A Toroidal LHC Ap-

29 4. Experimental Setup paratuS) and CMS (Compact Muon Solenoid) are the two general-purpose detectors. LHCb (LHC beauty) focusses on b quark physics, whereas ALICE (A Large Ion Collider Experiment) is optimized to study heavy ion collisions.

4.2. The Compact Muon Solenoid Experiment

The CMS experiment, as a general-purpose detector, is designed to measure a wide range of physics. Therefore, its setup is determined by the aim to detect different kinds of particles. The views of the CMS detector in Figs. 4.3 and 4.4 show the layered structure of its components. Based on Ref. [57], a short introduction of the coordinate system as well as the major detector components, from the innermost to the outermost, is given in this section.

4.2.1. The Coordinate System

For the description of the CMS detector, a right-handed Cartesian coordinate system (x,y,z) can be used. Its origin coincides with the nominal collision point. The x-axis points radially inward towards the center of the LHC ring, the y-axis points vertically upwards and the z-axis points along the beam in counterclockwise direction. However, a more appropriate description is given by a cylindrical coordinate system (r,φ,θ), which reflects the detector design and accounts for the angular dependencies of pp collisions. Thus, r is the radial distance to the z-axis, the azimuth φ is the angle in the x-y-plane enclosed with the x-axis, and the polar angle θ spans between the x-y-plane and the z-axis. In pp collisions, the momentum of the initial state partons along the beam axis is not known, but the coordinates used should be Lorentz invariant in z- direction. As r and φ already fulfill this constraint, the pseudorapidity η is introduced to replace θ, " θ !# η = −ln tan , (4.4) 2 such that ∆η is Lorentz invariant. Consequently, also the angular distance ∆R between two points in the η-φ-plane, defined as

q ∆R = (∆η)2 + (∆φ)2, (4.5) is invariant under Lorentz transformations in z-direction. The four-momentum of a particle is therefore speciﬁed in terms of (E,px,py,pz) → (E,pT,η,φ) with the transverse momentum q 2 2 pT = px + py.

30 4.2. The Compact Muon Solenoid Experiment

Figure 4.3. Cutaway view of the CMS detector. Taken from Ref. [55].

Figure 4.4. Sketch of different particle trajectories and signatures in a transverse slice of the CMS detector. Taken from Ref. [56].

31 4. Experimental Setup

Figure 4.5. Schematic view on the upper half of the CMS tracker in the r-z-plane. The star marks the nominal interaction point. Taken from Ref. [58].

4.2.2. Detector Components

Tracking System

The innermost detector component is the tracking system. It directly surrounds the interaction point and aims at a precise reconstruction of trajectories of charged particles. The cylindrical tracker has a length of ∼ 5.8 m and a diameter of ∼ 2.5 m, covering a region of |η| < 2.5. The layout shown in Fig. 4.5 consists of two different types of silicon detectors: pixel and strip sensors.

Closest located to the interaction point is the pixel detector (PIXEL). In the data-taking period of 2016, it comprised three pixel layers in the barrel region at r = 4.4,7.3,10.2 cm, and two pairs of endcap disks at z = ±34.5,±46.5 cm in each forward region. In total, the 66 million pixel sensors cover an area of ∼ 1m2, each cell of the size 100 × 150µm2.

Around the pixel detector in the region r = 20−116 cm, silicon strip trackers are built. In the barrel region, they are divided into tracker inner barrel (TIB) and tracker outer barrel (TOB). The TIB extends to r < 55 cm, |z| < 65 cm and consists of four layers of strip sensors, each 320 µm thick and with a pitch of 80 − 120 µm. Further outside, the TOB covers the region to r < 116 cm, |z| < 118 cm with six layers of strips of 500 µm thickness and 122 − 183 µm pitch. The endcap systems tracker inner disk (TID) and tracker endcap (TEC) extend the covered region to |z| < 282 cm and consist of three and nine layers, respectively.

32 4.2. The Compact Muon Solenoid Experiment

Figure 4.6. Transverse section through the ECAL. The values at the dashed lines correspond to constant values of η. Taken from Ref. [59].

Electromagnetic Calorimeter

The electromagnetic calorimeter (ECAL), shown in Fig. 4.6, surrounds the tracking system and measures energy deposits mainly from electromagnetically interacting particles, i.e. electrons (or positrons) and photons.

It is a homogeneous calorimeter made of 61200 lead tungstate (PbWO4) crystals in the barrel (EB) and 7324 crystals in the endcap region (EE). This speciﬁc scintillating material has a high 3 density (ρ = 8.28g/cm ), a short radiation length (X0 = 0.89 cm) and a small Molière radius

(RM = 2.2 cm), resulting in a compact calorimeter with ﬁne granularity. In addition, about 80% of the scintillation light is emitted within the bunch crossing time of 25 ns. The EB has an inner radius of 1.29 m and covers the region |η| < 1.479. The crystal size increases from 22 × 22mm2 at the front to 26 × 26mm2 at the rear face with a length of 3 23.0 cm corresponding to 25.8X0. In total, the barrel has a crystal volume of 8.14m and it weighs 67.4 t. The EE however, covers the region 1.479 < |η| < 3.0, has crystal sizes from 2 2 3 28.6 × 28.6mm to 30 × 30mm with a length of 22.0 cm (24.7X0), a volume of 2.90m and a weight of 24.0 t. Additional preshower modules (ES) located in front of the EEs cover 1.653 < |η| < 2.6 and help to identify neutral pions decaying predominantly to photon pairs. The resulting excellent energy resolution of the CMS ECAL is parametrized as [57]

σE 2.8% 12% = q ⊕ ⊕ 0.30%, (4.6) E E [GeV] E [GeV] where the first term accounts for stochastic effects from the shower development, the second term specifies electronic noise and the third constant term reflects calibration errors and non- uniform light collection.

33 4. Experimental Setup

Figure 4.7. Longitudinal view of the CMS detector including the HCAL. The values at the dashed lines are correspondent to η. Taken from Ref. [57].

Hadronic Calorimeter

Around the ECAL, the hadronic calorimeter (HCAL) is built. Its purpose is to measure the hadronic jets as well as missing transverse energy (MET). Hadrons typically have a higher interaction length λI than the radiation length of electrons and photons, such that hadrons traverse the ECAL. The HCAL—in constrast to the ECAL—is a sampling calorimeter consisting of al- ternating layers of brass absorber and plastic scintillator plates. It is further divided into two barrel parts, the hadron barrel (HB) and hadron outer (HO), as well as two endcap parts, the hadron endcap (HE) and hadron forward (HF), see Fig. 4.7.

The barrel is restricted by the ECAL on the inside (r = 1.77 m) and the magnet coil on the outside (r = 2.95 m). The HB covers |η| < 1.3 and consists of 36 azimuthal wedges which in turn contain 18 absorber plates each and active scintillator material. The latter is further grouped into multiple towers, each of them covering 0.087 × 0.087 in the η-φ-plane. The HO extends the HB in the central η-region outside the solenoid to increase the sampling depth for the containment of hadron showers.

The outer η-region is covered by the HEs with a tower granularity of 0.087 × 0.087 for |η| < 1.6 and 0.17 × 0.17 for 1.6 < |η| < 3.0. For higher values, 2.9 < |η| < 5.2, i.e. in the region close to the beam pipe, the HFs complete the calorimeter. Since these have to be especially radiation hard, their absorber and scintillator materials are steel and quartz ﬁbres, respectively.

34 4.2. The Compact Muon Solenoid Experiment

The energy resolution of the HCAL is inferior to that of the ECAL (cf. Eq. (4.6)),

σE 115.3% = q ⊕ 5.5%. (4.7) E E [GeV]

Solenoid Magnet

The superconducting solenoid magnet is the heart of the CMS detector. It has a length of 12.9 m and a bore of radius 5.9 m where the inner components tracker, ECAL and HCAL are located. Inside the solenoid, a magnetic ﬁeld of 3.8 T is produced2. The purpose is to bend the trajectories of charged particles in order to determine their charges and momenta by measuring their curvature radii. In the muon system and the return yoke outside the solenoid, an oppositely aligned ﬁeld of 2 T bends muons to the opposite direction and thus improves measuring muon momenta.

Muon System

Muons—considered as minimal ionizing particles (MIPs)—are the only particles besides neutrinos that traverse the whole inner detector without signiﬁcant energy loss. Thus, they are detected in the outermost component of the CMS detector: the muon system. As depicted in Fig. 4.8, three components are differentiated. In the barrel region up to |η| < 1.2, drift tube chambers (DTs, yellow) ﬁlled with a gaseous mixture of 85% Ar and 15%CO2 detect muons via ionization and corresponding drift time measurement. The muon systems endcap region (ME), 0.9 < |η| < 2.4, is covered by four layers of gaseous cathode strip chambers (CSCs, green). Resistive plate chambers (RPCs, blue) complement DTs and CSCs in the central part up to |η| < 1.6 providing a fast response and a good time resolution.

Data Acquisition and Trigger System

Assuming the LHC design luminosity, proton bunch crossings happen at intervals of 25 ns. Since each bunch crossing in turn causes & 25 proton-proton interactions (pile-up, PU), an enormous amount of potential collision data is produced every second. Storing such amount of data is not feasible and furthermore only a small fraction is of physical interest. Therefore, a two-stage trigger process is applied in order to reduce the event rate. The Level-1 (L1) trigger is hardware-based and uses coarsely segmented data from the calorimeters and the muon system only. Its purpose is to reject soft QCD events within the allowed

2The design value of 4 T was reduced to enhance longevity [60].

35 4. Experimental Setup

Figure 4.8. Cross section of a quadrant of the CMS detector in the r-z-plane showing the components of the muon system (colored). Taken from Ref. [61]. trigger latency of 3.2µs by requiring high-energetic jets, leptons, photons or signiﬁcant missing transverse energy. In this stage, the event rate is reduced to about 100 kHz. The second step is performed by the high-level trigger (HLT). It is software-based, accesses the complete read-out data and uses more sophisticated algorithms similar to ofﬂine analysis to further discard events within 50 ms. Hence, the total event rate is reduced to ∼ 100 Hz, such that only a millionth of the initial events are stored.

36 5. Leptoquark Analysis by CMS

In this chapter, the search for leptoquarks coupled to third-generation quarks performed by the CMS Collaboration [1] is presented. Subsequently, it is remodeled using DELPHES fast simulation in Chapter6 and is used for a reinterpretation of the recorded data within a more sophisticated LQ model in Chapter7. Section 5.1 introduces the data set and the event generation, whereas Section 5.2 focuses on the event selection. The reconstruction of the leptoquark mass is explained in Section 5.3 and in Sec. 5.4 results are shown and discussed.

5.1. Data Set and Event Generation

The analysis presented in the following adopts the ansatz of pair-produced LQs which exclusively decay into top quarks and muons,

pp → LQLQ → tµ−tµ+. (5.1) √ The data used was recorded in pp collisions at s = 13 TeV by the CMS detector in 2016 and corresponds to an integrated luminosity of 35.9fb−1. Signal events, i.e. events of the process shown in Eq. (5.1), are simulated with the PYTHIA 8.205 [62] MC Generator at LO for LQ mass values ranging from 200 to 2000 GeV, see Ta- ble 5.1. The NWA for the LQ mass is used. Various SM background events are generated with several different generators. A complete overview can be found in Table A.1. Pile-up simulations are included for all event samples and the detector response is simulated with the GEANT4 package [64]. Simulated events pass through the same software chain as collision data. Afterwards, a reweighting is applied so that the observed distribution of the number of pile-up interactions matches with data.

37 5. Leptoquark Analysis by CMS

MLQ [GeV] σ [pb] N 200 6.06 × 101 74079 300 8.04 × 100 73905 400 1.74 × 100 74516 500 4.96 × 10−1 74478 600 1.69 × 10−1 71639 700 6.48 × 10−2 74723 800 2.73 × 10−2 74571 900 1.23 × 10−2 73216 1000 5.86 × 10−3 73496 1200 1.50 × 10−3 74730 1400 4.32 × 10−4 74095 1700 7.73 × 10−5 73934 2000 1.55 × 10−5 74731

Table 5.1. Summary of simulated signal samples with PYTHIA 8.205. The values in the columns correspond to the generated leptoquark mass MLQ, production cross section σ at NLO (adapted from Ref. [50]) and number of generated events N. Taken from Ref. [63].

5.2. Event Selection

The CMS experiment uses the particle-flow (PF) algorithm [56] to reconstruct events. Since it uses an optimized combination of information from different components of the detector, it provides an excellent description of the recorded data. The vertex with the largest reconstructed 2 pT of physics objects is taken as the primary pp interaction vertex (PV). All detected particles are reconstructed either as electrons, muons, photons, charged or neutral hadrons. This analysis requires electrons and muons to have pT ≥ 30 GeV and |η| ≤ 2.4. Furthermore, they have to be isolated. The muon isolation is PF-based and defined relative to the transverse momentum µ pT [65], P P P 1 PPU h± pT + max 0, h0 ET + γ ET − 2 h± pT Irel = µ < 0.15, (5.2) pT ± 0 where the summed transverse momenta pT or energies ET of charged (neutral) hadrons h (h ) or photons γ are considered in a cone with radius ∆R = 0.4 around the muon. In order to 1 PPU approximately correct pile-up (PU) contributions, 2 h± pT is subtracted from the overall sum PPU where h± pT denotes the sum of transverse momenta of all charged hadrons from PU vertices. Muons have to fulfill Irel < 0.15, which corresponds to a muon isolation efficiency of ε ∼ 95%. The electron isolation is defined similarly, see Ref. [66]. Jets are clustered from charged and neutral PF candidates from the primary vertex using the anti-kT jet-clustering algorithm [67,68]

38 5.3. Leptoquark Mass Reconstruction

pre-selection full selection

≥ 2 isolated jets with pT ≥ 30 GeV, |η| ≤ 2.4 pre-selection ≥ 2 isolated muons with pT ≥ 30 GeV, |η| ≤ 2.4 Nb-jets ≥ 1 ST ≥ 350 GeV Mµµ ≥ 111 GeV lep ST ≥ 200 GeV

category A category B ≥ 3`±, ≥ 1µ−, ≥ 1µ+ all other events

Table 5.2. Tables with the cuts applied in the pre-selection (top left) and the full selection (top right) as well as the categorization scheme (bottom). with a distance parameter of 0.4, referred to as AK4 jets. The pile-up mitigation technique used is the charged hadron substraction (CHS) method [69]. The jets are also required to have pT ≥ 30 GeV and |η| ≤ 2.4. Additionally, using the combined secondary vertex v2 (CSVv2) algorithm [70], one b-tagged jet is required. The loose working point with an efﬁciency of ∼ 90% and a mistag rate of ∼ 10% is chosen. Events must have at least two muons and at least two jets, of which at least one must be b-tagged, to be considered. Requiring the invariant mass of each pair of muons to exceed the Z boson mass, i.e. Mµµ ≥ 111 GeV, suppresses events from Z boson production with additional jet radiation. As decays of heavy LQs are expected to produce high-pT leptons and lep jets, ST ≥ 200 GeV and ST ≥ 350 GeV are required furthermore to suppress SM backgrounds. lep Herein, ST denotes the scalar pT sum of all selected electrons and muons, whereas ST is the lep miss sum of ST , pT and pT of all selected jets. All events passing these selection criteria fall into the signal region (SR) phase space and are divided into two complementary categories: A) there are at least three leptons present—i.e. at least one additional lepton to the two muons required in the pre-selection—and at least one muon of each electric charge, and B) all remaining events. In Table 5.2, the pre- and full selection requirements as well as the categorization scheme are summarized.

5.3. Leptoquark Mass Reconstruction

This section describes the three steps of the mass reconstruction of the LQs, MLQ, for events in category A. For all other events in category B, the distribution of ST is used for the ﬁnal statistical analysis.

39 5. Leptoquark Analysis by CMS

µ ` W + p ν g LQ t b

b p g t LQ q, `

µ W − q0, ν

Figure 5.1. Feynman diagram of pair-produced LQs decaying to top quarks and muons including further decays of the tops. Taken from Ref. [63].

5.3.1. Reconstruction of the Neutrino

The ﬁrst step in the reconstruction of the pair of LQs for events in category A is the reconstruction of the neutrino. Since neutrinos do not interact with the detector, they only contribute to missing transverse energy. In this analysis, it is assumed that one top quark decays fully hadron- ically, thad, whereas the other top, tlep, produces an additional lepton along with its associated neutrino, see Fig. 5.1. This ensures that there is exactly one neutrino in the event, whose trans- ν verse momentum is then assumed to match the missing transverse energy, pT = E T. From the constraint that the invariant mass of the additional lepton and its neutrino equals the W boson mass, 2 2 2 PW = MW = (P` + Pν) (5.3) where Pi denotes the four-momentum of the particle i, the z-component of the neutrinos momentum is calculated via v u 2 2 2 2 2 ± µpz,` uµ pz,` E` pT,ν − µ pz,ν = 2 ± t 4 − 2 . (5.4) pT,` pT,` pT,`

2 Here, µ = MW/2 + pT,ν pT,` cos(∆φ), where ∆φ is the angle between the vectorial missing transverse energy and the additional lepton. Eq. (5.4) has either zero, one or two real solutions. In the ﬁrst case, the real part of the complex solution is chosen whereas in the third case, both solutions are considered as independent candidates.

40 5.3. Leptoquark Mass Reconstruction

5.3.2. Reconstruction of the Top Quarks

In the second step, the top quark tlep is reconstructed from the neutrino ν`, the additional lepton ` and a combination of AK4 jets. Since at most seven leading1 jets in an event are considered and one jet is always reserved for the decay of thad, n ∈ [1, max(Njets,6)] candidates for tlep are built, where Njets states the number of jets in the event. If there is more than one additional lepton, the reconstruction depends on the ﬂavor of this lepton. In case of at least one electron in the event, the leading electron is taken as the additional lepton `. For zero electrons, there must be at least three muons in the event due to the requirements of the categorization scheme. The three leading muons are taken for constructing tlep. Furthermore, two of these muons must have opposite-sign electric charges (OS) as they arise directly from the LQ decays. Therefore, both muons with the same charge (SS) could stem from the tlep decay which doubles the number of tlep candidates.

For each tlep candidate, candidates for thad are built from the remaining jets. With n jets used for constructing the tlep, m ∈ [1, min(Njets − n,6)] jets are left for building the thad candidate.

As a result, the four-momenta of each one tlep and one thad candidate are obtained from the four-momenta of their decay products,

n m X X Ptlep = Pi,jet + P` + Pν` and Pthad = Pi,jet. (5.5) i=1 i=1

5.3.3. Reconstruction of the Leptoquarks

LQ candidates are assembled by combining top quark candidates and muons. As can be seen from Fig. 5.1, the additional lepton from the tlep decay always has OS charge with respect to the prompt muon from the associated LQ decay. Thus, always the muon with OS charge is assigned to LQlep. For the LQhad construction, both muons with SS charge are possible to be paired with thad which again doubles the number of candidates. The four-momenta of the LQ candidates are given by P = P + P P = P + P . LQlep tlep µOS and LQhad thad µSS (5.6) Finally, the reconstructed LQ mass is deﬁned as the average invariant mass of the LQ candidate pair, MLQ + MLQ M rec = lep had . (5.7) LQ 2 From all pairs of LQ candidates, the one most compatible with the assumed LQ decay has to

1In is meaningful to arrange physics objects in descending order with respect to their transverse momenta. The term leading then refers to the one(s) with highest pT.

41 5. Leptoquark Analysis by CMS be chosen. For this purpose, a χ2-variable is considered which is deﬁned as

2   ! !2 ∆M rel − ∆M rel 2 Mtlep − M tlep Mt − M t LQ LQ χ = + had had +   . (5.8) σlep σhad σ∆M

Each of the three terms tests a different reconstructed property. Mtlep and Mthad are the invariant rel masses of the tlep and thad candidates, respectively. The variable ∆MLQ, deﬁned as

M − M rel LQlep LQhad ∆MLQ = rec , (5.9) MLQ denotes the relative difference in the invariant mass of both LQ candidates. The value of χ2 is rel small, if the candidate properties Mtlep , Mthad and ∆MLQ are close to the respective expected rel values, which are denoted by M tlep , M thad and ∆M LQ. Those values together with the widths σlep, σhad and σ∆M are extracted from simulation using Monte Carlo truth information (see Ref. [71]). The pair of LQ candidates with the smallest value of χ2 is chosen as the best rec hypothesis and its value of MLQ is used in the ﬁnal statistical analysis for events in category A.

5.4. Results

rec For the distributions MLQ in category A and ST in category B, a statistical procedure is applied to investigate a potential LQ signal. The final SM predictions in both categories are obtained by a simultaneous binned maximum-likelihood template fit of the backgrounds to the data performed with the THETA software package [72]. In this fit, all systematic uncertainties are treated rec as nuisance parameters. The distributions of MLQ and ST after the background-only fit are shown in Fig. 5.2. No signal of LQ pair production is observed, as the data agrees well with the fitted SM distribution in both categories. Hence, a Bayesian likelihood-based method [72–74] is used to set upper limits on the product of the LQ pair production cross section and the squared branching fraction B2 at 95% C.L. as a function of the LQ mass, see Fig. 5.3. It is assumed that pair-produced LQs decay exclusively to top quarks and muons, B(LQ → tµ) = 1, such that these LQs are excluded up to masses of MLQ = 1420 GeV at 95% C.L. This is the first and only limit in this decay mode. To further constrain the parameter space, the results of this analysis can be combined with results of two other analyses each: a search for third-generation scalar leptoquarks decaying to tτ [36] and a reinterpretation [76] of a search for pair-produced bottom squarks decaying to a SM b quark and the lightest supersymmetric particle (LSP). Since the LSP is assumed to interact

42 5.4. Results

rec Figure 5.2. Final distributions of the reconstructed LQ mass MLQ (category A, left) and ST (category B, right). Data (black markers), SM backgrounds (colored) and LQ signal distributions for various masses (dashed lines) are shown. The hatched areas in the upper panels correspond to the total uncertainty. In category B, the major backgrounds from tt + Drell-Yan (DY) + jets are estimated from data. Taken from Ref. [1].

35.9 fb-1 (13 TeV) 104 95% CL upper limit

) [pb] Supplementary CMS Observed µ

t Expected → 102 68% expected

(LQ 95% expected 2

× LQ pair production

1 Scalar LQ

LQLQ Vector LQ (κ = 0) σ Vector LQ (κ = 1)

10−2

10−4 500 1000 1500 2000 MLQ [GeV]

Figure 5.3. Expected and observed upper limits on the product of the LQ pair production cross 2 section σLQLQ and the squared branching fraction B (LQ → tµ) at 95% C.L. as a function of the LQ mass MLQ. Unit branching fraction is assumed, B = 1. The black (colored) dashed lines correspond to the pair production cross sections of scalar (vector) LQs at NLO [50] (LO [75]). Taken from Ref. [1].

43 5. Leptoquark Analysis by CMS

Figure 5.4. Expected and observed upper limits on cross section for pair-produced LQs decaying to tµ or tτ (left) and LQs decaying to tµ or bν at 95% C.L. in the plane of MLQ and B(LQ → tµ). Lower mass exclusion limits on scalar (vector) LQs are derived from predictions at NLO [50] (LO [75]) and are depicted by black (colored) lines. Taken from Ref. [1]. only via the weak force, for vanishing masses of the LSP, the final state corresponds to the final state of pair-produced LQs that exclusively decay into b quarks and neutrinos. Fig. 5.4 presents upper limits on the product of the production cross section and the squared branching fraction for B(LQ → tµ) = 1 − B(LQ → tτ) (left) and B(LQ → tµ) = 1 − B(LQ → bν) (right). For Fig. 5.4 left, a full statistical combination of both decay channels is performed by reweighting the LQ pair production samples and subsequent decays to the possible final states tµtµ, tτtτ and tµtτ2. For Fig. 5.4 right, the LQs are assumed to decay either to tµ or bν, so that for each value of B(LQ → tµ) the strongest of both limits is considered. This explains the weakest limits in the transition region B(LQ → tµ) ≈ 0.3, as none of the analyses is sensitive to events with exactly one muon or one neutrino arising from the LQ decays. In summary, pair-produced scalar LQs decaying exclusively into tµ or tτ are excluded up to

MLQ = 900 GeV for all values of B(LQ → tµ). For pair-produced scalar LQs that exclusively decay into tµ or bν, the lower mass exclusion limit is MLQ = 980 GeV.

2Such a statistical combination is allowed here, since the event selections of both analyses are mutually exclusive and thus provide statistically independent data.

44 6. Remodeling the CMS Analysis

In this chapter, results of the search for scalar leptoquarks decaying exclusively to top quarks and muons performed by the CMS Collaboration [1] are reproduced. This analysis remodeling uses the SM background predictions, the statistical and systematic uncertainties, and data points of the public CMS results [77]. The signal predictions are generated with PYTHIA version 8.230 [62] and the detector response is simulated with the DELPHES framework [2, 78]. A detailed comparison to the original analysis constitutes an important ﬁrst step to investigate the performance of DELPHES fast simulation. Section 6.1 covers the generation of LQ event samples, whereas Section 6.2 introduces DELPHES and discusses its characteristics. Subsequently, results of this remodeling as well as comparisons to the original analysis are presented in Section 6.3.

6.1. Signal Event Generation

In this thesis, DELPHES fast simulation is used for the CMS detector simulation. In order to study potential differences to the full detector simulation performed with GEANT4, the LQ signal samples used in the CMS analysis are reproduced. They are generated with PYTHIA version 8.230 and contain 100000 events for each simulated LQ mass, ranging from 400 to 2000 GeV in steps of 100 GeV. A summary is given in Table 6.1. Potential differences between both simulations with GEANT4 and DELPHES are investigated in the following. At ﬁrst, kinematic distributions of generator level quantities of the simulated LQs, top quarks and muons are compared. In Fig. 6.1, the generated mass (left column), pT (center column) and η (right column) of these particles are shown for the samples used in the CMS analysis (PYTHIA 8.205) and those generated with PYTHIA 8.230. The corresponding distributions of the generated LQs are shown in the upper row. On the left, the MLQ- distributions are found to agree well and the earlier mentioned NWA used for the LQ mass is evident. The pT- and η-distributions of the LQ (center and right, respectively) show good agreement between both simulations as well. The center row shows the same distributions for the top quark on generator level. For all distributions of mt (left), pT (center) and η (right), good

45 6. Remodeling the CMS Analysis

MLQ [GeV] σ [pb] N 400 1.74 × 100 100000 500 4.96 × 10−1 100000 600 1.69 × 10−1 100000 700 6.48 × 10−2 100000 800 2.73 × 10−2 100000 900 1.23 × 10−2 100000 1000 5.86 × 10−3 100000 1100 2.91 × 10−3 100000 1200 1.50 × 10−3 100000 1300 7.96 × 10−4 100000 1400 4.32 × 10−4 100000 1500 2.40 × 10−4 100000 1600 1.35 × 10−4 100000 1700 7.73 × 10−5 100000 1800 4.49 × 10−5 100000 1900 2.62 × 10−5 100000 2000 1.55 × 10−5 100000

Table 6.1. Summary of simulated LQ event samples with PYTHIA 8.230. The values in the columns correspond to the generated leptoquark mass MLQ, production cross section σ at NLO (adapted from Ref. [50]) and number of generated events N. agreement is found. In case of muons (lower row), the corresponding distributions of the CMS analysis are not available. It is evident that the muon mass is treated as a ﬁxed value in PYTHIA

8.230, as shown on the left. The pT- and η-distributions of the muon (center and right, respectively) are similar to those of the LQ and the top quark. The shape of the pT-distributions of the particles is consistent with the simulated values of MLQ, showing slightly harder spectra with growing MLQ. The distributions of η of both simulation techniques show the expected behavior as the particles become more central with increasing generated LQ mass. In all considered distributions, a very good agreement is found.

6.2. Detector Simulation with DELPHES

DELPHES fast simulation [2, 78] is a C++ framework that provides a fast multipurpose detector response simulation for phenomenological studies. In this work, version 3.4.1 with the con- ﬁguration of the CMS detector corresponding to the 2016 data-taking period is used. Although DELPHES is not designed for detailed detector studies, it is a well-suited tool for the approach followed in this thesis. Compared to a GEANT-based full simulation, fast simulation techniques

46 6.2. Detector Simulation with DELPHES

(13 TeV) (13 TeV) (13 TeV) 1.4 0.16 0.09 PYTHIA 8.230 PYTHIA 8.205 PYTHIA 8.230 PYTHIA 8.205 PYTHIA 8.230 PYTHIA 8.205 M = 0.4 TeV M = 0.4 TeV M = 0.4 TeV M = 0.4 TeV 0.08 M = 0.4 TeV M = 0.4 TeV 1.2 LQ LQ 0.14 LQ LQ LQ LQ M = 0.8 TeV M = 0.8 TeV M = 0.8 TeV M = 0.8 TeV M = 0.8 TeV M = 0.8 TeV LQ LQ LQ LQ 0.07 LQ LQ MLQ = 1.2 TeV MLQ = 1.2 TeV 0.12 MLQ = 1.2 TeV MLQ = 1.2 TeV MLQ = 1.2 TeV MLQ = 1.2 TeV 1 0.06 0.1 0.8 0.05 0.08 Fraction of events Fraction of events Fraction of events 0.6 0.04 0.06 0.03 0.4 0.04 0.02 0.2 0.02 0.01

0 500 1000 1500 0 500 1000 1500 2000 −5 −4 −3 −2 −1 0 1 2 3 4 5 p [GeV] η MLQ [GeV] T,LQ LQ

(13 TeV) (13 TeV) (13 TeV) 0.3 0.18 PYTHIA 8.230 PYTHIA 8.205 PYTHIA 8.230 PYTHIA 8.205 0.12 PYTHIA 8.230 PYTHIA 8.205

MLQ = 0.4 TeV MLQ = 0.4 TeV 0.16 MLQ = 0.4 TeV MLQ = 0.4 TeV MLQ = 0.4 TeV MLQ = 0.4 TeV 0.25 M = 0.8 TeV M = 0.8 TeV M = 0.8 TeV M = 0.8 TeV M = 0.8 TeV M = 0.8 TeV LQ LQ 0.14 LQ LQ 0.1 LQ LQ MLQ = 1.2 TeV MLQ = 1.2 TeV MLQ = 1.2 TeV MLQ = 1.2 TeV MLQ = 1.2 TeV MLQ = 1.2 TeV

0.2 0.12 0.08 0.1 0.15

Fraction of events Fraction of events Fraction of events 0.06 0.08

0.1 0.06 0.04 0.04 0.05 0.02 0.02

150 160 170 180 190 200 0 500 1000 1500 2000 −5 −4 −3 −2 −1 0 1 2 3 4 5 p [GeV] η mt [GeV] T,t t

(13 TeV) (13 TeV) (13 TeV) 1 0.12 PYTHIA 8.230 PYTHIA 8.230 PYTHIA 8.230 0.9 MLQ = 0.4 TeV 0.1 MLQ = 0.4 TeV MLQ = 0.4 TeV M = 0.8 TeV M = 0.8 TeV 0.1 M = 0.8 TeV 0.8 LQ LQ LQ MLQ = 1.2 TeV MLQ = 1.2 TeV MLQ = 1.2 TeV 0.7 0.08 0.08 0.6 0.5 0.06 0.06 Fraction of events Fraction of events Fraction of events 0.4 0.04 0.04 0.3 0.2 0.02 0.02 0.1

0 0.2 0.4 0.6 0.8 1 0 200 400 600 800 1000 −5 −4 −3 −2 −1 0 1 2 3 4 5 p [GeV] η mµ [GeV] T,µ µ

Figure 6.1. Normalized distributions of the mass (left column), transverse momentum (center column) and pseudorapidity (right column) for LQs (upper row), top quarks (center row) and muons (lower row) on generator level.

47 6. Remodeling the CMS Analysis like DELPHES are up to three orders of magnitudes faster, which is crucial for a phenomenological investigation of a large parameter space. The simulation of the detector response is simplified and is based on parametrization. It includes an inner tracker, electromagnetic and hadronic calorimeters as well as a muon system, all being cylindrically arranged around the beam axis and embedded in a magnetic field. For each detector component, a specific response is considered. Fig. 6.2 shows a simplified chart of the workflow in DELPHES. DELPHES allows to access data from different file formats. Event files from external MC generators are first processed by a reader. Pile-up collisions are simulated by overlapping events from a pre-generated minimum bias sample and the simulated signal. The simulated PU profile matches the one of the recorded data in the year 2016. Stable particles are propagated to the calorimeters within a uniform magnetic field. When reaching the calorimeters, the particles deposit their energy and an emulation of the PF algorithm produces two collections of four-momenta, PF tracks and towers. True photons and electrons that reach the ECAL without a reconstructed track are reconstructed as photons. Muons and electrons with reconstructed tracks are selected and their four-momenta are smeared according to the detector resolution. Charged hadrons originating from PU vertices are discarded and the residual event PU density is calculated, which is in turn used to perform PU subtraction on jets (with the FastJet package [68, 79] version 3.2.1) and the isolation variable of muons, electrons and photons. No PU subtraction is performed on the MET. The PF algorithm further yields improved treatment of b- and τ-tagging as well as jet and missing energy resolutions. Last, duplicates of the objects are removed and the resulting physics objects that can be reconstructed are jets, MET, isolated electrons and muons as well as photons and τ leptons. However, electrons, muons and photons are assumed to be perfectly identified and without any misidentification. As output, DELPHES stores the events in a tree format of the ROOT framework [80]. A validation of DELPHES against the two major general purpose detectors ATLAS and CMS for high-level objects such as electrons, muons, photons, jets and MET can be found in Ref. [2]. In the following sections, further validation for this specific analysis is given.

6.2.1. Tuning DELPHES

The aim of this analysis remodeling is to reproduce the results shown in Figs. 5.2 and 5.3. Therefore, due to possible differences to a GEANT-based full simulation, a crucial part is the tuning of DELPHES at reconstruction level. This concerns several characteristics of the analysis as presented in the following, ordered by their appearance in the event selection.

48 6.2. Detector Simulation with DELPHES

Figure 6.2. Workﬂow diagram of the DELPHES fast simulation. Taken from Ref. [2].

49 6. Remodeling the CMS Analysis

Lepton Isolation

In the pre-selection, at least two isolated muons with pT ≥ 30 GeV and |η| ≤ 2.4 are required.

DELPHES itself includes a relative isolation variable Irel, which is defined as in Eq. (5.2). Con- total sidering the muons from signal events Nµ that fulfill the pT- and η-cuts and those muons isolated Nµ that further satisfy the tight isolation working point Irel < 0.15, the isolation efficiency isolated total is εµ = Nµ /Nµ ≈ 100%, which exceeds the reference value of εµ ∼ 95% from Ref. [65]. The higher efficiency obtained is due to the fact that there is no simulation of misidentified tracks included DELPHES, i.e. charged particles that are reconstructed in the detector but do not correspond to any particle at generator level are not simulated. This causes less low pT activity inside a cone of R = 0.5 around the muon, cf. Section 5.2. Therefore, the muon isolation requirement has to be tuned as a much tighter cut to reduce the efficiency. The cut value is found to be Irel = 0.02, corresponding to a muon isolation efficiency of

N isolated 3172222 ε = µ = ≈ 94.79%. µ total (6.1) Nµ 3346586

For electrons, the same argumentation holds such that the same cut value is applied, resulting in an efﬁciency of N isolated 188482 ε = e = ≈ 80.35%. e total (6.2) Ne 234590

Fig. 6.3 shows the distributions of Irel for selected muons and electrons as well as the applied cut at Irel = 0.02. The tuning of the muon isolation is the crucial one; the pT-distributions of muons and electrons are compared in Fig. 6.4 for two different requirements on Irel.

Jet-Lepton Cleaning

Since prompt leptons clustered into jets can provoke double-counting of the energy, leptons need to be removed from jets. Hence, the angular distance ∆R(jet,`) of every combination of jets and leptons in the event is calculated. If a combination shows ∆R(jet,`) < 0.4, i.e. the lepton is located inside the AK4 jet, the four-momentum of the lepton is subtracted from that of the jet. Distributions of ∆R(jet,`) for muons and electrons before and after the cleaning are shown in Fig. 6.5. The peaks around zero in both distributions before the cleaning show that indeed some leptons are reconstructed inside jets. With the jet-lepton cleaning applied, these peaks vanish. Furthermore, the peak around π ≈ 3.14 in the ∆R(jet,µ)-spectrum indicates that jets and muons are mostly produced back-to-back. This is expected since jets most likely arise from the top quark decays, see Fig. 5.1. As electrons often involve photon radiation affecting

50 6.2. Detector Simulation with DELPHES

35.9 fb-1 (13 TeV)

muons 5 10 electrons Events

104

103

102

0 0.05 0.1

Irel

Figure 6.3. Distribution of Irel for the selected muons (blue) and electrons (red) at reconstruction level of the MLQ = 1.2 TeV sample. The vertical dashed line indicates the applied cut at Irel = 0.02 to achieve εµ ≈ 95%.

-1 -1 5 35.9 fb (13 TeV) 35.9 fb (13 TeV) I < 0.02 I < 0.02 4.5 rel 1.2 rel Irel < 0.15 Irel < 0.15

Events 4 Events 1 3.5 3 0.8 2.5 0.6 2 1.5 0.4 1 0.2 0.5

0 500 1000 1500 0 200 400 600 800 p [GeV] p [GeV] T,µ T,e

Figure 6.4. pT of selected muons (left) and electrons (right) of the MLQ = 1.2 TeV sample for two different values of Irel.

51 6. Remodeling the CMS Analysis

Δ Δ

Figure 6.5. ∆R between jets and muons (left) as well as jets and electrons (right) before (dotted) and after the cleaning (solid) for the MLQ = 1.2 TeV sample.

working point b-tag efﬁciency [%] mistag rate [%] 1 89.95 11.00 2 65.75 1.10 3 58.85 0.20 4 30.57 0.11 5 28.82 0.01 6 20.37 < 0.001 7 17.41 < 0.00001

Table 6.2. b-tag efﬁciencies and mistag rates for several working points. These values are obtained from combining all mass samples. the direction of the electron, their spectrum is much more balanced. The impact on the jet kinematics, however, is negligible as shown for the jet pT in Fig. 6.6. b-Tagging

Tuning the b-tagging efficiency is also possible with DELPHES, which uses built-in pre-defined working points. Seven working points from 1 (loose) to 7 (tight) are considered in this analysis. Table 6.2 shows the corresponding b-tagging efficiencies and mistag rates. The closest working point to the reference values (efficiency of ∼ 90%, mistag rate of ∼ 10%), i.e. the loosest working point 1, is chosen. Both the b-tag efficiency and the mistag rate are found to agree well. The mistag rate in this context considers misidentification of light partons only, i.e. contributions

52 6.2. Detector Simulation with DELPHES

35.9 fb-1 (13 TeV)

before cleaning after cleaning 25 Events

0 500 1000 1500 p [GeV] T,jet

Figure 6.6. Transverse momentum pT of selected jets before (dotted) and after (solid) jet-lepton cleaning for the MLQ = 1.2 TeV mass sample.

from charm quarks are not included.

Data-Simulation Scale Factors

In the original CMS analysis, scale factors (SFs) are derived from the full detector simulation with GEANT and are used to fit the selection efficiencies of simulated events to those of data. These SFs do not correspond to the selection efficiencies that would be measured with DELPHES and therefore no SFs are applied in this remodeling.

Still, the impact of the muon isolation SF and the muon trigger SF is studied due to the direct effect on the pre-selection. The muon isolation and trigger SFs are pT- and η-dependent and take values of 0.96 − 0.99 and 0.95 − 1.00, respectively. Whereas the muon isolation SF is applied for each muon in the event, the muon trigger SF is applied once for the leading muon. Consequently, the total number of weighted events expected from hypothetical LQ decays is scaled down by a few percent. However, this does not signiﬁcantly affect the shape of kinematic distributions, as shown for the muon pT in Fig. 6.7 before and after applying the SFs discussed above.

53 6. Remodeling the CMS Analysis

35.9 fb-1 (13 TeV) 5 no SFs 4.5 µ iso + trig SFs Events

3.5

2.5

1.5

0.5

0 200 400 600 800 1000 1200 1400 p [GeV] T,µ

Figure 6.7. Muon pT-distributions of the MLQ = 1.2 TeV sample with (dotted) and without (solid) scale factors applied.

6.3. Results

The full analysis strategy of the CMS search described in Sections 5.2 and 5.3 is reimplemented. This includes the requirements of the pre- and full selection, the categorization scheme and the different steps in the LQ mass reconstruction. The aim of tuning the remodeling with DELPHES is to reproduce the kinematic distributions observed in the analysis performed by CMS with high precision. Indicators to validate this are the number of reconstructed objects N and kinematic observables like pT and η. For muons and jets, these are compared in Fig. 6.8. Excellent agreement is observed for all distributions except for the jet multiplicity Njets (lower row left), which is lower in case of the remodeling with DELPHES. This can be explained by the use of a different pile-up mitigation technique implementated in DELPHES, namely the pile-up per particle identiﬁcation (PUPPI) algorithm

[81]. The spiky tail in the respective pT-spectrum for the lowest mass sample is due to a low number of selected events in the high pT-region. Not only kinematic observables, but also the selection efficiencies of the cuts applied in the pre- and full selection can be used to validate this analysis remodeling. For the pre-selection, they are shown as a function of the generated LQ mass in Fig. 6.9. The requirement of at least two muons with pT ≥ 30 GeV, |η| ≤ 2.4 and Irel < 0.02 as defined previously is dominant with a selection efficiency between ∼ 70−80% (Fig. 6.9 left) and thus determines the behavior visible in the total pre-selection efficiency (black solid line in Fig. 6.9 right). The observed deviation

54 6.3. Results

35.9 fb-1 (13 TeV) 35.9 fb-1 (13 TeV) 35.9 fb-1 (13 TeV) 7 DELPHES 3.4.1 GEANT4 6 DELPHES 3.4.1 GEANT4 DELPHES 3.4.1 GEANT4 10 10 106 M = 0.4 TeV M = 0.4 TeV M = 0.4 TeV M = 0.4 TeV M = 0.4 TeV M = 0.4 TeV 6 LQ LQ LQ LQ LQ LQ 10 5 5

Events M = 1.2 TeV M = 1.2 TeV Events M = 1.2 TeV M = 1.2 TeV Events M = 1.2 TeV M = 1.2 TeV LQ LQ 10 LQ LQ 10 LQ LQ 5 M = 2.0 TeV M = 2.0 TeV M = 2.0 TeV M = 2.0 TeV M = 2.0 TeV M = 2.0 TeV 10 LQ LQ LQ LQ LQ LQ 104 104 104 3 103 103 10 2 102 102 10 10 10 10 1 1 1 −1 10 10−1 −1 −2 10 10 10−2 − − 10 3 10 2 0 1 2 3 4 5 6 7 8 9 10 0 500 1000 1500 −2 −1 0 1 2 p [GeV] η Nµ T,µ µ

35.9 fb-1 (13 TeV) 35.9 fb-1 (13 TeV) 35.9 fb-1 (13 TeV) 7 DELPHES 3.4.1 GEANT4 6 DELPHES 3.4.1 GEANT4 DELPHES 3.4.1 GEANT4 10 10 6 10 6 MLQ = 0.4 TeV MLQ = 0.4 TeV MLQ = 0.4 TeV MLQ = 0.4 TeV MLQ = 0.4 TeV MLQ = 0.4 TeV 10 5

Events MLQ = 1.2 TeV MLQ = 1.2 TeV Events 10 MLQ = 1.2 TeV MLQ = 1.2 TeV Events 5 MLQ = 1.2 TeV MLQ = 1.2 TeV 5 10 10 MLQ = 2.0 TeV MLQ = 2.0 TeV MLQ = 2.0 TeV MLQ = 2.0 TeV MLQ = 2.0 TeV MLQ = 2.0 TeV 4 104 10 104 3 10 103 103 102 102 10 102 10 1 10 −1 10 1 10−2 1 −1 −3 10 10 10−1 10−4 10−2 10−2 0 2 4 6 8 10 12 14 16 18 20 500 1000 1500 −2 −1 0 1 2 N p [GeV] η jets T,jets jets

Figure 6.8. Comparison between DELPHES and GEANT. Distributions of N (left), pT (center) and η (right) for muons (upper row) and jets (lower row) on reconstruction level are shown for different mass samples.

55 6. Remodeling the CMS Analysis

1 1

0.8 0.8

0.6 0.6 total efficiency

single-cut efficiency 0.4 0.4

DELPHES 3.4.1 GEANT4 DELPHES 3.4.1 GEANT4 ≥ ≥ ≥ ≥ 0.2 Nµ 2 Nµ 2 0.2 Nµ 2 Nµ 2 ≥ ≥ ≥ ≥ Njets 2 Njets 2 Njets 2 Njets 2 ≥ ≥ ≥ ≥ ST 350 GeV ST 350 GeV ST 350 GeV ST 350 GeV 500 1000 1500 2000 500 1000 1500 2000

MLQ [GeV] MLQ [GeV]

Figure 6.9. Signal selection efficiencies of the requirements imposed in the pre-selection as a function of MLQ for the remodeling with DELPHES (solid) and the original CMS analysis using GEANT (dashed). In the left plot, the efficiencies are calculated with respect to the previous selection, whereas in the right plot they are calculated with respect to all generated events. in this selection efficiency between the original analysis and the remodeling is likely due to the differences regarding the muon isolation as discussed previously. The two remaining selection steps applied afterwards are then almost fully efficient. A continuous rise of this efficiency with increasing generated LQ mass is expected, as the muons also have higher pT. Scale factors applied in the original analysis cancel out in the selection efficiencies shown in this thesis, which ensures a reasonable comparison. The overall agreement between the two simulations is good as the selection efficiencies differ not more than 5%. In Fig. 6.10, the relative and total selection efficiencies are shown for the full selection requirements. It is evident that the pre-selection is the dominant criterion, such that the requirement of at least two isolated muons with pT ≥ 30 GeV, |η| ≤ 2.4 and Irel < 0.02 is the one with the largest effect on the final selection efficiencies of the analysis. The behavior in the b-tagging efficiency is opposite to the one observed in the pre-selection efficiency such that these trends partially cancel. This might be retraced to the rather coarsely tuned b-tagging in the DELPHES lep remodeling. Both further requirements on the invariant mass of muon pairs, Mµµ, and ST agree within 1% and are fully efficient apart from low generated LQ masses. As a result, the full selection efficiencies agree well within 3%. rec 1 Fig. 6.11 shows the final distributions of MLQ in category A and ST in category B. Overall,

1The reconstruction of the LQ mass is described in Section 5.3.

56 6.3. Results

1 1

0.8 0.8

0.6 0.6 Total efficiency

Single-cut efficiency 0.4 0.4 DELPHES 3.4.1 GEANT4 DELPHES 3.4.1 GEANT4 pre-selection pre-selection pre-selection pre-selection N ≥ 1 N ≥ 1 N ≥ 1 N ≥ 1 0.2 b-tags b-tags 0.2 b-tags b-tags Mµµ ≥ 110 GeV Mµµ ≥ 110 GeV Mµµ ≥ 110 GeV Mµµ ≥ 110 GeV lep ≥ lep ≥ lep ≥ lep ≥ ST 200 GeV ST 200 GeV ST 200 GeV ST 200 GeV

500 1000 1500 2000 500 1000 1500 2000

MLQ [GeV] MLQ [GeV]

Figure 6.10. Signal selection efﬁciencies of the requirements imposed in the full selection as a function of MLQ for the remodeling with DELPHES (solid) and the CMS analysis using GEANT (dashed). In the left plot, the efﬁciencies are calculated with respect to the previous selection, whereas in the right plot they are calculated with respect to all generated events.

35.9 fb-1 (13 TeV) 35.9 fb-1 (13 TeV) 107 DELPHES 3.4.1 GEANT4 107 DELPHES 3.4.1 GEANT4 M = 0.4 TeV M = 0.4 TeV M = 0.4 TeV M = 0.4 TeV 106 LQ LQ 106 LQ LQ events

Events M = 1.2 TeV M = 1.2 TeV M = 1.2 TeV M = 1.2 TeV 105 LQ LQ 105 LQ LQ MLQ = 2.0 TeV MLQ = 2.0 TeV MLQ = 2.0 TeV MLQ = 2.0 TeV 104 104 103 103 102 102 10 10 1 1 10−1 10−1 10−2 10−2 − − 10 3 10 3 10−4 10−4 − − 10 5 10 5 0 200 400 600 800 1000 0 1000 2000 3000 rec MLQ [GeV] ST [GeV]

rec Figure 6.11. Final distributions of MLQ (category A, left) and ST (category B, right) from the remodeling with DELPHES (solid) and the original analysis using GEANT (dashed) for several generated LQ masses.

57 6. Remodeling the CMS Analysis

the distributions are similar. However, the ST-distributions obtained from DELPHES are softer in general since less jets in the event are reconstructed, which in turn results in a smaller contribution to the value of ST. In addition, for lower generated LQ masses more events fall into category A and less into category B. This migration might be caused by differences in the lepton reconstruction. As no excess in data was observed in the CMS analysis, the same statistical procedure as described in Section 5.4 is used to derive upper limits on the product of the LQ pair production 2 cross section σLQLQ and the squared branching fraction B at 95% C.L. as a function of the LQ mass. Fig. 6.12 shows a detailed comparison to the original limits. Although there is a sig- niﬁcant deviation for the lowest mass point MLQ = 400 GeV, all other mass points are in good agreement within 10%. The expected and observed limits are shown in Fig. 6.13. The resulting lower exclusion limit on the LQ mass for pair-produced scalar LQs that exclusively decay into top quarks and muons is given by the intersection of the theoretically predicted production cross section and the experimental observation and is found to be MLQ = 1432.7GeV. A comparison to the reference value of MLQ = 1420GeV shows a deviation of less than 1%, which further validates the analysis remodeling. Since the agreement is particularly good in the region around 1.4 TeV, the obtained mass exclusion limit conforms well. In summary, the remodelling with DELPHES fast simulation presented here is tuned, such that a good level of agreement with the results of the CMS analysis [1] is achieved. The DELPHES simulation used to explore a wider parameter space as presented in the following chapter.

58 6.3. Results

35.9 fb-1 (13 TeV) 10−1 [pb] 2

LQ LQ σ −2 DELPHES 3.4.1 10 observed 95% C.L. upper limit expected 95% C.L. upper limit GEANT4 observed 95% C.L. upper limit expected 95% C.L. upper limit

− 10 3

1.4200 400 600 800 1000 1200 1400 1600 1800 2000 MLQ 1.2 1 0.8 PRL 121, 241802

DELPHES fast sim 0.6 200 400 600 800 1000 1200 1400 1600 1800 2000

MLQ [GeV]

Figure 6.12. Comparison of expected and observed upper limits obtained from fast and full simulation. The lower panel shows the respective ratio with the 10%-deviation range indicated by the gray horizontal lines.

35.9 fb-1 (13 TeV) 10 observed 95% C.L. upper limit [pb] 2 expected 95% C.L. upper limit Β

× 68% expected

1 95% expected LQ

LQ scalar LQ pair production σ 10−1

10−2

− 10 3

10−4 500 1000 1500 2000 MLQ [GeV]

Figure 6.13. Expected and observed upper limits on the product of the LQ pair production cross 2 section σLQLQ and the squared branching fraction B (LQ → tµ) at 95% C.L. as a function of the LQ mass for the remodeled analysis. Unit branching fraction is assumed, B = 1. The black dashed lines correspond to the pair production cross section of scalar LQs at NLO [50].

59 7. Search for Scalar Leptoquarks

Having validation of the fast-simulation-based analysis as presented in the previous chapter, a phenomenological study of the LQ parameter space is presented. Henceforth, the LQ ﬂavor model introduced in Section 3.5 is considered, in which not only LQ pair production but also further production processes that lead to the same ﬁnal state are included, such that a more realistic physical description of LQs is obtained. In addition, the impact of the Yukawa coupling

λ is investigated for all allowed couplings of the S3. The statistical analysis presented previously is used to study the sensitivity to LQs producing different ﬁnal states allowing to constrain coupling, masses and observed cross sections of the LQs predicted in the LQ ﬂavor model. The generation of the LQ event samples is described in Section 7.1, whereas results are presented for different LQ couplings in Section 7.2.

7.1. Signal Event Generation

In order to study the parameter space spanned by the LQ mass MLQ and the Yukawa coupling λ, a set of LQ event samples is generated in the range of MLQ = 0.4 − 2.0 TeV and λ = 0.25 − 2.25. The SM background predictions, the statistical and systematic uncertainties, and the data of the public CMS results are taken from Ref. [77]. Scan grids are produced for four decay scenarios:

−1/3 − • S3 → tµ ,

−1/3 − • S3 → tµ ,bν,

−4/3 − • S3 → bµ ,

+2/3 • S3 → tν, and the corresponding couplings of anti-particles, respectively. The ﬁrst decay scenario is studied to allow a reasonable comparison to the results obtained from LQ pair production only, whereas the other three scenarios constitute the allowed couplings of the S3 in the considered

60 7.2. Results

LQ ﬂavor model. The statistical procedure described in Section 5.4 is used to derive upper limits on the product of the inclusive LQ production cross section and the squared branching fraction at 95% C.L. as a function of MLQ and λ. The branching fraction for a decay scenario considering a single coupling to a quark and a lepton, i.e. tµ, bµ or tν, is assumed to be B = 1.

In case of two S3 couplings considered simultaneously, i.e. tµ and bν, equally strong Yukawa couplings λ are assumed. The LQ ﬂavor model is implemented in FeynRules [82], a Mathematica package for the calculation of Feynman rules. Its universal FeynRules Output (UFO) [83] is passed to the MC generator MadGraph5_aMC@NLO [84] and the obtained production cross section are rescaled by a K-factor of 1.5 to account for NLO QCD corrections, as described in Section 3.5. The narrow width-approximation for the generated LQ mass is not used here. The further analysis procedure including the detector simulation with DELPHES and its tuning remains unchanged. As the uncertainties on the cross sections calculated by MadGraph5_aMC@NLO are typically of the order ∼ 1% and thus may underestimate physically realistic uncertainties, the relative uncertainties on the cross sections are taken from Ref. [50]. The simulation of parton-showering and underlying events is performed with PYTHIA8 using the PDFs NNPDF31_NNLO [85].

7.2. Results

In the following, the four decay scenarios mentioned above are studied with the previously validated remodeling of the LQ analysis, which is tailored for the investigation of the final state tµ−tµ+. Therefore, the interplay of the production cross section for a given LQ coupling and the sensitivity to its corresponding final state is crucial for the final limits to be set on mass, coupling and observed cross section.

−1/3 − 7.2.1. Decay Scenario: S3 → tµ

In order to compare the results of inclusive LQ production to those of pair production, the 1 coupling of the S3-representation with the electric charge Q = ± 3 e to a top quark and a muon is studied ﬁrst. The production cross section for this decay scenario were shown and discussed in Section 3.5 Fig. 3.10. A summary of all produced LQ event samples can be found in Table A.2. The LQ pair production studied previously is compared to inclusive LQ production on generator level for this decay scenario. Fig. 7.1 shows distributions of the mass and transverse momentum of LQs as well as that of muon transverse momentum. In Fig. 7.1 left, the effect of the LQ

61 7. Search for Scalar Leptoquarks

(13 TeV) (13 TeV) (13 TeV) 1.4 MadGraph5 PYTHIA 8.230 0.14 MadGraph5 PYTHIA 8.230 0.14 MadGraph5 PYTHIA 8.230 M = 0.4 TeV M = 0.4 TeV M = 0.4 TeV M = 0.4 TeV M = 0.4 TeV M = 0.4 TeV 1.2 LQ LQ LQ LQ LQ LQ M = 0.8 TeV M = 0.8 TeV M = 0.8 TeV M = 0.8 TeV M = 0.8 TeV M = 0.8 TeV LQ LQ 0.12 LQ LQ 0.12 LQ LQ MLQ = 1.2 TeV MLQ = 1.2 TeV MLQ = 1.2 TeV MLQ = 1.2 TeV MLQ = 1.2 TeV MLQ = 1.2 TeV 1 0.1 0.1 0.8 0.08 0.08 Fraction of events Fraction of events Fraction of events 0.6 0.06 0.06

0.4 0.04 0.04

0.2 0.02 0.02

0 0 500 1000 1500 0 500 1000 1500 2000 0 200 400 600 800 1000 p [GeV] p [GeV] MLQ [GeV] T,LQ T,µ

Figure 7.1. Generator level distributions of MLQ (left), pT,LQ (center) and pT,µ (right) of inclusive production generated with MadGraph5 (solid) and pair production generated with PYTHIA8 (dotted) for several LQ masses (λ = 1.0). mass peaks being significantly broader for inclusive LQ production increases for higher LQ mass samples. It is evident that no NWA for the LQ mass is used in case of inclusive production events generated with MadGraph5_aMC@NLO. The LQ pT-spectra, shown in Fig. 7.1 center, differ slightly, especially for high generated LQ masses the distributions peak at lower values for inclusive LQ production. Similar observations are made for the pT-distributions of the muons (Fig. 7.1 right), since they most likely originate from a LQ decay. The deviations observed in the distributions between both considered production mechanisms have their origin in the additional processes contributing to the inclusive production. With growing mass of the LQs generated, increasing values of x are required to produce two on-shell LQs. As the PDFs of the proton decrease strongly for high values of x, cf. Fig. 2.2, the probability to produce two LQs also decreases. Hence, contributions of off-shell LQ production sets in and becomes dominant for high LQ masses generated, which is reflected in the softer pT-distributions of the LQs and muons for inclusive production. Since the muons have less pT for high generated LQ masses, also the pre-selection efficiency decreases in this region, see Fig. 7.2. This is, however, a minor rec effect in the LQ coupling to tµ. Fig. 7.3 shows the final distributions of MLQ (left) and ST (right) on reconstruction level. The significantly lower number of events in both distributions is mainly due to the lower production cross sections mentioned above. In addition, the softer muon pT-spectra at high generated LQ masses are propagated to the ST-distribution that in turn becomes softer as well.

In order to constrain the LQ parameter space of MLQ and λ, upper limits on the inclusive LQ production cross section are set for each value of λ. Fig. 7.4 shows upper limits on the observed cross section and the resulting lower limits on the LQ mass in the plane of MLQ and λ. A novel ﬁnding is the λ-dependency of the obtained lower limits on the LQ mass. With

62 7.2. Results

0.9

0.8 total efficiency

0.7

0.6

0.5

0.4

0.3 pair-production inclusive production pre-selection pre-selection 0.2 ≥ ≥ Nb-tags 1 Nb-tags 1

Mµµ ≥ 110 GeV Mµµ ≥ 110 GeV 0.1 lep ≥ lep ≥ ST 200 GeV ST 200 GeV

400 600 800 1000 1200 1400 1600 1800 2000

MLQ [GeV]

Figure 7.2. Total selection efﬁciencies of each requirement imposed in the full selection as a function of the generated LQ mass for inclusive production (solid) and pair production (dotted) of the S3 coupling to tµ.

35.9 fb-1 (13 TeV) 35.9 fb-1 (13 TeV) 105 105 inclusive pair inclusive pair 4 M = 0.4 TeV 4 M = 0.4 TeV Events 10 LQ Events 10 LQ MLQ = 1.2 TeV MLQ = 1.2 TeV MLQ = 2.0 TeV MLQ = 2.0 TeV 103 103

102 102

10 10

1 1

10−1 10−1

10−2 10−2

− − 10 3 10 3

10−4 10−4

− − 10 5 10 5 0 100 200 300 400 500 600 700 800 900 1000 0 500 1000 1500 2000 2500 3000

MLQ [GeV] ST [GeV]

rec Figure 7.3. Final distributions of MLQ (left) and ST (right) for inclusive production (solid) and pair production (dotted) of the S3 coupling to tµ for several generated LQ masses (λ = 1.0).

63 7. Search for Scalar Leptoquarks

35.9 fb-1 (13 TeV) λ

2 10−2 coupling

1.5

− 10 3 LQ exclusion limit Observed 0.5 Expected 68% expected

400 600 800 1000 1200 1400 1600 1800 2000 Observed cross section upper limit at 95% CL [pb]

MLQ [GeV]

Figure 7.4. Observed and expected lower exclusion limits on the LQ mass and upper limits on the observed cross section at 95% C.L. in the plane of MLQ and λ for the S3 coupling to tµ.

64 7.2. Results

10 LQ → tµ LQ → tµ, bν

[pb] λ = 0.5 λ = 0.5

σ 1 λ = 1.0 λ = 1.0 λ = 1.5 λ = 1.5 10−1

10−2

10−3

10−4

10−5

10−6

10−7 400 600 800 1000 1200 1400 1600 1800 2000

MLQ [GeV]

Figure 7.5. Inclusive production cross section σ for the LQ coupling tµ,bν (red) as a function of MLQ for several values of λ compared to those of tµ (blue). Values on σ obtained from MadGraph5_aMC@NLO are rescaled by a factor of 1.5 to account for NLO QCD corrections. growing coupling λ, also the mass exclusion limits increase until λ ≈ 1.5 and saturate at around

MLQ ∼ 1.2 TeV for even higher values. The resulting observed lower LQ mass limits are listed in Table A.6 for all values of λ studied.

−1/3 − 7.2.2. Decay Scenario: S3 → tµ , bν

After having discussed the coupling of the S3 to a top quark and a muon only, now both LQ couplings to tµ and bν are considered simultaneously and are assumed to be equally strong. Fig. 7.5 shows the inclusive LQ production cross sections for both cases. It is evident that the production cross sections depend on the allowed couplings, as the those for both couplings tµ and bν, are in general higher than the ones for tµ-coupling only. Especially in the region of high generated LQ masses, this behavior is observed. Since the b quark has a smaller mass than the top quark, consequently the b quark PDFs are significantly higher compared to the top quark’s, such that off-shell LQ production via bν-coupling sets in at lower energies than for tµ-coupling. A summary of all produced LQ event samples can be found in Table A.3. The pre-selection efficiency is shown in Fig. 7.6 for simulated events considering both LQ couplings. It is lower compared to the pre-selection efficiency for tµ-coupling, since the production of the two selected muons is unlikely for the LQ decay into bν. Additionally, the decrease of the efficiency for increasing MLQ is due to the off-shell LQ production contributing to the

65 7. Search for Scalar Leptoquarks

0.9

0.8 total efficiency

0.7

0.6

0.5 LQ → tµ LQ → tµ,bν pre-selection pre-selection N ≥ 1 N ≥ 1 0.4 b-tags b-tags Mµµ ≥ 110 GeV Mµµ ≥ 110 GeV lep lep S ≥ 200 GeV S ≥ 200 GeV 0.3 T T

0.2

0.1

400 600 800 1000 1200 1400 1600 1800 2000

MLQ [GeV]

Figure 7.6. Total selection efﬁciencies of each requirement imposed in the full selection as a function of the generated LQ mass for inclusive production of the S3 coupling to tµ,bν (solid) and tµ only (dotted).

35.9 fb-1 (13 TeV) 35.9 fb-1 (13 TeV) 105 105 t µ, b ν t µ t µ, b ν t µ 4 4

events M = 0.4 TeV events M = 0.4 TeV 10 LQ 10 LQ MLQ = 1.2 TeV MLQ = 1.2 TeV MLQ = 2.0 TeV MLQ = 2.0 TeV 103 103

102 102

10 10

1 1

10−1 10−1

10−2 10−2

− − 10 3 10 3

10−4 10−4

− − 10 5 10 5 0 100 200 300 400 500 600 700 800 900 1000 0 500 1000 1500 2000 2500 3000

MLQ [GeV] ST [GeV]

rec Figure 7.7. Final distributions of MLQ (left) and ST (right) for inclusive production of the S3 coupling to tµ,bν (solid) and tµ (dotted) for several generated LQ masses (λ = 1.0).

66 7.2. Results

35.9 fb-1 (13 TeV) λ

2 10−2 coupling

1.5

− 10 3 LQ exclusion limit Observed 0.5 Expected 68% expected

400 600 800 1000 1200 1400 1600 1800 2000 Observed cross section upper limit at 95% CL [pb]

MLQ [GeV]

Figure 7.8. Observed and expected lower exclusion limits on the LQ mass and upper limits on the observed cross section at 95% C.L. in the plane of MLQ and λ for the S3 coupling to tµ,bν.

67 7. Search for Scalar Leptoquarks

10 LQ → t µ LQ → b µ

[pb] λ = 0.5 λ = 0.5

σ 1 λ = 1.0 λ = 1.0 λ = 1.5 λ = 1.5 10−1

10−2

10−3

10−4

10−5

10−6

10−7 400 600 800 1000 1200 1400 1600 1800 2000

MLQ [GeV]

Figure 7.9. Inclusive production cross section σ for the LQ coupling to bµ (green) as a function of MLQ for several values of λ compared to those of tµ (blue). Values on σ obtained from MadGraph5_aMC@NLO are already rescaled by a factor of 1.5. overall production cross section increasingly strongly. Fig. 7.7 shows the ﬁnal distributions of

MLQ (left) and ST (right). They do not deviate much from the ones obtained for the tµ-coupling only, indicating that the effects of increased cross sections and decreased selection efficiency mostly cancel. Only for high generated LQ masses (MLQ = 2.0 TeV, red), in total more events are found in both categories due to the increased production cross sections with respect to the tµ-coupling. In Fig. 7.8, the lower exclusion limits on the LQ mass and observed upper limits on the production cross section are displayed in the MLQ − λ plane. Exact values are listed in Table A.7. In comparison to the previous results obtained for a coupling to tµ only, these are found to be very similar, because the gain in the cross section is compensated by the loss in selection efficiency. The upper limits on the observed LQ production cross section, however, are weaker in this case due to the lower selection efficiency.

−4/3 − 7.2.3. Decay Scenario: S3 → bµ

4 In the model considered, the S3-representation with the electric charge of Q = ± 3 e couples to a b quark and a muon only. In Fig. 7.9, the corresponding production cross section of inclusive LQ production is shown. A summary of all produced LQ event samples for this decay scenario can be found in Table A.4. As for the tµ,bν-coupling, a higher production cross section with respect

68 7.2. Results

0.9

0.8 total efficiency

0.7

0.6

0.5

0.4

0.3 LQ → t µ LQ → b µ pre-selection pre-selection 0.2 ≥ ≥ Nb-tags 1 Nb-tags 1

Mµµ ≥ 110 GeV Mµµ ≥ 110 GeV 0.1 lep ≥ lep ≥ ST 200 GeV ST 200 GeV

400 600 800 1000 1200 1400 1600 1800 2000

MLQ [GeV]

Figure 7.10. Total selection efficiencies of each requirement imposed in the full selection as a function of the generated LQ mass for inclusive production of the S3 coupling to bµ (solid) and tµ only (dotted). to the tµ-coupling is observed, along with the effect of off-shell LQ production as described above. Fig. 7.10 shows the total selection efficiencies of the requirements in the full selection for the decay scenario to bµ. Because of the similarity of final states in this scenario, bµ−bµ+, and to which the utilized analysis is tailored to, tµ−tµ+, a good selection efficiency is found. The decreasing pre-selection efficiency for increasing LQ masses generated is due to the onset rec of off-shell LQ production. Fig. 7.11 shows the final distributions of MLQ (category A, left) and ST (category B, right). As the occurrence of additional leptons in this decay scenario is unlikely, the number of events that fall into category A is significantly lower than for the tµ-coupling. Thus, most events fall into category B. For high generated LQ masses, the ST-distributions in this decay scenario show a peak at low values due to off-shell contributions as well. Fig. 7.12 shows the the lower exclusion limits on the LQ mass and observed upper limits on the production cross section in the MLQ − λ-plane. Exact values of the LQ mass exclusion limits are listed in Table A.8. In this decay scenario, a significant λ-dependence of the LQ mass exclusion limits is evident. Due to the large predicted production cross section and the reasonably high selection efficiency for this coupling, the limits are more stringent than those of the tµ-coupling. These limits constitute the first constraints on LQs coupling to a b quark and a muon. Regarding the scalar leptoquark S3 in this analysis, the LQ mass limits obtained in this decay scenario are the most stringent. For values of λ > 1.5, the observed exclusion limits

69 7. Search for Scalar Leptoquarks

35.9 fb-1 (13 TeV) 35.9 fb-1 (13 TeV) 105 105 b µ t µ b µ t µ 4 4

events M = 0.4 TeV events M = 0.4 TeV 10 LQ 10 LQ MLQ = 1.2 TeV MLQ = 1.2 TeV MLQ = 2.0 TeV MLQ = 2.0 TeV 103 103

102 102

10 10

1 1

10−1 10−1

10−2 10−2

− − 10 3 10 3

10−4 10−4

− − 10 5 10 5 0 100 200 300 400 500 600 700 800 900 1000 0 500 1000 1500 2000 2500 3000

MLQ [GeV] ST [GeV]

rec Figure 7.11. Final distributions of MLQ (left) and ST (right) for inclusive production of the S3 coupling to bµ (solid) and tµ (dotted) for several generated LQ masses (λ = 1.0).

35.9 fb-1 (13 TeV) λ LQ exclusion limit 2 Observed 10−2

coupling Expected 68% expected

1.5

− 10 3

0.5

400 600 800 1000 1200 1400 1600 1800 2000 Observed cross section upper limit at 95% CL [pb]

MLQ [GeV]

Figure 7.12. Observed and expected lower exclusion limits on the LQ mass and observed upper limits on the production cross section at 95% C.L. in the plane of MLQ and λ for the S3 coupling to bµ.

70 7.2. Results

10 LQ → t µ LQ → t ν

[pb] λ = 0.5 λ = 0.5

σ 1 λ = 1.0 λ = 1.0 λ = 1.5 λ = 1.5 10−1

10−2

10−3

10−4

10−5

10−6

10−7 400 600 800 1000 1200 1400 1600 1800 2000

MLQ [GeV]

Figure 7.13. Inclusive production cross section σ for the LQ coupling to tν (orange) as a function of MLQ for several values of λ compared to those of tµ (blue). Values on σ obtained from MadGraph5_aMC@NLO are already rescaled by a factor of 1.5.

exceed the investigated mass region, MLQ > 2000 GeV.

+2/3 7.2.4. Decay Scenario: S3 → tν

Last, the coupling to a top quark and a neutrino is studied for the S3 with the electric charge of 2 Q = ± 3 e. Fig. 7.13 shows the corresponding inclusive production cross section as a function of the generated LQ mass. A summary of all produced LQ event samples can be found in Table A.5. Some values of the highest LQ mass sample are found to be negative, such that the obtained values from MadGraph5_aMC@NLO are not considered for MLQ > 1.6 TeV. Fig. 7.14 shows the total selection efficiencies of each requirement imposed in the full selection. Since the full selection efficiency (black line) is of order ∼ 0.1%, the sensitivity is too small to be compensated by the gain in cross sections. It is further unlikely that three or more leptons are produced in this decay scenario so that no event falls into category A, see Fig. 7.15 left. Those events that fulfill the full selection requirements thus fall into category B, see Fig. 7.15 right. However, as the statistical analysis shows, even for the highest value of λ = 2.25, no mass exclusion limits can be obtained, see Fig. 7.16. Since the analysis is not sensitive to the tν- coupling, another search would be needed to constrain this decay scenario, e.g. a SUSY stop search with the final state of two top quarks and two neutralinos, see Ref. [86].

71 7. Search for Scalar Leptoquarks

0.01

LQ → t ν 0.009 pre-selection ≥ Nb-tags 1 0.008 Mµµ ≥ 110 GeV total efficiency lep ≥ ST 200 GeV 0.007

0.006

0.005

0.004

0.003

0.002

0.001

400 600 800 1000 1200 1400 1600 1800 2000

MLQ [GeV]

Figure 7.14. Total selection efﬁciencies of each requirement imposed in the full selection as a function of the generated LQ mass for inclusive production of the S3 coupling to tν.

35.9 fb-1 (13 TeV) 35.9 fb-1 (13 TeV) 105 105 t ν t µ t ν t µ 104 104 events MLQ = 0.4 TeV events MLQ = 0.4 TeV MLQ = 1.2 TeV MLQ = 1.2 TeV 3 3 10 MLQ = 2.0 TeV 10 MLQ = 2.0 TeV

102 102

10 10

1 1

10−1 10−1

10−2 10−2

− − 10 3 10 3

10−4 10−4

− − 10 5 10 5

− − 10 6 10 6

10−7 10−7 0 100 200 300 400 500 600 700 800 900 1000 0 500 1000 1500 2000 2500 3000

MLQ [GeV] ST [GeV]

rec Figure 7.15. Final distributions MLQ (center) and ST (right) of inclusive production in the decay scenarios tν (solid) and tµ (dotted) for several LQ masses (λ = 1.0).

72 7.2. Results

35.9 fb-1 (13 TeV) 103 observed 95% C.L. upper limit 102 expected 95% C.L. upper limit 68% expected + X) [pb] 95% expected 2/3 3

S 10 scalar LQ →

(pp 1 σ

10−1

10−2

− 10 3

10−4 500 1000 1500 2000 MLQ [GeV]

Figure 7.16. Expected and observed upper limits on the inclusive LQ production cross section at 95% C.L. as a function of the LQ mass. The inclusive production cross section of scalar LQs obtained from MadGraph5_aMC@NLO is already rescaled by a K-factor of 1.5 (black dashed line).

73 8. Conclusion and Outlook

Although the Standard Model of particle physics is an extremely successful theory tested in numerous experiments, it cannot explain some phenomena observed. Leptoquarks are hypothetical particles that appear in many theories beyond the Standard Model and could explain hints for lepton flavor non-universality in B meson decays observed recently. Many searches for leptoquarks have been performed, but no evidence for their existence was found so far. In this thesis, a remodeling of the CMS search for pair-produced scalar leptoquarks decaying exclusively into top quarks and muons has been presented. Instead of a GEANT-based full simulation, the DELPHES framework has been used to simulate the CMS detector. Since DELPHES fast simulation uses a simplified approach based on parametrization, the remodeled analysis has been tuned in terms of lepton isolation, jet-lepton cleaning and b-tagging to reproduce the results of the original analysis. Distributions of kinematic variables as well as selection efficiencies at reconstruction level have been compared for both simulation techniques confirming the validity of the remodeling. The validated DELPHES simulation has been used for a reinterpretation of CMS data within a leptoquark flavor model motivated by recent hints for lepton flavor non-universality in B meson decays. All allowed couplings of the scalar leptoquark S3 to third-generation quarks and muons or neutrinos have been studied in final states with two third-generation quarks and two second-generation leptons. Additional leptoquark production processes beyond pair production have been considered, which have been found to be dependent on the strength of the Yukawa coupling λ. The contribution of leptoquarks produced off-shell becomes more relevant with increasing generated leptoquark mass and is more significant for couplings to a light b quark.

For all leptoquark couplings investigated, exclusion limits on the lower leptoquark mass MLQ and the upper leptoquark production cross section σ have been set in the two-dimensional plane as a function of MLQ and λ. A novel result is the λ-dependency of the obtained lower limits on the leptoquark mass. Limits on leptoquarks coupling to a b quark and a muon have been set for the ﬁrst time, which are the most stringent for the S3. It has been demonstrated that published data can be used to obtain more realistic results on exclusion limits for searches for new physics. Particularly, it has been shown that it is crucial

74 to study more realistic leptoquark production mechanisms beyond the simpliﬁed approach of leading order pair production only. Since the mass exclusion limits have been found to be λ- dependent, simple pair production models might exclude too large regions of the leptoquark parameter space, especially for low values for of λ.

The constraints on scalar leptoquarks presented are expected to be valid for vector leptoquarks as well, because they have higher production cross sections. However, this analysis performed for vector leptoquarks would provide significantly more stringent limits. In addition, a sound calculation of uncertainties on the theoretically predicted cross sections would contribute to a more precise estimation of the exclusion limits. To further explore the leptoquark parameter space, not only an expansion to the full Run II data set is needed, but also the remodeling of different analyses would be beneficial, as results obtained from statistically independent event selections allow for a combination of exclusion limits. The most stringent limits have been found for the S3 coupling to a b quark and a muon, i.e. a lower limit of MLQ = 1520 GeV for λ = 1, although the analysis used is not tailored towards this coupling. Therefore, a dedicated search for this decay scenario would provide significantly stronger constraints.

75 A. Additional Tables

76 Process σ [pb] Generator N [106] 2 tt + jets 8.3 · 10 POWHEG + PYTHIA 155.2 2 W(→ `ν) + jets, pˆT ∈ [100,250) GeV 6.9 · 10 AMC@NLO + PYTHIA 176792.6 1 W(→ `ν) + jets, pˆT ∈ [250,400) GeV 2.5 · 10 AMC@NLO + PYTHIA 617.7 0 W(→ `ν) + jets, pˆT ∈ [400,600) GeV 3.1 · 10 AMC@NLO + PYTHIA 11.7 −1 W(→ `ν) + jets, pˆT ∈ [250,400) GeV 4.7 · 10 AMC@NLO + PYTHIA 1.8 2 DY(Z/γ → ``) + jets, HT ∈ [70,100) GeV 2.2 · 10 MADGRAPH + PYTHIA 9.6 2 DY(Z/γ → ``) + jets, HT ∈ [100,200) GeV 1.8 · 10 MADGRAPH + PYTHIA 10.6 1 DY(Z/γ → ``) + jets, HT ∈ [200,400) GeV 5.0 · 10 MADGRAPH + PYTHIA 9.6 0 DY(Z/γ → ``) + jets, HT ∈ [400,600) GeV 7.0 · 10 MADGRAPH + PYTHIA 10.0 0 DY(Z/γ → ``) + jets, HT ∈ [600,800) GeV 1.7 · 10 MADGRAPH + PYTHIA 8.3 −1 DY(Z/γ → ``) + jets, HT ∈ [800,1200) GeV 7.8 · 10 MADGRAPH + PYTHIA 2.7 −1 DY(Z/γ → ``) + jets, HT ∈ [1200,2500) GeV 1.9 · 10 MADGRAPH + PYTHIA 0.6 −3 DY(Z/γ → ``) + jets, HT ∈ [2500,∞) GeV 4.4 · 10 MADGRAPH + PYTHIA 0.4 2 Single t, t-channel 1.4 · 10 POWHEG + PYTHIA 6.0 1 Single t, t-channel 8.1 · 10 POWHEG + PYTHIA 3.9 0 Single t / t, s-channel 3.4 · 10 AMC@NLO + PYTHIA 3.4 1 Single t, tW-channel 3.6 · 10 POWHEG + PYTHIA 6.9 1 Single t, tW-channel 3.6 · 10 POWHEG + PYTHIA 6.9 1 Diboson (WW→ 2`2ν) 1.2 · 10 POWHEG + PYTHIA 2.0 1 Diboson (WW→ `ν2q) 5.0 · 10 POWHEG + PYTHIA 9.0 1 Diboson (WZ→ `ν2q) 1.1 · 10 AMC@NLO + PYTHIA 420.5 0 Diboson (WZ→ 2`2q) 5.6 · 10 AMC@NLO + PYTHIA 233.1 0 Diboson (WZ→ 3`ν) 4.4 · 10 POWHEG + PYTHIA 2.0 −1 Diboson (ZZ→ 2`2ν) 5.6 · 10 POWHEG + PYTHIA 8.8 0 Diboson (ZZ→ 2`2q) 3.2 · 10 AMC@NLO + PYTHIA 77.9 0 Diboson (ZZ→ 4`) 1.2 · 10 AMC@NLO + PYTHIA 20.5 −1 tt + W(→ `ν) 2.0 · 10 AMC@NLO + PYTHIA 3.5 −1 tt + Z(→ `` / νν) 2.5 · 10 AMC@NLO + PYTHIA 1.8 6 QCD, µ enr., pˆT ∈ [15,20) GeV 3.8 · 10 PYTHIA 4.1 6 QCD, µ enr., pˆT ∈ [20,30) GeV 3.0 · 10 PYTHIA 31.5 6 QCD, µ enr., pˆT ∈ [30,50) GeV 1.7 · 10 PYTHIA 29.9 5 QCD, µ enr., pˆT ∈ [50,80) GeV 4.4 · 10 PYTHIA 19.8 5 QCD, µ enr., pˆT ∈ [80,120) GeV 1.1 · 10 PYTHIA 13.8 4 QCD, µ enr., pˆT ∈ [120,170) GeV 2.5 · 10 PYTHIA 8.0 3 QCD, µ enr., pˆT ∈ [170,300) GeV 8.7 · 10 PYTHIA 7.9 2 QCD, µ enr., pˆT ∈ [300,470) GeV 8.0 · 10 PYTHIA 7.9 1 QCD, µ enr., pˆT ∈ [470,600) GeV 7.9 · 10 PYTHIA 3.9 1 QCD, µ enr., pˆT ∈ [600,800) GeV 2.5 · 10 PYTHIA 4.0 0 QCD, µ enr., pˆT ∈ [800,1000) GeV 4.7 · 10 PYTHIA 4.0 0 QCD, µ enr., pˆT ∈ [1000,∞) GeV 1.6 · 10 PYTHIA 4.0 6 QCD, EM enr., pˆT ∈ [20,30) GeV 5.4 · 10 PYTHIA 9.2 6 QCD, EM enr., pˆT ∈ [30,50) GeV 9.9 · 10 PYTHIA 4.7 6 QCD, EM enr., pˆT ∈ [50,80) GeV 2.9 · 10 PYTHIA 23.5 5 QCD, EM enr., pˆT ∈ [80,120) GeV 4.2 · 10 PYTHIA 35.8 4 QCD, EM enr., pˆT ∈ [120,170) GeV 7.7 · 10 PYTHIA 77.8 4 QCD, EM enr., pˆT ∈ [170,300) GeV 1.9 · 10 PYTHIA 11.5 3 QCD, EM enr., pˆT ∈ [300,∞) GeV 1.4 · 10 PYTHIA 7.4 5 QCD, bc → e, pˆT ∈ [15,20) GeV 2.5 · 10 PYTHIA 2.7 5 QCD, bc → e, pˆT ∈ [20,30) GeV 3.3 · 10 PYTHIA 10.9 5 QCD, bc → e, pˆT ∈ [30,80) GeV 4.1 · 10 PYTHIA 15.3 4 QCD, bc → e, pˆT ∈ [80,170) GeV 3.8 · 10 PYTHIA 15.0 3 QCD, bc → e, pˆT ∈ [170,250) GeV 2.6 · 10 PYTHIA 9.5 2 QCD, bc → e, pˆT ∈ [250,∞) GeV 7.1 · 10 PYTHIA 9.8

Table A.1. Summary of simulated samples of SM background processes used in the analysis in Ref. [1, 77]. In the second column, σ denotes the production cross section of the respective process. Filter efﬁciencies and K factors are already included in the given numbers. In the third column, the generator used for simulating the events is stated and N in the fourth column is the weighted number of generated events in each sample. Taken from [63].

77 Appendix A. Additional Tables r ecldb a by rescaled are al A.3. Table MadGraph5_aMC@NLO A.2. Table r produced. are M LQ 801 1800 607 1600 402 1400 201 1200 006 1000 005 2000 0 2 800 0 1 9 600 400 [GeV] rs etosi bfralgnrtdL vnsfrtescenario the for events LQ generated all for pb in sections Cross rs etosi bfralgnrtdL vnsfrtedcyscenario decay the for events LQ generated all for pb in sections Cross K ...... 793 489 429 924 949 253 876 270 035 λ fco of -factor 0 = × × × × × × × × × r ecldb a by rescaled are . 10 10 10 10 10 10 10 10 10 25 − − − − − − − − − M 9 8 8 7 6 6 5 4 4 LQ 001 2000 803 1800 605 1600 401 1400 204 1200 001 1000 0 3 400 0 7 800 0 4 600 [GeV] 3 1 8 3 2 1 9 2 1 1 ...... 108 819 034 978 677 106 735 001 280 λ 5 0 = oacutfrNOQDcretos o ahentry, each For corrections. QCD NLO for account to × × × × × × × × × . 10 10 10 10 10 10 10 10 10 50 ...... 781 104 949 392 194 688 388 098 542 − − − − − − − − − λ 6 5 5 4 3 2 8 7 6 0 = × × × × × × × × × K . 10 10 10 10 10 10 10 10 10 5 4 1 4 1 7 3 1 7 25 fco of -factor ...... 211 235 329 629 419 087 417 727 031 − − − − − − − − − λ 4 3 7 7 7 6 6 5 5 0 = × × × × × × × × × . 10 10 10 10 10 10 10 10 10 2 4 9 2 6 2 1 5 4 75 ...... 126 092 268 005 591 854 879 746 345 − − − − − − − − − λ 2 7 6 6 5 5 4 3 3 0 = × × × × × × × × × 1 . 10 10 10 10 10 10 10 10 10 . 1 3 1 3 1 7 3 1 1 50 5 ...... 735 737 098 239 748 144 298 228 046 − − − − − − − − − λ oacutfrNOQDcretos o ahentry, each For corrections. QCD NLO for account to 6 6 6 5 5 4 3 3 2 1 = × × × × × × × × × . 10 10 10 10 10 10 10 10 10 7 1 2 2 9 5 4 4 00 7 ...... 252 647 520 193 277 724 417 168 . − − − − − − − − − λ 517 6 6 5 5 4 4 3 2 1 1 = × × × × × × × × × . 10 10 10 10 10 10 10 10 1 7 3 1 5 2 1 2 6 00 10 ...... 971 918 996 985 607 060 224 562 957 − − − − − − − − λ 4 5 4 4 3 3 2 1 5 1 = × × × × × × × × × . 10 10 10 10 10 10 10 10 10 7 2 1 2 3 6 1 2 25 1 ...... 189 558 093 199 756 991 964 511 . − − − − − − − − − λ 256 S 5 5 4 3 3 2 1 6 6 1 = 3 × × × × × × × × × → . 10 10 10 10 10 10 10 10 7 4 2 5 1 3 1 4 1 50 10 ...... 553 260 458 151 304 778 925 254 831 − − − − − − − − λ t 0 µ 3 2 1 4 4 4 3 3 1 = × × × × × × × × × , b . 10 10 10 10 10 10 10 10 10 6 1 1 3 7 1 6 2 50 ν ...... 2 071 794 279 052 853 057 834 765 − − − − − − − − − λ bandvle from values Obtained . . 25 2 1 6 5 5 4 4 3 3 N 2 = × × × × × × × × × 100000 = . 10 10 10 10 10 10 10 10 10 9 1 5 1 5 2 1 5 3 00 ...... 118 578 471 325 014 418 626 425 982 − − − − − − − − λ 0 4 3 3 3 3 2 2 1 1 = × × × × × × × × × S . 10 10 10 10 10 10 10 10 10 1 1 2 4 1 2 8 3 75 3 2 ...... 519 090 546 050 635 742 964 032 . − − − − − − − − − λ 774 → 6 5 5 4 4 3 2 2 1 2 = vnsaeproduced. are events × × × × × × × × × t . 10 10 10 10 10 10 10 10 3 7 2 6 2 1 6 4 1 25 µ 10 ...... 426 292 497 066 113 042 882 810 213 − − − − − − − − λ bandvle from values Obtained . 0 3 3 3 3 2 2 2 1 2 = × × × × × × × × × . 10 10 10 10 10 10 10 10 10 00 MadGraph5_aMC@NLO − − − − − − − − − N 5 5 4 4 3 2 2 1 5 100000 = 8 3 1 7 4 2 4 9 2 ...... 234 263 260 538 162 254 368 254 823 λ 2 = × × × × × × × × × . 10 10 10 10 10 10 10 10 10 25 − − − − − − − − − 4 3 2 2 1 5 5 5 4 events

78 MLQ [GeV] λ = 0.25 λ = 0.50 λ = 0.75 λ = 1.00 λ = 1.25 λ = 1.50 λ = 1.75 λ = 2.00 λ = 2.25 400 1.153 × 10−2 1.536 × 10−1 6.074 × 10−1 1.401 × 100 2.562 × 100 3.888 × 100 5.382 × 100 6.800 × 100 8.393 × 100 500 3.635 × 10−3 4.976 × 10−2 1.916 × 10−1 4.628 × 10−1 8.325 × 10−1 1.292 × 100 1.806 × 100 2.280 × 100 2.966 × 100 600 1.346 × 10−3 ×10−3 1.850 × 10−2 7.272 × 10−2 1.719 × 10−1 3.182 × 10−1 5.303 × 10−1 7.008 × 10−1 9.530 × 10−1 700 5.496 × 10−4 7.500 × 10−3 3.000 × 10−2 7.208 × 10−2 1.332 × 10−1 2.141 × 10−1 3.092 × 10−1 4.238 × 10−1 5.645 × 10−1 800 2.436 × 10−4 3.413 × 10−3 1.352 × 10−2 3.216 × 10−2 6.281 × 10−2 9.977 × 10−2 1.447 × 10−1 2.076 × 10−1 2.900 × 10−1 900 1.168 × 10−4 1.631 × 10−3 6.573 × 10−3 1.598 × 10−2 3.147 × 10−2 5.286 × 10−2 7.785 × 10−2 1.172 × 10−1 1.608 × 10−1 1000 5.837 × 10−5 8.297 × 10−4 3.452 × 10−3 8.574 × 10−3 1.671 × 10−2 2.945 × 10−2 4.587 × 10−2 6.887 × 10−2 9.783 × 10−2 1100 3.101 × 10−5 4.481 × 10−5 1.860 × 10−3 4.890 × 10−3 9.692 × 10−3 1.724 × 10−2 2.795 × 10−2 4.212 × 10−2 6.101 × 10−2 1200 1.773 × 10−5 2.546 × 10−4 1.093 × 10−3 2.855 × 10−3 5.934 × 10−3 1.060 × 10−2 1.758 × 10−2 2.787 × 10−2 4.101 × 10−2 1300 1.061 × 10−5 1.530 × 10−4 6.632 × 10−4 1.800 × 10−3 3.893 × 10−3 6.927 × 10−3 1.205 × 10−2 1.892 × 10−2 2.828 × 10−2 1400 6.639 × 10−6 9.746 × 10−5 4.244 × 10−4 1.183 × 10−4 2.550 × 10−3 4.848 × 10−3 8.133 × 10−3 1.294 × 10−2 2.021 × 10−2 1500 4.169 × 10−6 6.399 × 10−5 2.871 × 10−4 7.851 × 10−4 1.760 × 10−3 3.447 × 10−3 5.825 × 10−3 9.048 × 10−3 1.469 × 10−2 1600 2.909 × 10−6 4.361 × 10−5 1.992 × 10−4 5.774 × 10−4 1.258 × 10−3 2.540 × 10−3 4.380 × 10−3 7.345 × 10−3 1.062 × 10−2 1700 2.003 × 10−6 3.026 × 10−5 1.445 × 10−4 4.263 × 10−4 9.542 × 10−4 1.862 × 10−3 3.435 × 10−3 5.457 × 10−3 8.261 × 10−3 1800 1.470 × 10−6 2.186 × 10−5 1.053 × 10−4 3.240 × 10−4 7.140 × 10−4 1.487 × 10−3 2.652 × 10−3 4.179 × 10−3 6.540 × 10−3 1900 1.033 × 10−6 1.682 × 10−5 7.905 × 10−5 2.519 × 10−4 5.820 × 10−4 1.141 × 10− 1.935 × 10−3 3.282 × 10−3 5.178 × 10−3 2000 8.228 × 10−7 1.237 × 10−5 6.206 × 10−5 1.889 × 10−4 4.575 × 10−4 9.303 × 10−4 1.680 × 10−3 2.661 × 10−3 4.040 × 10−3

Table A.4. Cross sections in pb for all generated LQ events for the decay scenario S3 → bµ. Obtained values from MadGraph5_aMC@NLO are rescaled by a K-factor of 1.5 to account for NLO QCD corrections. For each entry, N = 100000 events are produced.

MLQ [GeV] λ = 0.25 λ = 0.50 λ = 1.00 λ = 1.50 λ = 2.00 λ = 2.25 400 9.285 × 10−3 1.282 × 10−1 1.236 × 100 3.153 × 100 5.018 × 100 5.717 × 100 600 1.475 × 10−3 2.000 × 10−2 1.745 × 10−1 4.362 × 10−1 6.564 × 10−1 7.349 × 10−1 800 2.880 × 10−4 3.848 × 10−3 3.284 × 10−2 7.986 × 10−2 1.202 × 10−1 1.360 × 10−1 1000 6.284 × 10−5 8.411 × 10−4 7.244 × 10−3 1.767 × 10−2 2.702 × 10−2 3.042 × 10−2 1200 − 1.995 × 10−4 1.703 × 10−3 4.263 × 10−3 6.653 × 10−3 7.670 × 10−3 1400 3.128 × 10−6 4.181 × 10−5 4.023 × 10−4 9.954 × 10−4 1.652 × 10−3 1.998 × 10−3 1600 5.954 × 10−7 7.916 × 10−6 7.590 × 10−5 2.397 × 10−4 4.473 × 10−4 5.804 × 10−4 1800 5.547 × 10−8 7.937 × 10−7 1.168 × 10−5 5.270 × 10−5 1.308 × 10−4 1.998 × 10−4 2000 2.895 × 10−8 3.642 × 10−7 6.540 × 10−7 1.065 × 10−5 4.632 × 10−5 7.782 × 10−5

Table A.5. Cross sections in pb for all generated LQ events for the decay scenario S3 → tν. Obtained values from MadGraph5_aMC@NLO are rescaled by a K-factor of 1.5 to account for NLO QCD corrections. For each entry, N = 100000 events are produced. 79 Appendix A. Additional Tables

λ observed lower limit on MLQ [GeV] 0.25 – 0.50 700 0.75 930 1.00 1030 1.25 1140 1.50 1180 1.75 1190 2.00 1220 2.25 1250

Table A.6. Observed lower exclusions limits on the LQ mass for different values of the Yukawa coupling λ for the S3 coupling to tµ. For the value of λ = 0.25, the mass exclusion limit can not be obtained as it is not located within the studied MLQ-range.

λ observed lower limit on MLQ [GeV] 0.25 – 0.50 680 1.00 1030 1.50 1180 2.00 1240 2.25 1250

Table A.7. Observed lower exclusions limits on the LQ mass for different values of the Yukawa coupling λ for the S3 coupling to tµ,bν.

λ observed lower limit on MLQ [GeV] 0.25 420 0.50 960 0.75 1280 1.00 1520 1.25 1720 1.50 1900 1.75 > 2000 2.00 > 2000 2.25 > 2000

Table A.8. Observed lower exclusions limits on the LQ mass for different values of the Yukawa coupling λ for the S3 coupling to bµ.

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88 Danksagung

An dieser Stelle möchte ich mich bei all denjenigen bedanken, die mich auf meinem Weg durch das Studium bis hin zu dieser Arbeit begleitet haben. Zuerst bedanke ich mich bei Prof. Dr. Johannes Haller für die Möglichkeit, meine Master- arbeit in seiner Forschungsgruppe zu absolvieren. Das vielleicht etwas ungewöhnliche Thema einer phänomenologischen Studie hat mir extrem gut gefallen und mir viele interessante Ein- blicke theoretischer und experimenteller Hinsicht erlaubt. Auch für die vielen hilfreichen Tipps und Kommentare in den wöchentlichen Montagsmeetings bin ich sehr dankbar. Ganz herzlich bedanke ich mich auch bei Dr. Roman Kogler, nicht nur für die Übernahme des Zweitgutachtens, sondern insbesondere für die zahlreichen Gespräche und Ideen, die meinen Horizont stets erweitert haben. Ein großes Dankeschön geht an Dr. Paolo Gunnellini, hier ausnahmsweise mal auf Deutsch. Vielen Dank für die tolle Betreuung! Die durchgängige Unterstützung war unverzichtbar für das Gelingen dieser Arbeit. Grazie mille! Um meinen Dank gegenüber Arne Reimers auszudrücken, reichen diese Zeilen definitiv nicht aus. Als designierter Leptoquark-Experte musste er für unzählige Fragen vom ersten bis zum letzten Tag herhalten. Vielen Dank für alles, was du für mich getan hast! Ich hoffe mein Remo- deling ist deiner Analyse gerecht geworden ;) Der restlichen Arbeitsgruppe, bzw. allen Personen mit denen ich im Laufe der Masterarbeit in Kontakt war, danke ich für die freundschaftliche Arbeitsatmosphäre und die mir entgegenge- kommene Hilfsbereitschaft. Insbesondere sind hier meine “office buddies” Ksenia, Christopher und Nino hervorzuheben, die mich über viele Monate hinweg unterstützt und ertragen haben. Hinzu kommt Jan, der glücklicherweise seine Masterarbeit im selben Zeitraum wie Nino und ich absolviert hat, sodass viele Probleme gemeinsam gelöst werden konnten. Die Gemeinschaft und Freundschaft mit euch beiden haben mir das Leben sehr erleichtert. Außerdem möchte ich mich noch bei Andrea für viele hilfreiche Tipps und Hinweise sowie das Korrekturlesen bedanken. Zu guter Letzt bedanke ich mich meiner Familie und bei meinen Freunden, die mich über die vielen Jahre des Studiums hinweg unterstützt haben. Natürlich sind hier meine Eltern zu nennen. Vielen Dank nicht nur für die finanzielle Unterstützung, sondern auch für die Hilfe in verschiedensten Situationen. Bei meiner Freundin bedanke ich mich für die bedingungslose, liebevolle Unterstützung. Mein Dank gilt selbstverständlich auch den Personen, die hier nicht namentlich erwähnt wurden. Danke vielmals!

Eidesstattliche Erklärung

Ich versichere, dass ich die beigefügte schriftliche Masterarbeit selbstständig angefertigt und keine anderen als die angegebenen Hilfsmittel benutzt habe. Alle Stellen, die dem Wortlaut oder dem Sinn nach anderen Werken entnommen sind, habe ich in jedem einzelnen Fall unter genauer Angabe der Quelle deutlich als Entlehnung kenntlich gemacht. Dies gilt auch für alle Informationen, die dem Internet oder anderer elektronischer Datensammlungen entnommen wurden. Ich erkläre ferner, dass die von mir angefertigte Masterarbeit in gleicher oder ähnlicher Fassung noch nicht Bestandteil einer Studien- oder Prüfungsleistung im Rahmen meines Studi- ums war. Die von mir eingereichte schriftliche Fassung entspricht jener auf dem elektronischen Speichermedium. Ich bin damit einverstanden, dass die Masterarbeit veröffentlicht wird.

Ort, Datum, Unterschrift