Constraints of Leptoquark Models with CMS Data...Henrik Jabusch November 2019 Eingereicht am 27. November 2019 1. Gutachter: Prof. Dr. Johannes Haller 2. Gutachter: Dr. Roman Kogler

Constraints of Leptoquark Modelswith CMS Data

Masterarbeit

vorgelegt von

Henrik Jabusch

November 2019

Eingereicht am 27. November 2019

1. Gutachter: Prof. Dr. Johannes Haller2. Gutachter: Dr. Roman Kogler

Abstract

Recently observed deviations from the Standard Model prediction in B meson decays couldbe explained by existence of leptoquarks (LQs). LQs are new hypothetical bosons mediatingtransitions between leptons and quarks, and are predicted by several different theories beyondthe Standard Model. Many direct searches for LQs have been performed at the Large HadronCollider 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 scalarleptoquarks decaying exclusively into top quarks and muons is presented using a parameterizeddescription of the CMS detector. The results are validated against those obtained with a fulldetector simulation. Good agreement is found.

A reinterpretation of CMS data is performed to test a novel LQ flavor model motivated byrecent hints towards lepton flavor universality violation. It includes sophisticated productionprocesses of scalar leptoquarks beyond those of pair production only, which depend on thestrength of the Yukawa coupling λ between the LQs and the quarks and leptons. The impacton the LQ production cross section and the kinematics of such decays is studied. For the scalarleptoquark S3, different couplings to third-generation quarks and second-generation leptons arestudied and limits on the mass and the production cross section are derived. The LQ couplingto a b quark and a muon is constrained for the first time and found to yield the most stringentexclusion 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 neuehypothetische Bosonen, die Lepton-Quark-Übergänge vermitteln und von mehreren verschie-denen Theorien jenseits des Standardmodells vorhergesagt werden. Viele direkte Suchen nachLQs wurden am Large Hadron Collider am CERN durchgeführt, ohne dass derzeit Beweise fürderen 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 nachPaarproduktion von skalaren Leptoquarks gesucht, welche ausschließlich in Top-Quarks undMyonen 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 LQsjenseits der Paarproduktion, welche von der Stärke der Yukawa-Kopplung λ zwischen den LQsund 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 Leptonender dritten Generation untersucht und Grenzen auf die Masse sowie den Produktionswirkungs-querschnitt abgeleitet. Zum ersten Mal wird die LQ-Kopplung zu einem Bottom-Quark undeinem Muon eingeschränkt. Diese stellen zudem die stärksten unteren Ausschlussgrenzen derMasse des S3 dar. Für λ= 1 beträgt diese MLQ = 1520 GeV.

Contents

1. Introduction 1

2. The Standard Model and Leptoquarks in BSM Physics 3

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

7.2.1. Decay Scenario: S−1/33 → tµ− . . . . . . . . . . . . . . . . . . . . . . 61

7.2.2. Decay Scenario: S−1/33 → tµ−, bν . . . . . . . . . . . . . . . . . . . . 65

7.2.3. Decay Scenario: S−4/33 → bµ− . . . . . . . . . . . . . . . . . . . . . . 68

7.2.4. Decay Scenario: S+2/33 → tν . . . . . . . . . . . . . . . . . . . . . . . 71

8. Conclusion and Outlook 74

A. Additional Tables 76

Bibliography 81

v

1. Introduction

In particle physics, the Standard Model (SM) is a theory that describes three of the four knownfundamental forces (the electromagnetic, weak and strong interactions) and classifies all knownelementary particles. Formulated in the 1970’s as a gauge quantum field theory, the SM isextremely successful to date, tested in numerous experiments with unimagined precision. Al-though the SM is renormalizable and mathematically self-consistent, it leaves some questionsunanswered. 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 lat-est breaks down at energy scales where gravitation comes into play. This energy scale, calledPlanck scale, is of order 1019 GeV. Compared to the electroweak scale of about 100 GeV, thisgives 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, asquadratically 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. GrandUnified 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 flavoruniversality (LFU). Hints for such BSM effects have recently been observed in the decay of Bmesons. Since LQs could explain all observed deviations simultaneously, they are promisingcandidates for new physics. Searches for LQs have been performed in many experiments, wheremany 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 generallyobtained by simplified models considering leading-order diagrams for LQ pair production crosssection only. A deeper investigation with more sophisticated models is needed to identify theregions of the LQ parameter space that are already excluded by current measurements, and inparticular those that are not ruled out yet.

This thesis aims at an exploration of the LQ parameter space by performing a more physicallycomplete 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 per-formed by the CMS collaboration [1] is remodeled using the fast simulation approach of theDELPHES 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 amore sophisticated LQ model that includes additional LQ production processes, which addi-tionally depend on the Yukawa coupling λ between LQs and quarks and leptons. Using datacollected from the Compact Muon Solenoid (CMS) detector, constraints on the LQ mass, theLQ production cross section and also the Yukawa coupling are set.

This thesis is organized as follows. Chapter 2 discusses the theoretical foundations introduc-ing the SM and several BSM theories. The phenomenology of LQs is presented in Chapter 3,including a novel LQ flavor model. A brief introduction to the Large Hadron Collider (LHC)and the CMS experiment is given in Chapter 4. Chapter 5 summarizes the LQ analysis per-formed by the CMS collaboration, which is remodeled with DELPHES fast simulation in Chap-ter 6. Results of the search testing the novel LQ flavor model with the remodeled analysis arepresented in Chapter 7. The thesis is concluded and an outlook is given in Chapter 8.

2

2. The Standard Model andLeptoquarks 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 parti-cles and their interactions with each other, except gravity. As the SM has open questions andcannot explain some observed phenomena, a selection of its most important shortcomings ispresented in Section 2.2, whereas possible theories beyond the Standard Model are highlightedin Section 2.3.

2.1. The Standard Model of Particle Physics

The SM describes the fundamental components of matter consisting of fermions as well asthe way they interact with each other via bosons. Each interaction has an underlying gaugegroup that determines its properties. For the strong interaction, which is described by quan-

tum chromodynamics (QCD), the local symmetry group is SU(3)C . The weak and electro-magnetic interactions can be unified to the electroweak interaction whose symmetry group isSU(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 divergen-cies from higher-order loop corrections cancel and observables remain finite. The fundamentalobjects of the SM are quantum fields, which are defined at all points in the four-dimensionalspacetime (x,y,z, t). Particles are quantum excitations of such fields and are distinguished bytheir spin s: fermions have half-integer spin s = 1

2 and follow the Fermi-Dirac statistics andPauli’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 leftcorner denote the mass, charge and spin of the respective particle. For the neutrinos νe,µ,τ uppermass 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 aregrouped 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—withthe electric chargeQ= +2

3e, and the three down-type quarks—the down d, the strange s and thebottom b quark—withQ=−1

3e. For each of the twelve fermions there is an anti-fermion f withopposite electric charge and same properties otherwise. In contrast, spin-1 vector bosons—theW± bosons, the Z0 boson, the photon γ and the gluons g—mediate the fundamental gaugeinteractions between fermions. Thus, they are also called gauge bosons. With its discovery in2012, the scalar Higgs boson (H) completes the set of elementary particles and plays a centralrole in the SM since it explains how the gauge bosons W± and Z0 and the fermions obtain mass(see Section 2.1.3).

4


2.1.1. Quantum Chromodynamics: The Strong Interaction

The strong interaction is described by QCD, a non-Abelian gauge theory based on the symme-try group SU(3)C , where the subscript C denotes the color charge, the QCD equivalent to theelectric 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,

∂µ→Dµ = ∂µ− igsTaAaµ (2.2)

where gs is a free, real parameter—the gauge coupling of the strong interaction, T a are the eightgenerators of the SU(3)C group given by the Gell-Mann matrices λa/2, and Aaµ are eight vectorfields corresponding to the eight mediating gluons.

The full QCD Lagrangian reads2

LQCD =−14G

aµνG

µν,a+∑

fqf iγ

µDµ qf−mf qf qf. (2.3)

The first term accounts for the gluon kinematics containing the gluon field strength tensor Gaµν ,which allows self-interaction between gluons. Quark kinematics are described by the secondterm 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 fcarrying color charge, i.e. the six quarks. The last term represents the mass term with the quarkmasses mf.

A unique feature of the strong interaction comes with the behavior of its coupling gs. Sincegs is energy dependent, it is referred to as running coupling. It can be approximately describedby

αs(Q2) = gs(Q2)4π ∝ 1

log(Q2/Λ2) (2.4)

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 processcalled hadronization sets in. It describes the phenomenon that quarks and gluons can neitherbe 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 ofthe path integral formulation [8, 9], which are not included here.

5


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 fromRef. [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 becomeslarge enough to spontaneously produce a quark-antiquark pair. Color-neutral states with two orthree quarks are formed, mesons or baryons, respectively. Prominent examples of baryons to benamed 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 interactionstrength between quarks and gluons almost vanishes: they reside in asymptotic freedom. Sincethis effect plays an important role for the proton and its structure, more details on this as wellas 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 com-plex energy-dependent structure. This structure is typically investigated in deep-inelastic scat-

tering (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’sfour-momentum P and the rest of the proton fragments into hadrons. An important quantity is

6


the Bjorken scaling variable defined as

x= Q2

2qP , (2.5)

where Q2 = −q2 is the negative squared momentum transfer in the scattering process. The in-ternal structure of the proton is characterized by parton distribution functions (PDFs) f , whichdescribe the probabilities for finding a given parton dependent on its momentum fraction x atthe 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 con-tributions from gluons and sea quarks—virtual quarks produced by gluons as quark-antiquarkpairs in higher order processes—arise with decreasing x. Sea quarks can have any flavor, butlight quarks such as u,d,s and c are dominant. With higher energy scales Q2, finer structures be-come visible. Gluon and sea quark PDFs increase significantly and even b-flavored sea quarksappear. 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]. Butalso for the remaining phase space DGLAP equations allow extrapolations.

In proton-proton (pp) collisions, the matrix element of a given subprocess σij depends onthe energy scale Q2 and the momentum fractions x1,2 of the partons involved. One thereforeintroduces the effective center-of-mass energy

√s =√x1x2s, where

√s is the center-of-mass

energy in the pp collision. According to the factorization theorem [14], the inclusive crosssection of pp collisions is given by the convolution of σij and the PDFs,

σpp =∑i,j

∫∫dx1dx2 fi(x1,Q

2)fj(x2,Q2) σij(x1,x2,Q

2), (2.6)

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 accordingto Noether’s theorem [15], it therefore has a conserved quantity, the third component of the weakisospin T3. It is the weak equivalent to the electric charge in electromagnetism and the colorcharge in QCD. Thus, T3 serves as a quantum number and determines particle behavior in weakinteractions. For a detailed understanding, the concept of chirality is introduced. For masslessparticles, chirality is the same as helicity which is the sign of the projection of a spin of a particle

7


~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 thePoincaré group. The Wu experiment [16] in the 1950s showed that parity is violated in weakinteractions, i.e. its occurrence depends on chiral properties of the participating fermions: onlyleft-handed fermions and right-handed anti-fermions take part in charged-current (CC) weakinteractions. They can be arranged in isospin doublets with T3 = +1

2 in the upper and T3 =−12

in the lower entry,

ud′

L

,

cs′

L

,

tb′

L

and

νe

e

L

,

νµ

µ

L

,

ντ

τ

L

. (2.7)

Right-handed fermions and left-handed anti-fermions do not contribute to CC-weak interactionsand 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. Byexchanging W± bosons (T3 = ±1) leptons can change their flavor within a doublet, whereasquarks can also change their flavor to the one of a different doublet. This phenomenon is calledflavor mixing and is a consequence of the inequality of flavor and mass eigenstates3. Mass andflavor eigenstates are related via the complex unitary Cabibbo-Kobayashi-Maskawa (CKM)matrix VCKM,

d′

s′

b′

= VCKM

dsb

=

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

dsb

, (2.9)

where (d′,s′,b′) denotes the flavor eigenstates and (d,s,b) the mass eigenstates. The probabil-ity for a given quark transition is proportional to the absolute square of the respective matrixelement, |Vij|2. These matrix elements are measured by different experiments individually. Acombined global fit yields [17]

|Vij|=

0.97420±0.00021 0.2243±0.0005 (3.94±0.36)×10−3

0.218±0.004 0.997±0.017 (42.2±0.8)×10−3

(8.1±0.5)×10−3 (39.4±2.3)×10−3 1.019±0.025

. (2.10)

3By convention, the representation of down-type quarks is used here. Other conventions, e.g. a definition in termsof mass eigenstates of up-type quarks (u′,c′, t′), are equally valid.

8


Electroweak Symmetry Breaking: The Higgs Mechanism

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

∂µ→Dµ = ∂µ+ ig T aLWaµ + i

2 g′Y Bµ, (2.11)

to obtain local invariance under the symmetry group. Here, four vector fields W 1,2,3µ ,Bµ and

the generators T aL = σa/2 of SU(2)L, given by the Pauli matrices σa,a ∈ {1,2,3}, appear.

The Lagrangian results in

LEW =−14(Wµν,aW a

µν +BµνBµν)

+∑ψ

ψ iγµDµψ, (2.12)

containing vector-boson kinematics and self-interaction terms, as well as kinematic terms of thefermion fields ψ and their interaction to the vector-bosons W 1,2,3,B. The two parameters g andg′ in Eq. (2.11) are electroweak coupling constants related by the Weinberg angle θW,

tanθW = g

g′. (2.13)

Since g and g′ are running constants, θW is also scale-dependent. At the Z mass scale, it is givenby sin2 θW(MZ)≈ 0.231 [17]. Furthermore, the Weinberg angle θW describes a rotation relatedto the spontaneous symmetry breaking of the EWT. The fields of the four gauge bosons that arephysically observed—the photon field Aµ and the weak boson fields W±µ ,Zµ—are mixtures ofthe four vector fields W 1,2,3

µ ,Bµ:

W±µ = 1√2(W 1µ ∓ iW 2

µ

),

AµZµ

= cosθW sinθW

−sinθW cosθW

BµW 3µ

. (2.14)

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

9


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=φ+

φ0

= 1√2

φ1 + iφ2

φ3 + iφ4

, (2.15)

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,

LH = (Dµφ)†(Dµφ)−V (φ). (2.16)

Here, Dµ is the covariant derivative of the EWT from Eq. (2.11) and V (φ) is the so-calledHiggs potential. Invariance under rotations of φ+ and φ0 as well as invariance under changesof a complex phase require the potential to show a dependence on |φ|2 only. Further constraintsfrom 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, becauseotherwise the vacuum would not be stable. If µ2 is also positive, µ2 > 0, the ground stateremains at |φ|= 0. For µ2< 0 however, the symmetry is spontaneously broken and the minimumof the potential changes to the vacuum expectation value

v =√−µ2

λ, (2.18)

as depicted in Fig. 2.3. In four dimensions this is not a single minimum, but a continuum of

10


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

φvacuum = 1√2

0v

→ φ= 1√2

0v+H

. (2.19)

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

V (φ) =−µ2H2 +λvH3 + 14λH

4. (2.20)

The first term has the form of a Higgs mass term with mH =√−2µ2, whereas the H3- and

H4-terms account for self-interaction via three- and four-Higgs vertices. It is notable thatthe Higgs mass is a free parameter in this theory. In 2012, the Higgs boson was discoveredby the experiments ATLAS and CMS with the mass mH = 126.0±0.8 GeV [19] andmH = 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) canbe evaluated such that it contains all kinematic, (self-)interaction and mass terms of the HiggsH and the gauge boson vector fields W 1,2,3

µ ,Bµ. It further provides the W and Z masses

MW = 12gv and MZ = 1

2

√g2 +g′2, (2.21)

which are related via the weak mixing angle, MW =MZ cosθW . The experimentally measuredvalues are MW = (80.379±0.012) GeV and MZ = (91.1876±0.0021) GeV [17]. The mediatorparticles being massive is the main reason for the “weakness” of the weak interaction and itsshort range. Furthermore, the vacuum expectation value of the Higgs field can be determinedvia the Fermi coupling constant GF,

v = 1√√2GF

= 2MW

g' 246.22GeV. (2.22)

It marks the unification scale of the EWT.

The Higgs as an isospin doublet allows a connection of fermion doublets and singlets suchthat their mass terms become gauge invariant. For a given fermion f, the corresponding La-grangian reads

L =−mfψfψf−mf

vHψfψf, (2.23)

which further includes a chirality-changing process via the Higgs. The fermion mass mf is

11


interpreted asmf = λf

v√2, (2.24)

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 areneither 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 openquestions 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 currentunderstanding of gravity is still based on the general theory of relativity that Einstein formulatedover a hundred years ago. Modern approaches to describe gravity as a quantum field theory havenot been successful yet.

The Hierarchy Problem

The hierarchy problem addresses the large discrepancy between aspects of the three funda-mental forces described by the SM and gravity, e.g. gravity is ∼ 1024 weaker than the weakinteraction. Consequently, the Higgs mass mH is unstable with respect to large quantum cor-rections. Higher order contributions such as fermion-antifermion loops add quadratically di-vergent terms ∼ Λ2 to the Higgs mass, where Λ∼ 1019 GeV denotes the Planck scale, up towhich the SM would be valid in case of no new physics. Therefore, the Higgs mass is ex-pected to be of the order∼ 1014−17 GeV, at the Planck scale, which exceeds the measured valueof 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 theSM.

Dark Matter & Dark Energy

The presence of dark matter is known by various astrophysical observations such as measure-ments 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 neutralwith respect to the strong and electromagnetic interaction. The SM does not provide a suitablecandidate. 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 unknownform 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 naturalassumption would be a balanced distribution. Although the SM includes a CP-violating phasein the weak interactions CKM matrix, this is not sufficient to explain the matter-antimatterasymmetry.

Symmetry Between Leptons and Quarks

As fermions are arranged in three generations of matter, each containing two quarks and twoleptons, there might be an underlying symmetry for the fermions of the SM. Also that theelectric charges of quarks are exactly integer thirds of the leptons charge emay 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 phenomenaof 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 experimen-tally established [22] and require neutrinos to have mass. First predicted by B. Pontecorvo in1957 [23, 24], measuring neutrino masses is still a challenge in modern physics.


As the previous section highlights shortcomings of the SM, this section presents theories be-

yond the Standard Model. Since there are many of them, only a brief summary is given in thefollowing.

13


Grand Unified Theories

The aim of grand unified theories (GUTs) [25, 26] is to embed the SM gauge groupSU(3)C ⊗ SU(2)L ⊗ U(1)Y into a higher symmetry group GGUT. Consequently, also the threeSM coupling constants are assumed to unify to a single coupling constant gGUT at the GUT-scale MGUT ∼ 1015 GeV. The SM fermions—along with possible new fermions—are groupedinto multiplets relating the electric charges of leptons and quarks, which constitutes an elegantexplanation to the symmetry of these particles. Furthermore, requiring gauge invariance un-der GGUT gives rise to new gauge bosons that mediate transitions between fermions within amultiplet. Some of them violate lepton and baryon number as they mediate lepton-quark transi-tions. Such new bosons are called leptoquarks. In some models, they are predicted along witha mechanism for neutrino masses. As LQs could also mediate proton decays, “simple” GUTslike 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 eachSM particle it postulates a superpartner with same quantum numbers except the spin, whichdiffers by 1/2. These new sparticles bring additional loop contributions to the Higgs mass suchthat divergencies (partially) cancel when the superpartner masses (nearly) equal the masses ofthe SM particles. In addition to that, many SUSY models provide an excellent dark mattercandidate, the lightest supersymmetric particle (LSP), usually the neutralino χ0. However, noevidence 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] alsoattempts 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 seemsto be weak in 4D, not because the fundamental scale is large but gravity acts in more thanthree dimensions of space. This solves the hierarchy problem if the real fundamental scale isMD ∼ 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 compos-ite states of so-called preons. Such models provide a lepton-quark symmetry that explains the

14


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 tran-sitions between leptons and quarks. Furthermore, they can also arise in technicolor theoriesand composite Higgs models. In general, LQs could explain why there are three generations ofmatter 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 theSM gauge group and conserve both lepton and baryon number L and B, several LQ states areconsidered by the Buchmüller-Rückl-Wyler model in Ref. [30]. However, LQs have not beenobserved yet, but constraints on their masses were set and searches at the TeV-scale are ongoingat 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 in-troduction to the LQ production in pp collisions is given in Section 3.2, whereas Section 3.3summarizes the current status of LQ searches. Section 3.4 briefly discusses indirect constrainson 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 toSM predictions hint at BSM physics, as they seem to violate lepton flavor universality (LFU).Such ratios are the RD(∗) and RK(∗) rates, referring to B meson decays to D(∗) or K(∗) mesons,respectively. They are defined as

RD(∗) = B(B→ D(∗)τ−ντ)B(B→ D(∗)`−ν`)

and RK(∗) = B(B→ K(∗)µ−µ+)B(B→ K(∗)e−e+)

(3.1)

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

0.2 0.3 0.4 0.5R(D)

0.2

0.25

0.3

0.35

0.4R(D

*)

HFLAV average

Average of SM predictions

= 1.0 contours2χ∆

0.003±R(D) = 0.299 0.005±R(D*) = 0.258

HFLAV

Winter 2019

) = 27%2χP(

σ3

LHCb15

LHCb18

Belle17

Belle19 Belle15

BaBar12

HFLAVSpring 2019

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

b

q

c

q

`+

νW+

B D(∗)b

q

c

q

`+

ν

LQB D(∗)

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

17


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

µ µγ

γ

µ µLQ

t

γ

Figure 3.4. Feynman diagrams for contributions to the muon anomalous magnetic dipole mo-ment 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−

boson exchange with the CKM matrix element |Vcb|2. BSM theories containing LQs, however,allow additional processes contributing to RD(∗) , see Fig. 3.2 right, and therefore could explainthe higher values measured.

Fig. 3.3 summarizes measurements of the ratios RK and RK∗ performed by several exper-iments. The latest results from LHCb [33, 34] show that the experimentally measured valuesare 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-levelin 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 enhancethe SM prediction such that loop-induced LQ couplings are a candidate to explain the measuredsuppression.

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 loopeffects 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 adiagram.

Since the results are not yet conclusive, it remains unclear whether these are hints towardslepton non-universal new physics or not. Either way, new results are awaited to clarify thismatter.

3.2. Production of Leptoquarks in pp Collisions

At leading order (LO), there are two production mechanisms of LQs in pp collisions: singleand pair production. Figs. 3.5 and 3.6 show dominant Feynman diagrams for both types. Notethat only in case of singly produced LQs the production cross section is sensitive to the Yukawacoupling λq` between the LQ and the quark and the lepton. Thus, measuring such processesprovides direct information about the Yukawa coupling matrix λ. For LQ pair production, theflavor couplings come into play when the LQs decay.

One part of this thesis aims at a remodeling of an analysis conducted by the CMS collabo-ration [1]. Therein, a search for scalar leptoquarks coupled to third-generation quarks is per-formed. In particular, LQs that couple to a top quark and a muon only are studied. As singleproduction would require a top quark in the initial state, which is strongly suppressed by the

19


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. Takenfrom Ref. [36].

proton PDFs (cf. Fig. 2.2), that analysis focuses on pair-produced on-shell LQs that decay ex-clusively into top quarks and muons, such that it is tailored to investigate the final state ofpp→ LQLQ→ tµ−tµ+. More details on the analysis procedure can be found in Chapter 5.

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 wasfound 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 scalarLQs set by the ATLAS and CMS Experiments. In all of these searches the LO pair productionprocesses 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. Masslimits for vector LQs are higher in general due to higher production cross sections.

20

3.4. Indirect Constraints on Leptoquarks

decay modelower mass limit [GeV] lower mass limit [GeV]

by ATLAS by CMS

qe qe 1400 1435qe qν 1290 1270qµ qµ 1560 1530qµ qν 1230 1285qν qν – 980bν bν 970 1100bν tτ 800 800bτ bν 780 –bτ bτ 1030 1020tν tν 1000 1020tµ tµ – 1420tτ tτ 930 900

Table 3.1. Lower mass limits at 95% C.L. by ATLAS [37, 38] and CMS [1, 36, 39–42] onpair-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 cou-ple to any combination of SM fermions. The above mentioned quark transition b→ s, whichoccurs in B meson decays to K mesons, is an example for a FCNC at tree-level and is thereforesuppressed in the SM. However, LQs could invoke such processes on tree-level, placing strongindirect constraints on LQ parameters. As certain quark-quark transitions could affect the pro-ton stability, measurements of the proton lifetime strongly constrain corresponding couplings.For LQs coupling to more than one generation of leptons, lepton flavor violating processeswould arise. Examples are `→ `′γ and `→ 3`, mediated by LQ loops. The signatures of suchdecays would be observable in low-energy precision measurements. However, no evidence fortheir 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 physicseffects provoked by LQs concerning precision experiments and particle colliders can be foundin 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


in B decay observables as described above.

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

LYuk = λQCαL (iσ2)αβ(S3)βγLγL + Yκ QCαL (iσ2)αβ(S†3)βγQγL + h.c., (3.2)

where σ2 denotes the second Pauli matrix, α,β,γ are SU(2)L indices and ψC indicates thecharge 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 itsisospin components, the S3 can be written as

S3 = S

1/33

√2S4/3

3√2S−2/3

3 −S1/33

, (3.3)

where the superscripts denote the electric charge in units of e. Expanding the quark-lepton termof Eq. (3.2) yields

LQL =−√

2λdCL`LS4/33 −λdCLνLS

1/33 +

√2λuCLνLS

−2/33 −λuCL`LS

1/33 + h.c., (3.4)

in which the same couplings λ for each representation of the S3 appear. The Yukawa matricesare given by

λD =

λde λdµ λdτ

λse λsµ λsτ

λbe λbµ λbτ

and λU = V ∗CKMλU , (3.5)

with U = u,c, t and D = d,s,b, and indicate the couplings to up- and down-type quarks, respec-tively. At this point, two assumptions are made: i) The SM hierarchy for the Yukawa couplingsof the quarks also applies to those of the LQs, i.e. couplings to third generation quarks are dom-inant, and ii) since possible BSM effects of RK(∗) predominantly depend on the b→ sµ+µ−

observables, the dominant couplings are λbµ ≡ λ0 and λsµ ∼ ε2λ0. Here, ε ∼ 0.2 denotes aflavor parameter of the size of the sine of the Cabibbo angle as it is, for instance, realized with

22


Figure 3.7. Parameter space λ0(MS3) of the S3 leptoquark. The red band corresponds tothe RK(∗) data favored region of Eq. (3.7). Considering a narrow width, Γ/MS3 . 5%, yieldsλ0 . 1.1 which is depicted in yellow. Predictions from viable flavor models on λbµ [48] areshown as a green horizontal band. Taken from Ref. [45].

a Froggatt-Nielsen-Mechanism [46]. This leads to a simplified coupling matrix

λD ∼ λ0

O(ε3) O(ε3) O(ε3)∗ ε2 ∗∗ 1 ∗

. (3.6)

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

MS3

11.6 TeV. λ0 .

MS3

3.9 TeV. (3.7)

In Fig. 3.7 the relevant parameter space of the S−4/33 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. Neglectingthe masses of the decay products, the partial decay width is given by

Γ(S3→ q`) = c|λq`|2

16π MS3 , (3.8)

with c = 2 for S4/33 ,S

−2/33 and c = 1 for S1/3

3 , cf. Eq. (3.4). If λq` is the dominant coupling, Γ

23


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 Yukawacoupling λ is denoted in red.

approximates the total width. Possible decays are constrained by the assumptions made and theelectric charge. They are:

S+2/33 → tν, S

−1/33 → bν, tµ−, S

−4/33 → bµ−. (3.9)

Although its representations have different electric charges and thus different decay modes, theS3 leptoquark is a single particle with the mass MS3 .

In contrast to traditional LQ searches that assume simple LQ pair production processes, thismodel includes additional production processes at LO. Fig. 3.8 shows Feynman diagrams ofsuch inclusive production processes yielding the same final state q`q` as expected from LQ pairproduction. Since this model is not capable of NLO calculations, the obtained cross sectionsfrom the Monte Carlo (MC) generator MadGraph5_aMC@NLO are multiplied with aK-factor thataccounts for NLO QCD corrections. Fig. 3.9 shows that the K-factor for scalar LQs is found tobe 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 pro-duction for different values of the Yukawa coupling λ considering a coupling to tµ only. It isobserved that the cross sections for the inclusive LQ production are about one order of magni-tude 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 thecross sections for inclusive LQ production are higher than those of pair production. The impactof 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


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

400 600 800 1000 1200 1400 1600 1800 2000 [GeV]LQM

7−10

6−10

5−10

4−10

3−10

2−10

1−10

1

10

210

[pb]

σ

µ t →LQ pair prod. (PYTHIA 8.205)

= 0.5λincl. prod. (MadGraph5), = 1.0λincl. prod. (MadGraph5), = 1.5λincl. prod. (MadGraph5),

Figure 3.10. Inclusive production cross section σ for the LQ coupling to tµ (blue) as a functionof 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 forNLO QCD corrections.

25


1 2 3 4 5

λ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

[TeV

]Γ

= 0.7 TeVLQM = 1.0 TeVLQM = 1.3 TeVLQM

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

Eq. (3.8) is shown. The parameter c is set to unity, which corresponds to the S−1/33 . The

quadratic dependence of Γ on the strength of the Yukawa coupling λ is visible as well as thelinear dependence on the LQ mass MLQ. These dependencies show that for models allowingmore 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 quarksperformed by the CMS collaboration [1] with the DELPHES framework for detector simulationand verify its validation. In a further step, the analysis is used for a reinterpretation of CMSdata within a more sophisticated LQ model.

In order to understand possible differences in the detector simulation between GEANT andDELPHES, the LHC is introduced in Section 4.1, followed by an overview of the CMS detectorcomponents in Section 4.2.

4.1. The Large Hadron Collider

The Large Hadron Collider at CERN1 (the European Organization for Nuclear Research) isthe 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 ofthe LHC was and is to answer fundamental open questions in particle physics, like the dis-covery 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 pro-tons can be injected to the LHC tunnel of ∼ 27 km circumference, they need to pass severalstages of pre-acceleration. Starting with electrons from a thermionic cathode ionizing gaseoushydrogen, the resulting protons are extracted with an energy of Ep = 90 keV. After the subse-quent linear acceleration with Linear Accelerator 2 (LINAC2, Ep = 50 MeV), a set of circularcolliders 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 theSPS and are injected into the LHC as two beams with opposite directions, where they are fur-ther 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


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

28

4.1. The Large Hadron Collider

1 Apr1 M

ay1 Ju

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l1 Aug

1 Sep1 O

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Data included from 2010-03-30 11:22 to 2018-10-26 08:23 UTC

2010, 7 TeV, 45.0 pb¡1

2011, 7 TeV, 6.1 fb¡1

2012, 8 TeV, 23.3 fb¡1

2015, 13 TeV, 4.2 fb¡1

2016, 13 TeV, 41.0 fb¡1

2017, 13 TeV, 49.8 fb¡1

2018, 13 TeV, 67.9 fb¡1

0

20

40

60

80

100

CMS Integrated Luminosity Delivered, pp

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

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

L=Nbfrevn1n2

4πσxσy. (4.1)

Each beam consists of Nb = 2808 proton bunches uniformly separated in time by ∼ 25 ns witha length of∼ 30 cm. Every bunch contains ni ≈ 1.2×1011 protons. The revolution frequency isfrev = 11.245 kHz and 4πσxσy describes the spatial expansion of the bunches in the transverseplane perpendicular to the beam axis assuming Gaussian profiles. The designed peak luminosityof L= 1.0×1034 cm−2s−1 was already exceeded by 40% in the 2016 data-taking period of Run2. The event rate of a given physical process with the cross section σ is

d

dtN = σL. (4.2)

Integrating over time yields the expected number of events

N = σ∫Ldt= σLint, (4.3)

where Lint is the integrated luminosity. The integrated luminosity as a function of time forseveral data-taking periods is displayed in Fig. 4.2.

The LHC accommodates a total of four major experiments. ATLAS (A Toroidal LHC Ap-

29


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 ofphysics. Therefore, its setup is determined by the aim to detect different kinds of particles. Theviews 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 detectorcomponents, 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) canbe used. Its origin coincides with the nominal collision point. The x-axis points radially inwardtowards the center of the LHC ring, the y-axis points vertically upwards and the z-axis pointsalong the beam in counterclockwise direction. However, a more appropriate description is givenby a cylindrical coordinate system (r,φ,θ), which reflects the detector design and accounts forthe angular dependencies of pp collisions. Thus, r is the radial distance to the z-axis, theazimuth φ is the angle in the x-y-plane enclosed with the x-axis, and the polar angle θ spansbetween the x-y-plane and the z-axis. In pp collisions, the momentum of the initial state partonsalong 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 replaceθ,

η =− ln[tan

(θ

2

)], (4.4)

such that ∆η is Lorentz invariant. Consequently, also the angular distance ∆R between twopoints in the η-φ-plane, defined as

∆R =√

(∆η)2 + (∆φ)2, (4.5)

is invariant under Lorentz transformations in z-direction. The four-momentum of a particleis therefore specified in terms of (E,px,py,pz)→ (E,pT,η,φ) with the transverse momentumpT =

√p2x+p2

y.

30


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 theCMS detector. Taken from Ref. [56].

31


Figure 4.5. Schematic view on the upper half of the CMS tracker in the r-z-plane. The starmarks 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 interactionpoint and aims at a precise reconstruction of trajectories of charged particles. The cylindricaltracker has a length of ∼ 5.8 m and a diameter of ∼ 2.5 m, covering a region of |η| < 2.5. Thelayout shown in Fig. 4.5 consists of two different types of silicon detectors: pixel and stripsensors.

Closest located to the interaction point is the pixel detector (PIXEL). In the data-taking periodof 2016, it comprised three pixel layers in the barrel region at r= 4.4,7.3,10.2 cm, and two pairsof endcap disks at z = ±34.5,±46.5 cm in each forward region. In total, the 66 million pixelsensors 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 thebarrel 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, each320 µm thick and with a pitch of 80− 120 µm. Further outside, the TOB covers the region tor < 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 coveredregion to |z|< 282 cm and consist of three and nine layers, respectively.

32


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

Electromagnetic Calorimeter

The electromagnetic calorimeter (ECAL), shown in Fig. 4.6, surrounds the tracking system andmeasures 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 highdensity (ρ = 8.28g/cm3), 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 sizeincreases from 22× 22mm2 at the front to 26× 26mm2 at the rear face with a length of23.0 cm corresponding to 25.8X0. In total, the barrel has a crystal volume of 8.14m3 and itweighs 67.4 t. The EE however, covers the region 1.479 < |η| < 3.0, has crystal sizes from28.6×28.6mm2 to 30× 30mm2 with a length of 22.0 cm (24.7X0), a volume of 2.90m3

and a weight of 24.0 t. Additional preshower modules (ES) located in front of the EEs cover1.653< |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]

σEE

= 2.8%√E [GeV]

⊕ 12%E [GeV] ⊕0.30%, (4.6)

where the first term accounts for stochastic effects from the shower development, the secondterm specifies electronic noise and the third constant term reflects calibration errors and non-uniform light collection.

33


Figure 4.7. Longitudinal view of the CMS detector including the HCAL. The values at thedashed 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 thehadronic jets as well as missing transverse energy (MET). Hadrons typically have a higher in-teraction length λI than the radiation length of electrons and photons, such that hadrons traversethe 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 twobarrel parts, the hadron barrel (HB) and hadron outer (HO), as well as two endcap parts, thehadron 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 theoutside (r = 2.95 m). The HB covers |η| < 1.3 and consists of 36 azimuthal wedges whichin turn contain 18 absorber plates each and active scintillator material. The latter is furthergrouped into multiple towers, each of them covering 0.087× 0.087 in the η-φ-plane. The HOextends the HB in the central η-region outside the solenoid to increase the sampling depth forthe 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 re-gion close to the beam pipe, the HFs complete the calorimeter. Since these have to be especiallyradiation hard, their absorber and scintillator materials are steel and quartz fibres, respectively.

34


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

σEE

= 115.3%√E [GeV]

⊕5.5%. (4.7)

Solenoid Magnet

The superconducting solenoid magnet is the heart of the CMS detector. It has a length of12.9 m and a bore of radius 5.9 m where the inner components tracker, ECAL and HCAL arelocated. Inside the solenoid, a magnetic field of 3.8 T is produced2. The purpose is to bend thetrajectories of charged particles in order to determine their charges and momenta by measuringtheir curvature radii. In the muon system and the return yoke outside the solenoid, an oppositelyaligned field of 2 T bends muons to the opposite direction and thus improves measuring muonmomenta.

Muon System

Muons—considered as minimal ionizing particles (MIPs)—are the only particles besides neu-trinos that traverse the whole inner detector without significant energy loss. Thus, they aredetected in the outermost component of the CMS detector: the muon system. As depicted inFig. 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 muonsvia 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 partup 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), anenormous amount of potential collision data is produced every second. Storing such amount ofdata is not feasible and furthermore only a small fraction is of physical interest. Therefore, atwo-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 calorime-ters 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


Figure 4.8. Cross section of a quadrant of the CMS detector in the r-z-plane showing thecomponents of the muon system (colored). Taken from Ref. [61].

trigger latency of 3.2µs by requiring high-energetic jets, leptons, photons or significant missingtransverse 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, accessesthe complete read-out data and uses more sophisticated algorithms similar to offline analysis tofurther discard events within 50 ms. Hence, the total event rate is reduced to ∼ 100 Hz, suchthat 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 bythe CMS Collaboration [1] is presented. Subsequently, it is remodeled using DELPHES fastsimulation in Chapter 6 and is used for a reinterpretation of the recorded data within a moresophisticated LQ model in Chapter 7.

Section 5.1 introduces the data set and the event generation, whereas Section 5.2 focuses onthe event selection. The reconstruction of the leptoquark mass is explained in Section 5.3 andin 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 exclu-sively 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 35.9 fb−1.

Signal events, i.e. events of the process shown in Eq. (5.1), are simulated with the PYTHIA8.205 [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 generatedwith several different generators. A complete overview can be found in Table A.1. Pile-upsimulations are included for all event samples and the detector response is simulated with theGEANT4 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-upinteractions matches with data.

37


MLQ [GeV] σ [pb] N

200 6.06×101 74079300 8.04×100 73905400 1.74×100 74516500 4.96×10−1 74478600 1.69×10−1 71639700 6.48×10−2 74723800 2.73×10−2 74571900 1.23×10−2 732161000 5.86×10−3 734961200 1.50×10−3 747301400 4.32×10−4 740951700 7.73×10−5 739342000 1.55×10−5 74731

Table 5.1. Summary of simulated signal samples with PYTHIA 8.205. The values in thecolumns 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. Sinceit uses an optimized combination of information from different components of the detector, itprovides an excellent description of the recorded data. The vertex with the largest reconstructedp2

T of physics objects is taken as the primary pp interaction vertex (PV). All detected particlesare reconstructed either as electrons, muons, photons, charged or neutral hadrons. This analysisrequires electrons and muons to have pT ≥ 30 GeV and |η| ≤ 2.4. Furthermore, they have tobe isolated. The muon isolation is PF-based and defined relative to the transverse momentumpµT [65],

Irel =∑h± pT + max

(0,∑h0ET +∑

γET− 12∑PUh± pT

)pµT

< 0.15, (5.2)

where the summed transverse momenta pT or energies ET of charged (neutral) hadrons h± (h0)or photons γ are considered in a cone with radius ∆R = 0.4 around the muon. In order toapproximately correct pile-up (PU) contributions, 1

2∑PUh± pT is subtracted from the overall sum

where∑PUh± 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 andneutral PF candidates from the primary vertex using the anti-kT jet-clustering algorithm [67,68]

38

5.3. Leptoquark Mass Reconstruction

pre-selection

≥ 2 isolated jets with pT ≥ 30 GeV, |η| ≤ 2.4≥ 2 isolated muons with pT ≥ 30 GeV, |η| ≤ 2.4

ST ≥ 350 GeV

full selection

pre-selectionNb-jets ≥ 1

Mµµ ≥ 111 GeVS

lepT ≥ 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 (topright) as well as the categorization scheme (bottom).

with a distance parameter of 0.4, referred to as AK4 jets. The pile-up mitigation technique usedis the charged hadron substraction (CHS) method [69]. The jets are also required to havepT ≥ 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 beb-tagged, to be considered. Requiring the invariant mass of each pair of muons to exceedthe Z boson mass, i.e. Mµµ ≥ 111 GeV, suppresses events from Z boson production with ad-ditional jet radiation. As decays of heavy LQs are expected to produce high-pT leptons andjets, Slep

T ≥ 200 GeV and ST ≥ 350 GeV are required furthermore to suppress SM backgrounds.Herein, Slep

T denotes the scalar pT sum of all selected electrons and muons, whereas ST is thesum of Slep

T , pmissT 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) thereare at least three leptons present—i.e. at least one additional lepton to the two muons requiredin 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 aresummarized.


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

39


W+

W−

b

b

ν

`

q′, ν

q, `

LQ

LQ

g

g

µ

t

t

µ

p

p

Figure 5.1. Feynman diagram of pair-produced LQs decaying to top quarks and muons includ-ing 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 reconstruc-tion of the neutrino. Since neutrinos do not interact with the detector, they only contribute tomissing 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 associatedneutrino, see Fig. 5.1. This ensures that there is exactly one neutrino in the event, whose trans-verse momentum is then assumed to match the missing transverse energy, pνT =��ET. From theconstraint that the invariant mass of the additional lepton and its neutrino equals the W bosonmass,

P 2W =M2

W = (P`+Pν)2 (5.3)

where Pi denotes the four-momentum of the particle i, the z-component of the neutrinos mo-mentum is calculated via

p±z,ν = µpz,`p2

T,`±

√√√√µ2p2z,`

p4T,`−E2` p

2T,ν−µ2

p2T,`

. (5.4)

Here, µ = M2W/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, bothsolutions are considered as independent candidates.

40


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 consideredand one jet is always reserved for the decay of thad, n ∈ [1,max(Njets,6)] candidates for tlep arebuilt, 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 thislepton. In case of at least one electron in the event, the leading electron is taken as the addi-tional lepton `. For zero electrons, there must be at least three muons in the event due to therequirements of the categorization scheme. The three leading muons are taken for constructingtlep. Furthermore, two of these muons must have opposite-sign electric charges (OS) as theyarise directly from the LQ decays. Therefore, both muons with the same charge (SS) couldstem 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 usedfor 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 thefour-momenta of their decay products,

Ptlep =n∑i=1

Pi,jet +P`+Pν`and Pthad =

m∑i=1

Pi,jet. (5.5)

5.3.3. Reconstruction of the Leptoquarks

LQ candidates are assembled by combining top quark candidates and muons. As can be seenfrom Fig. 5.1, the additional lepton from the tlep decay always has OS charge with respect to theprompt muon from the associated LQ decay. Thus, always the muon with OS charge is assignedto LQlep. For the LQhad construction, both muons with SS charge are possible to be paired withthad which again doubles the number of candidates. The four-momenta of the LQ candidatesare given by

PLQlep = Ptlep +PµOS and PLQhad = Pthad +PµSS . (5.6)

Finally, the reconstructed LQ mass is defined as the average invariant mass of the LQ candi-date pair,

M recLQ =

MLQlep +MLQhad

2 . (5.7)

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. Theterm leading then refers to the one(s) with highest pT.

41


be chosen. For this purpose, a χ2-variable is considered which is defined as

χ2 =(Mtlep−M tlep

σlep

)2

+(Mthad−M thad

σhad

)2+∆M rel

LQ−∆M relLQ

σ∆M

. (5.8)

Each of the three terms tests a different reconstructed property. Mtlep and Mthad are the invariantmasses of the tlep and thad candidates, respectively. The variable ∆M rel

LQ, defined as

∆M relLQ =

MLQlep−MLQhad

M recLQ

, (5.9)

denotes the relative difference in the invariant mass of both LQ candidates. The value of χ2 issmall, if the candidate properties Mtlep , Mthad and ∆M rel

LQ are close to the respective expected

values, which are denoted by M tlep , M thad and ∆M relLQ. Those values together with the widths

σlep, σhad and σ∆M are extracted from simulation using Monte Carlo truth information (seeRef. [71]). The pair of LQ candidates with the smallest value of χ2 is chosen as the besthypothesis and its value of M rec

LQ is used in the final statistical analysis for events in category A.

5.4. Results

For the distributions M recLQ 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 obtainedby a simultaneous binned maximum-likelihood template fit of the backgrounds to the data per-formed with the THETA software package [72]. In this fit, all systematic uncertainties are treatedas nuisance parameters. The distributions of M rec

LQ and ST after the background-only fit areshown in Fig. 5.2. No signal of LQ pair production is observed, as the data agrees well with thefitted 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 squaredbranching fraction B2 at 95% C.L. as a function of the LQ mass, see Fig. 5.3. It is assumedthat pair-produced LQs decay exclusively to top quarks and muons, B(LQ→ tµ) = 1, such thatthese LQs are excluded up to masses of MLQ = 1420 GeV at 95% C.L. This is the first and onlylimit in this decay mode.

To further constrain the parameter space, the results of this analysis can be combined withresults of two other analyses each: a search for third-generation scalar leptoquarks decaying totτ [36] and a reinterpretation [76] of a search for pair-produced bottom squarks decaying to aSM b quark and the lightest supersymmetric particle (LSP). Since the LSP is assumed to interact

42

5.4. Results

Figure 5.2. Final distributions of the reconstructed LQ massM recLQ (category A, left) and ST (cat-

egory B, right). Data (black markers), SM backgrounds (colored) and LQ signal distributionsfor various masses (dashed lines) are shown. The hatched areas in the upper panels correspondto the total uncertainty. In category B, the major backgrounds from tt + Drell-Yan (DY) + jetsare estimated from data. Taken from Ref. [1].

[GeV]LQM500 1000 1500 2000

) [p

b]µ t

→(L

Q2

Β × LQ

LQσ

4−10

2−10

1

210

41095% CL upper limit

ObservedExpected68% expected95% expected

LQ pair productionScalar LQ

= 0)κVector LQ ( = 1)κVector LQ (

(13 TeV)-135.9 fb

CMS Supplementary

Figure 5.3. Expected and observed upper limits on the product of the LQ pair production crosssection σLQLQ and the squared branching fraction B2(LQ→ tµ) at 95% C.L. as a function ofthe LQ massMLQ. Unit branching fraction is assumed, B = 1. The black (colored) dashed linescorrespond to the pair production cross sections of scalar (vector) LQs at NLO [50] (LO [75]).Taken from Ref. [1].

43


Figure 5.4. Expected and observed upper limits on cross section for pair-produced LQs de-caying to tµ or tτ (left) and LQs decaying to tµ or bν at 95% C.L. in the plane of MLQ andB(LQ→ tµ). Lower mass exclusion limits on scalar (vector) LQs are derived from predictionsat 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 finalstate of pair-produced LQs that exclusively decay into b quarks and neutrinos. Fig. 5.4 presentsupper limits on the product of the production cross section and the squared branching fractionfor B(LQ→ tµ) = 1−B(LQ→ tτ) (left) and B(LQ→ tµ) = 1−B(LQ→ bν) (right). ForFig. 5.4 left, a full statistical combination of both decay channels is performed by reweight-ing the LQ pair production samples and subsequent decays to the possible final states tµtµ, tτtτand tµtτ2. For Fig. 5.4 right, the LQs are assumed to decay either to tµ or bν, so that for eachvalue of B(LQ→ tµ) the strongest of both limits is considered. This explains the weakest limitsin the transition region B(LQ→ tµ) ≈ 0.3, as none of the analyses is sensitive to events withexactly 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 toMLQ = 900 GeV for all values of B(LQ→ tµ). For pair-produced scalar LQs that exclusivelydecay 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 exclusiveand 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 quarksand muons performed by the CMS Collaboration [1] are reproduced. This analysis remodelinguses the SM background predictions, the statistical and systematic uncertainties, and data pointsof the public CMS results [77]. The signal predictions are generated with PYTHIA version8.230 [62] and the detector response is simulated with the DELPHES framework [2, 78]. Adetailed comparison to the original analysis constitutes an important first step to investigate theperformance of DELPHES fast simulation.

Section 6.1 covers the generation of LQ event samples, whereas Section 6.2 introducesDELPHES and discusses its characteristics. Subsequently, results of this remodeling as wellas 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 tostudy potential differences to the full detector simulation performed with GEANT4, the LQ signalsamples used in the CMS analysis are reproduced. They are generated with PYTHIA version8.230 and contain 100000 events for each simulated LQ mass, ranging from 400 to 2000 GeVin steps of 100 GeV. A summary is given in Table 6.1.

Potential differences between both simulations with GEANT4 and DELPHES are investigatedin the following. At first, kinematic distributions of generator level quantities of the simu-lated 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 inthe CMS analysis (PYTHIA 8.205) and those generated with PYTHIA 8.230. The correspond-ing 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 isevident. The pT- and η-distributions of the LQ (center and right, respectively) show good agree-ment between both simulations as well. The center row shows the same distributions for thetop quark on generator level. For all distributions of mt (left), pT (center) and η (right), good

45


MLQ [GeV] σ [pb] N

400 1.74×100 100000500 4.96×10−1 100000600 1.69×10−1 100000700 6.48×10−2 100000800 2.73×10−2 100000900 1.23×10−2 1000001000 5.86×10−3 1000001100 2.91×10−3 1000001200 1.50×10−3 1000001300 7.96×10−4 1000001400 4.32×10−4 1000001500 2.40×10−4 1000001600 1.35×10−4 1000001700 7.73×10−5 1000001800 4.49×10−5 1000001900 2.62×10−5 1000002000 1.55×10−5 100000

Table 6.1. Summary of simulated LQ event samples with PYTHIA 8.230. The values in thecolumns 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 CMSanalysis are not available. It is evident that the muon mass is treated as a fixed value in PYTHIA8.230, as shown on the left. The pT- and η-distributions of the muon (center and right, respec-tively) are similar to those of the LQ and the top quark. The shape of the pT-distributions of theparticles is consistent with the simulated values of MLQ, showing slightly harder spectra withgrowing MLQ. The distributions of η of both simulation techniques show the expected behav-ior as the particles become more central with increasing generated LQ mass. In all considereddistributions, 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 detectorresponse 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. AlthoughDELPHES is not designed for detailed detector studies, it is a well-suited tool for the approachfollowed in this thesis. Compared to a GEANT-based full simulation, fast simulation techniques

46


0 500 1000 1500 [GeV]LQM

0.2

0.4

0.6

0.8

1

1.2

1.4

Fra

ctio

n of

eve

nts

PYTHIA 8.205 = 0.4 TeVLQM = 0.8 TeVLQM = 1.2 TeVLQM


(13 TeV)

0 500 1000 1500 2000 [GeV]

T,LQp

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Fra

ctio

n of

eve

nts



(13 TeV)

5− 4− 3− 2− 1− 0 1 2 3 4 5

LQη

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Fra

ctio

n of

eve

nts



(13 TeV)

150 160 170 180 190 200

[GeV]tm

0.05

0.1

0.15

0.2

0.25

0.3

Fra

ctio

n of

eve

nts



(13 TeV)

0 500 1000 1500 2000 [GeV]

T,tp

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Fra

ctio

n of

eve

nts



(13 TeV)

5− 4− 3− 2− 1− 0 1 2 3 4 5

tη

0.02

0.04

0.06

0.08

0.1

0.12

Fra

ctio

n of

eve

nts



(13 TeV)

0 0.2 0.4 0.6 0.8 1 [GeV]µm

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Fra

ctio

n of

eve

nts


(13 TeV)

0 200 400 600 800 1000 [GeV]

µT,p

0.02

0.04

0.06

0.08

0.1

Fra

ctio

n of

eve

nts


(13 TeV)

5− 4− 3− 2− 1− 0 1 2 3 4 5

µη

0.02

0.04

0.06

0.08

0.1

0.12

Fra

ctio

n of

eve

nts


(13 TeV)

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

47


like DELPHES are up to three orders of magnitudes faster, which is crucial for a phenomenolog-ical investigation of a large parameter space.

The simulation of the detector response is simplified and is based on parametrization. It in-cludes 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. Foreach detector component, a specific response is considered. Fig. 6.2 shows a simplified chart ofthe workflow in DELPHES. DELPHES allows to access data from different file formats. Event filesfrom external MC generators are first processed by a reader. Pile-up collisions are simulated byoverlapping events from a pre-generated minimum bias sample and the simulated signal. Thesimulated PU profile matches the one of the recorded data in the year 2016. Stable particles arepropagated 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 collectionsof four-momenta, PF tracks and towers. True photons and electrons that reach the ECAL with-out a reconstructed track are reconstructed as photons. Muons and electrons with reconstructedtracks 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 densityis calculated, which is in turn used to perform PU subtraction on jets (with the FastJet pack-age [68, 79] version 3.2.1) and the isolation variable of muons, electrons and photons. No PUsubtraction is performed on the MET. The PF algorithm further yields improved treatment ofb- and τ-tagging as well as jet and missing energy resolutions. Last, duplicates of the objectsare removed and the resulting physics objects that can be reconstructed are jets, MET, isolatedelectrons and muons as well as photons and τ leptons. However, electrons, muons and photonsare assumed to be perfectly identified and without any misidentification. As output, DELPHESstores the events in a tree format of the ROOT framework [80].

A validation of DELPHES against the two major general purpose detectors ATLAS and CMSfor 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 thetuning of DELPHES at reconstruction level. This concerns several characteristics of the analysisas presented in the following, ordered by their appearance in the event selection.

48


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

49


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-sidering the muons from signal events N total

µ that fulfill the pT- and η-cuts and those muonsN isolated

µ that further satisfy the tight isolation working point Irel < 0.15, the isolation efficiencyis εµ =N isolated

µ /N totalµ ≈ 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 misidentifiedtracks included DELPHES, i.e. charged particles that are reconstructed in the detector but do notcorrespond to any particle at generator level are not simulated. This causes less low pT activityinside a cone of R = 0.5 around the muon, cf. Section 5.2. Therefore, the muon isolation re-quirement has to be tuned as a much tighter cut to reduce the efficiency. The cut value is foundto be Irel = 0.02, corresponding to a muon isolation efficiency of

εµ =N isolated

µ

N totalµ

= 31722223346586 ≈ 94.79%. (6.1)

For electrons, the same argumentation holds such that the same cut value is applied, resultingin an efficiency of

εe = N isolatede

N totale

= 188482234590 ≈ 80.35%. (6.2)

Fig. 6.3 shows the distributions of Irel for selected muons and electrons as well as the appliedcut at Irel = 0.02. The tuning of the muon isolation is the crucial one; the pT-distributions ofmuons 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, leptonsneed to be removed from jets. Hence, the angular distance ∆R(jet, `) of every combination ofjets and leptons in the event is calculated. If a combination shows ∆R(jet, `) < 0.4, i.e. thelepton is located inside the AK4 jet, the four-momentum of the lepton is subtracted from thatof the jet. Distributions of ∆R(jet, `) for muons and electrons before and after the cleaning areshown in Fig. 6.5. The peaks around zero in both distributions before the cleaning show thatindeed some leptons are reconstructed inside jets. With the jet-lepton cleaning applied, thesepeaks vanish. Furthermore, the peak around π ≈ 3.14 in the ∆R(jet,µ)-spectrum indicates thatjets and muons are mostly produced back-to-back. This is expected since jets most likely arisefrom the top quark decays, see Fig. 5.1. As electrons often involve photon radiation affecting

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

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

51


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 11.002 65.75 1.103 58.85 0.204 30.57 0.115 28.82 0.016 20.37 < 0.0017 17.41 < 0.00001

Table 6.2. b-tag efficiencies and mistag rates for several working points. These values areobtained from combining all mass samples.

the direction of the electron, their spectrum is much more balanced. The impact on the jetkinematics, 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-definedworking 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 workingpoint to the reference values (efficiency of ∼ 90%, mistag rate of ∼ 10%), i.e. the loosest work-ing point 1, is chosen. Both the b-tag efficiency and the mistag rate are found to agree well. Themistag rate in this context considers misidentification of light partons only, i.e. contributions

52


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Figure 6.6. Transverse momentum pT of selected jets before (dotted) and after (solid) jet-leptoncleaning 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 simulationwith 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 DELPHESand 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 directeffect on the pre-selection. The muon isolation and trigger SFs are pT- and η-dependent andtake values of 0.96− 0.99 and 0.95− 1.00, respectively. Whereas the muon isolation SF isapplied 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 isscaled down by a few percent. However, this does not significantly affect the shape of kinematicdistributions, as shown for the muon pT in Fig. 6.7 before and after applying the SFs discussedabove.

53


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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 thedifferent steps in the LQ mass reconstruction.

The aim of tuning the remodeling with DELPHES is to reproduce the kinematic distributionsobserved in the analysis performed by CMS with high precision. Indicators to validate this arethe number of reconstructed objects N and kinematic observables like pT and η. For muonsand jets, these are compared in Fig. 6.8. Excellent agreement is observed for all distributionsexcept for the jet multiplicity Njets (lower row left), which is lower in case of the remodelingwith DELPHES. This can be explained by the use of a different pile-up mitigation techniqueimplementated 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 lownumber of selected events in the high pT-region.

Not only kinematic observables, but also the selection efficiencies of the cuts applied in thepre- 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 leasttwo muons with pT ≥ 30 GeV, |η| ≤ 2.4 and Irel < 0.02 as defined previously is dominant with aselection efficiency between∼ 70−80% (Fig. 6.9 left) and thus determines the behavior visiblein the total pre-selection efficiency (black solid line in Fig. 6.9 right). The observed deviation

54

6.3. Results

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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 fordifferent mass samples.

55


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Figure 6.9. Signal selection efficiencies of the requirements imposed in the pre-selection as afunction of MLQ for the remodeling with DELPHES (solid) and the original CMS analysis usingGEANT (dashed). In the left plot, the efficiencies are calculated with respect to the previousselection, 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 thedifferences regarding the muon isolation as discussed previously. The two remaining selectionsteps applied afterwards are then almost fully efficient. A continuous rise of this efficiency withincreasing generated LQ mass is expected, as the muons also have higher pT. Scale factorsapplied 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 isgood 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 re-quirements. It is evident that the pre-selection is the dominant criterion, such that the require-ment of at least two isolated muons with pT ≥ 30 GeV, |η| ≤ 2.4 and Irel < 0.02 is the one withthe largest effect on the final selection efficiencies of the analysis. The behavior in the b-taggingefficiency is opposite to the one observed in the pre-selection efficiency such that these trendspartially cancel. This might be retraced to the rather coarsely tuned b-tagging in the DELPHESremodeling. Both further requirements on the invariant mass of muon pairs, Mµµ, and S

lepT

agree within 1% and are fully efficient apart from low generated LQ masses. As a result, thefull selection efficiencies agree well within 3%.

Fig. 6.11 shows the final distributions of M recLQ in category A1 and ST in category B. Overall,

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

56

6.3. Results

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Figure 6.10. Signal selection efficiencies of the requirements imposed in the full selection as afunction 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.

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Figure 6.11. Final distributions of M recLQ (category A, left) and ST (category B, right) from the

remodeling with DELPHES (solid) and the original analysis using GEANT (dashed) for severalgenerated LQ masses.

57


the distributions are similar. However, the ST-distributions obtained from DELPHES are softerin general since less jets in the event are reconstructed, which in turn results in a smaller con-tribution to the value of ST. In addition, for lower generated LQ masses more events fall intocategory A and less into category B. This migration might be caused by differences in the leptonreconstruction.

As no excess in data was observed in the CMS analysis, the same statistical procedure asdescribed in Section 5.4 is used to derive upper limits on the product of the LQ pair productioncross section σLQLQ and the squared branching fraction B2 at 95% C.L. as a function of the LQmass. 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 goodagreement within 10%. The expected and observed limits are shown in Fig. 6.13. The resultinglower exclusion limit on the LQ mass for pair-produced scalar LQs that exclusively decay intotop quarks and muons is given by the intersection of the theoretically predicted production crosssection and the experimental observation and is found to be MLQ = 1432.7GeV. A comparisonto the reference value of MLQ = 1420GeV shows a deviation of less than 1%, which furthervalidates the analysis remodeling. Since the agreement is particularly good in the region around1.4 TeV, the obtained mass exclusion limit conforms well.

In summary, the remodelling with DELPHES fast simulation presented here is tuned, such thata good level of agreement with the results of the CMS analysis [1] is achieved. The DELPHESsimulation used to explore a wider parameter space as presented in the following chapter.

58

6.3. Results

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expected 95% C.L. upper limit

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

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Figure 6.13. Expected and observed upper limits on the product of the LQ pair production crosssection σLQLQ and the squared branching fraction B2(LQ→ tµ) at 95% C.L. as a function ofthe LQ mass for the remodeled analysis. Unit branching fraction is assumed, B = 1. The blackdashed 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, aphenomenological study of the LQ parameter space is presented. Henceforth, the LQ flavormodel introduced in Section 3.5 is considered, in which not only LQ pair production but alsofurther production processes that lead to the same final state are included, such that a morerealistic physical description of LQs is obtained. In addition, the impact of the Yukawa couplingλ is investigated for all allowed couplings of the S3. The statistical analysis presented previouslyis used to study the sensitivity to LQs producing different final states allowing to constraincoupling, 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 arepresented 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 cou-pling λ, a set of LQ event samples is generated in the range of MLQ = 0.4−2.0 TeV andλ= 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 forfour decay scenarios:

• S−1/33 → tµ−,

• S−1/33 → tµ−,bν,

• S−4/33 → bµ−,

• S+2/33 → tν,

and the corresponding couplings of anti-particles, respectively. The first decay scenario is stud-ied 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 upperlimits on the product of the inclusive LQ production cross section and the squared branchingfraction at 95% C.L. as a function of MLQ and λ. The branching fraction for a decay scenarioconsidering 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 Yukawacouplings λ are assumed.

The LQ flavor model is implemented in FeynRules [82], a Mathematica package for thecalculation of Feynman rules. Its universal FeynRules Output (UFO) [83] is passed to the MCgenerator MadGraph5_aMC@NLO [84] and the obtained production cross section are rescaled bya K-factor of 1.5 to account for NLO QCD corrections, as described in Section 3.5. The narrowwidth-approximation for the generated LQ mass is not used here. The further analysis procedureincluding the detector simulation with DELPHES and its tuning remains unchanged.

As the uncertainties on the cross sections calculated by MadGraph5_aMC@NLO are typicallyof the order ∼ 1% and thus may underestimate physically realistic uncertainties, the relativeuncertainties on the cross sections are taken from Ref. [50]. The simulation of parton-showeringand 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 previouslyvalidated remodeling of the LQ analysis, which is tailored for the investigation of the final statetµ−tµ+. Therefore, the interplay of the production cross section for a given LQ coupling andthe sensitivity to its corresponding final state is crucial for the final limits to be set on mass,coupling and observed cross section.

7.2.1. Decay Scenario: S−1/33 → tµ−

In order to compare the results of inclusive LQ production to those of pair production, thecoupling of the S3-representation with the electric charge Q =±1

3e to a top quark and a muonis studied first.

The production cross section for this decay scenario were shown and discussed in Section 3.5Fig. 3.10. A summary of all produced LQ event samples can be found in Table A.2. The LQpair production studied previously is compared to inclusive LQ production on generator levelfor this decay scenario. Fig. 7.1 shows distributions of the mass and transverse momentumof LQs as well as that of muon transverse momentum. In Fig. 7.1 left, the effect of the LQ

61


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Figure 7.1. Generator level distributions of MLQ (left), pT,LQ (center) and pT,µ (right) of inclu-sive 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 LQmass samples. It is evident that no NWA for the LQ mass is used in case of inclusive productionevents generated with MadGraph5_aMC@NLO. The LQ pT-spectra, shown in Fig. 7.1 center, differslightly, especially for high generated LQ masses the distributions peak at lower values forinclusive 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 observedin the distributions between both considered production mechanisms have their origin in theadditional processes contributing to the inclusive production. With growing mass of the LQsgenerated, increasing values of x are required to produce two on-shell LQs. As the PDFs of theproton decrease strongly for high values of x, cf. Fig. 2.2, the probability to produce two LQsalso decreases. Hence, contributions of off-shell LQ production sets in and becomes dominantfor high LQ masses generated, which is reflected in the softer pT-distributions of the LQs andmuons 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 minoreffect in the LQ coupling to tµ. Fig. 7.3 shows the final distributions of M rec

LQ (left) and ST

(right) on reconstruction level. The significantly lower number of events in both distributionsis mainly due to the lower production cross sections mentioned above. In addition, the softermuon pT-spectra at high generated LQ masses are propagated to the ST-distribution that in turnbecomes softer as well.

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

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Figure 7.3. Final distributions of M recLQ (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).

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

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Figure 7.5. Inclusive production cross section σ for the LQ coupling tµ,bν (red) as a functionof MLQ for several values of λ compared to those of tµ (blue). Values on σ obtained fromMadGraph5_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 aroundMLQ ∼ 1.2 TeV for even higher values. The resulting observed lower LQ mass limits are listedin Table A.6 for all values of λ studied.

7.2.2. Decay Scenario: S−1/33 → tµ−, bν

After having discussed the coupling of the S3 to a top quark and a muon only, now both LQcouplings 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 theproduction cross sections depend on the allowed couplings, as the those for both couplings tµand bν, are in general higher than the ones for tµ-coupling only. Especially in the region of highgenerated LQ masses, this behavior is observed. Since the b quark has a smaller mass than thetop 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 LQcouplings. It is lower compared to the pre-selection efficiency for tµ-coupling, since the produc-tion of the two selected muons is unlikely for the LQ decay into bν. Additionally, the decreaseof the efficiency for increasing MLQ is due to the off-shell LQ production contributing to the

65


400 600 800 1000 1200 1400 1600 1800 2000 [GeV]LQM

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

tota

l effi

cien

cy

µ t→LQ

pre-selection

1≥ b-tagsN

110 GeV≥ µµM

200 GeV≥ lep

TS

ν,bµ t→LQ

pre-selection

1≥ b-tagsN

110 GeV≥ µµM

200 GeV≥ lep

TS

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

0 100 200 300 400 500 600 700 800 900 1000 [GeV]LQM

5−10

4−10

3−10

2−10

1−10

1

10

210

310

410

510

even

ts

ν, b µt µt = 0.4 TeVLQM = 1.2 TeVLQM = 2.0 TeVLQM

(13 TeV)-135.9 fb

0 500 1000 1500 2000 2500 3000 [GeV]TS

5−10

4−10

3−10

2−10

1−10

1

10

210

310

410

510

even

ts

ν, b µt µt = 0.4 TeVLQM = 1.2 TeVLQM = 2.0 TeVLQM

(13 TeV)-135.9 fb

Figure 7.7. Final distributions of M recLQ (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

[GeV]LQM400 600 800 1000 1200 1400 1600 1800 2000

λco

uplin

g

0.5

1

1.5

2

Obs

erve

d cr

oss

sect

ion

uppe

r lim

it at

95%

CL

[pb]

3−10

2−10

LQ exclusion limit

Observed

Expected

68% expected

(13 TeV)-135.9 fb

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

67


400 600 800 1000 1200 1400 1600 1800 2000 [GeV]LQM

7−10

6−10

5−10

4−10

3−10

2−10

1−10

1

10

[pb]

σ

µ t →LQ = 0.5λ = 1.0λ = 1.5λ

µ b →LQ = 0.5λ = 1.0λ = 1.5λ

Figure 7.9. Inclusive production cross section σ for the LQ coupling to bµ (green) as a functionof MLQ for several values of λ compared to those of tµ (blue). Values on σ obtained fromMadGraph5_aMC@NLO are already rescaled by a factor of 1.5.

overall production cross section increasingly strongly. Fig. 7.7 shows the final distributions ofMLQ (left) and ST (right). They do not deviate much from the ones obtained for the tµ-couplingonly, indicating that the effects of increased cross sections and decreased selection efficiencymostly cancel. Only for high generated LQ masses (MLQ = 2.0 TeV, red), in total more eventsare found in both categories due to the increased production cross sections with respect to thetµ-coupling.

In Fig. 7.8, the lower exclusion limits on the LQ mass and observed upper limits on the pro-duction 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 bevery similar, because the gain in the cross section is compensated by the loss in selection effi-ciency. The upper limits on the observed LQ production cross section, however, are weaker inthis case due to the lower selection efficiency.

7.2.3. Decay Scenario: S−4/33 → bµ−

In the model considered, the S3-representation with the electric charge ofQ=±43e couples to a

b quark and a muon only. In Fig. 7.9, the corresponding production cross section of inclusive LQproduction is shown. A summary of all produced LQ event samples for this decay scenario canbe found in Table A.4. As for the tµ,bν-coupling, a higher production cross section with respect

68

7.2. Results

400 600 800 1000 1200 1400 1600 1800 2000 [GeV]LQM

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

tota

l effi

cien

cy

µ t →LQ

pre-selection

1≥ b-tagsN

110 GeV≥ µµM

200 GeV≥ lep

TS

µ b →LQ

pre-selection

1≥ b-tagsN

110 GeV≥ µµM

200 GeV≥ lep

TS

Figure 7.10. Total selection efficiencies of each requirement imposed in the full selection as afunction of the generated LQ mass for inclusive production of the S3 coupling to bµ (solid) andtµ only (dotted).

to the tµ-coupling is observed, along with the effect of off-shell LQ production as describedabove. Fig. 7.10 shows the total selection efficiencies of the requirements in the full selectionfor 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 onsetof off-shell LQ production. Fig. 7.11 shows the final distributions of M rec

LQ (category A, left)and ST (category B, right).

As the occurrence of additional leptons in this decay scenario is unlikely, the number ofevents that fall into category A is significantly lower than for the tµ-coupling. Thus, mostevents fall into category B. For high generated LQ masses, the ST-distributions in this decayscenario 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 limitson the production cross section in the MLQ−λ-plane. Exact values of the LQ mass exclusionlimits are listed in Table A.8. In this decay scenario, a significant λ-dependence of the LQmass exclusion limits is evident. Due to the large predicted production cross section and thereasonably high selection efficiency for this coupling, the limits are more stringent than thoseof the tµ-coupling. These limits constitute the first constraints on LQs coupling to a b quarkand a muon. Regarding the scalar leptoquark S3 in this analysis, the LQ mass limits obtained inthis decay scenario are the most stringent. For values of λ > 1.5, the observed exclusion limits

69


0 100 200 300 400 500 600 700 800 900 1000 [GeV]LQM

5−10

4−10

3−10

2−10

1−10

1

10

210

310

410

510

even

ts

µb µt = 0.4 TeVLQM = 1.2 TeVLQM = 2.0 TeVLQM

(13 TeV)-135.9 fb

0 500 1000 1500 2000 2500 3000 [GeV]TS

5−10

4−10

3−10

2−10

1−10

1

10

210

310

410

510

even

ts

µb µt = 0.4 TeVLQM = 1.2 TeVLQM = 2.0 TeVLQM

(13 TeV)-135.9 fb

Figure 7.11. Final distributions of M recLQ (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).

[GeV]LQM400 600 800 1000 1200 1400 1600 1800 2000

λco

uplin

g

0.5

1

1.5

2

Obs

erve

d cr

oss

sect

ion

uppe

r lim

it at

95%

CL

[pb]

3−10

2−10

LQ exclusion limit

Observed

Expected

68% expected

(13 TeV)-135.9 fb

Figure 7.12. Observed and expected lower exclusion limits on the LQ mass and observed upperlimits on the production cross section at 95% C.L. in the plane ofMLQ and λ for the S3 couplingto bµ.

70

7.2. Results

400 600 800 1000 1200 1400 1600 1800 2000 [GeV]LQM

7−10

6−10

5−10

4−10

3−10

2−10

1−10

1

10

[pb]

σ

µ t →LQ = 0.5λ = 1.0λ = 1.5λ

ν t →LQ = 0.5λ = 1.0λ = 1.5λ

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

exceed the investigated mass region, MLQ > 2000 GeV.

7.2.4. Decay Scenario: S+2/33 → tν

Last, the coupling to a top quark and a neutrino is studied for the S3 with the electric charge ofQ = ±2

3e. Fig. 7.13 shows the corresponding inclusive production cross section as a functionof the generated LQ mass. A summary of all produced LQ event samples can be found inTable A.5. Some values of the highest LQ mass sample are found to be negative, such that theobtained values from MadGraph5_aMC@NLO are not considered for MLQ > 1.6 TeV. Fig. 7.14shows the total selection efficiencies of each requirement imposed in the full selection. Sincethe full selection efficiency (black line) is of order ∼ 0.1%, the sensitivity is too small to becompensated by the gain in cross sections. It is further unlikely that three or more leptons areproduced in this decay scenario so that no event falls into category A, see Fig. 7.15 left. Thoseevents 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 massexclusion 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 stopsearch with the final state of two top quarks and two neutralinos, see Ref. [86].

71


400 600 800 1000 1200 1400 1600 1800 2000 [GeV]LQM

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

tota

l effi

cien

cy

ν t →LQ

pre-selection

1≥ b-tagsN

110 GeV≥ µµM

200 GeV≥ lep

TS

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

0 100 200 300 400 500 600 700 800 900 1000 [GeV]LQM

7−10

6−10

5−10

4−10

3−10

2−10

1−10

1

10

210

310

410

510

even

ts

νt µt = 0.4 TeVLQM = 1.2 TeVLQM = 2.0 TeVLQM

(13 TeV)-135.9 fb

0 500 1000 1500 2000 2500 3000 [GeV]TS

7−10

6−10

5−10

4−10

3−10

2−10

1−10

1

10

210

310

410

510

even

ts

νt µt = 0.4 TeVLQM = 1.2 TeVLQM = 2.0 TeVLQM

(13 TeV)-135.9 fb

Figure 7.15. Final distributions M recLQ (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

[GeV]LQM500 1000 1500 2000

+ X

) [p

b]2/

3

3 S

→(p

p σ

4−10

3−10

2−10

1−10

1

10

210

310observed 95% C.L. upper limit


68% expected

95% expected

scalar LQ

(13 TeV)-135.9 fb

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

73

8. Conclusion and Outlook

Although the Standard Model of particle physics is an extremely successful theory tested innumerous experiments, it cannot explain some phenomena observed. Leptoquarks are hypo-thetical particles that appear in many theories beyond the Standard Model and could explainhints for lepton flavor non-universality in B meson decays observed recently. Many searchesfor 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 decayingexclusively into top quarks and muons has been presented. Instead of a GEANT-based full sim-ulation, the DELPHES framework has been used to simulate the CMS detector. Since DELPHESfast simulation uses a simplified approach based on parametrization, the remodeled analysishas been tuned in terms of lepton isolation, jet-lepton cleaning and b-tagging to reproduce theresults of the original analysis. Distributions of kinematic variables as well as selection effi-ciencies at reconstruction level have been compared for both simulation techniques confirmingthe validity of the remodeling.

The validated DELPHES simulation has been used for a reinterpretation of CMS data withina leptoquark flavor model motivated by recent hints for lepton flavor non-universality in Bmeson decays. All allowed couplings of the scalar leptoquark S3 to third-generation quarks andmuons or neutrinos have been studied in final states with two third-generation quarks and twosecond-generation leptons. Additional leptoquark production processes beyond pair productionhave been considered, which have been found to be dependent on the strength of the Yukawacoupling λ. The contribution of leptoquarks produced off-shell becomes more relevant withincreasing 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 planeas a function of MLQ and λ. A novel result is the λ-dependency of the obtained lower limits onthe leptoquark mass. Limits on leptoquarks coupling to a b quark and a muon have been set forthe 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 onexclusion 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 ofleading 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 leptoquarkparameter space, especially for low values for of λ.

The constraints on scalar leptoquarks presented are expected to be valid for vector lepto-quarks as well, because they have higher production cross sections. However, this analysisperformed for vector leptoquarks would provide significantly more stringent limits. In addi-tion, a sound calculation of uncertainties on the theoretically predicted cross sections wouldcontribute to a more precise estimation of the exclusion limits.

To further explore the leptoquark parameter space, not only an expansion to the full Run IIdata set is needed, but also the remodeling of different analyses would be beneficial, as resultsobtained from statistically independent event selections allow for a combination of exclusionlimits. 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 tailoredtowards this coupling. Therefore, a dedicated search for this decay scenario would providesignificantly stronger constraints.

75

A. Additional Tables

76

Process σ [pb] Generator N [106]

tt + jets 8.3 ·102 POWHEG + PYTHIA 155.2W(→ `ν) + jets, pT ∈ [100,250) GeV 6.9 ·102 AMC@NLO + PYTHIA 176792.6W(→ `ν) + jets, pT ∈ [250,400) GeV 2.5 ·101 AMC@NLO + PYTHIA 617.7W(→ `ν) + jets, pT ∈ [400,600) GeV 3.1 ·100 AMC@NLO + PYTHIA 11.7W(→ `ν) + jets, pT ∈ [250,400) GeV 4.7 ·10−1 AMC@NLO + PYTHIA 1.8DY(Z/γ→ ``) + jets, HT ∈ [70,100) GeV 2.2 ·102 MADGRAPH + PYTHIA 9.6DY(Z/γ→ ``) + jets, HT ∈ [100,200) GeV 1.8 ·102 MADGRAPH + PYTHIA 10.6DY(Z/γ→ ``) + jets, HT ∈ [200,400) GeV 5.0 ·101 MADGRAPH + PYTHIA 9.6DY(Z/γ→ ``) + jets, HT ∈ [400,600) GeV 7.0 ·100 MADGRAPH + PYTHIA 10.0DY(Z/γ→ ``) + jets, HT ∈ [600,800) GeV 1.7 ·100 MADGRAPH + PYTHIA 8.3DY(Z/γ→ ``) + jets, HT ∈ [800,1200) GeV 7.8 ·10−1 MADGRAPH + PYTHIA 2.7DY(Z/γ→ ``) + jets, HT ∈ [1200,2500) GeV 1.9 ·10−1 MADGRAPH + PYTHIA 0.6DY(Z/γ→ ``) + jets, HT ∈ [2500,∞) GeV 4.4 ·10−3 MADGRAPH + PYTHIA 0.4Single t, t-channel 1.4 ·102 POWHEG + PYTHIA 6.0Single t, t-channel 8.1 ·101 POWHEG + PYTHIA 3.9Single t / t, s-channel 3.4 ·100 AMC@NLO + PYTHIA 3.4Single t, tW-channel 3.6 ·101 POWHEG + PYTHIA 6.9Single t, tW-channel 3.6 ·101 POWHEG + PYTHIA 6.9Diboson (WW→ 2`2ν) 1.2 ·101 POWHEG + PYTHIA 2.0Diboson (WW→ `ν2q) 5.0 ·101 POWHEG + PYTHIA 9.0Diboson (WZ→ `ν2q) 1.1 ·101 AMC@NLO + PYTHIA 420.5Diboson (WZ→ 2`2q) 5.6 ·100 AMC@NLO + PYTHIA 233.1Diboson (WZ→ 3`ν) 4.4 ·100 POWHEG + PYTHIA 2.0Diboson (ZZ→ 2`2ν) 5.6 ·10−1 POWHEG + PYTHIA 8.8Diboson (ZZ→ 2`2q) 3.2 ·100 AMC@NLO + PYTHIA 77.9Diboson (ZZ→ 4`) 1.2 ·100 AMC@NLO + PYTHIA 20.5tt + W(→ `ν) 2.0 ·10−1 AMC@NLO + PYTHIA 3.5tt + Z(→ `` / νν) 2.5 ·10−1 AMC@NLO + PYTHIA 1.8QCD, µ enr., pT ∈ [15,20) GeV 3.8 ·106 PYTHIA 4.1QCD, µ enr., pT ∈ [20,30) GeV 3.0 ·106 PYTHIA 31.5QCD, µ enr., pT ∈ [30,50) GeV 1.7 ·106 PYTHIA 29.9QCD, µ enr., pT ∈ [50,80) GeV 4.4 ·105 PYTHIA 19.8QCD, µ enr., pT ∈ [80,120) GeV 1.1 ·105 PYTHIA 13.8QCD, µ enr., pT ∈ [120,170) GeV 2.5 ·104 PYTHIA 8.0QCD, µ enr., pT ∈ [170,300) GeV 8.7 ·103 PYTHIA 7.9QCD, µ enr., pT ∈ [300,470) GeV 8.0 ·102 PYTHIA 7.9QCD, µ enr., pT ∈ [470,600) GeV 7.9 ·101 PYTHIA 3.9QCD, µ enr., pT ∈ [600,800) GeV 2.5 ·101 PYTHIA 4.0QCD, µ enr., pT ∈ [800,1000) GeV 4.7 ·100 PYTHIA 4.0QCD, µ enr., pT ∈ [1000,∞) GeV 1.6 ·100 PYTHIA 4.0QCD, EM enr., pT ∈ [20,30) GeV 5.4 ·106 PYTHIA 9.2QCD, EM enr., pT ∈ [30,50) GeV 9.9 ·106 PYTHIA 4.7QCD, EM enr., pT ∈ [50,80) GeV 2.9 ·106 PYTHIA 23.5QCD, EM enr., pT ∈ [80,120) GeV 4.2 ·105 PYTHIA 35.8QCD, EM enr., pT ∈ [120,170) GeV 7.7 ·104 PYTHIA 77.8QCD, EM enr., pT ∈ [170,300) GeV 1.9 ·104 PYTHIA 11.5QCD, EM enr., pT ∈ [300,∞) GeV 1.4 ·103 PYTHIA 7.4QCD, bc→ e, pT ∈ [15,20) GeV 2.5 ·105 PYTHIA 2.7QCD, bc→ e, pT ∈ [20,30) GeV 3.3 ·105 PYTHIA 10.9QCD, bc→ e, pT ∈ [30,80) GeV 4.1 ·105 PYTHIA 15.3QCD, bc→ e, pT ∈ [80,170) GeV 3.8 ·104 PYTHIA 15.0QCD, bc→ e, pT ∈ [170,250) GeV 2.6 ·103 PYTHIA 9.5QCD, bc→ e, pT ∈ [250,∞) GeV 7.1 ·102 PYTHIA 9.8

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

77

Appendix A. Additional Tables

ML

Q[G

eV]

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

4009.429×

10−

41.280×

10−

25.031×

10−

21.144×

10−

11.971×

10−

12.831×

10−

13.626×

10−

14.292×

10−

14.823×

10−

1

6001.489×

10−

42.001×

10−

37.727×

10−

31.748×

10−

22.957×

10−

24.254×

10−

25.418×

10−

26.426×

10−

27.254×

10−

2

8002.793×

10−

53.735×

10−

41.417×

10−

33.239×

10−

35.562×

10−

37.925×

10−

31.014×

10−

21.213×

10−

21.368×

10−

2

10006.035×

10−

68.106×

10−

53.087×

10−

47.098×

10−

41.224×

10−

31.778×

10−

32.325×

10−

32.810×

10−

33.254×

10−

3

12001.270×

10−

61.677×

10−

57.419×

10−

51.737×

10−

43.060×

10−

44.304×

10−

45.471×

10−

46.882×

10−

48.162×

10−

4

14002.876×

10−

73.978×

10−

61.629×

10−

53.735×

10−

57.607×

10−

51.151×

10−

41.578×

10−

42.042×

10−

42.538×

10−

4

16007.253×

10−

81.034×

10−

64.329×

10−

61.046×

10−

51.985×

10−

53.458×

10−

55.118×

10−

57.113×

10−

59.260×

10−

5

18001.949×

10−

82.819×

10−

71.235×

10−

63.228×

10−

66.996×

10−

61.260×

10−

51.982×

10−

53.066×

10−

54.263×

10−

5

20005.924×

10−

99.108×

10−

84.211×

10−

71.298×

10−

62.918×

10−

65.553×

10−

69.425×

10−

61.497×

10−

52.234×

10−

5

TableA

.2.C

rosssections

inpb

forall

generatedL

Qevents

forthe

decayscenario

S3→

tµ.

Obtained

valuesfrom

MadGraph5_aMC@NLOare

rescaledby

aK

-factorof1.5

toaccountfor

NL

OQ

CD

corrections.For

eachentry,

N=

100000events

areproduced.

ML

Q[G

eV]

λ=

0.25

λ=

0.50

λ=

1.00

λ=

1.50

λ=

2.00

λ=

2.25

4003.542×

10−

34.854×

10−

24.647×

10−

11.256×

100

2.25×

100

2.774×

100

6004.098×

10−

45.591×

10−

35.252×

10−

21.511×

10−

12.834×

10−

13.546×

10−

1

8007.388×

10−

51.005×

10−

39.168×

10−

32.964×

10−

26.057×

10−

28.090×

10−

2

10001.688×

10−

52.268×

10−

42.417×

10−

37.991×

10−

31.853×

10−

22.519×

10−

2

12004.194×

10−

66.092×

10−

57.517×

104

2.756×

10−

37.052×

10−

31.032×

10−

2

14001.392×

10−

62.126×

10−

52.724×

10−

41.199×

10−

33.279×

10−

34.964×

10−

3

16005.949×

10−

79.345×

10−

61.277×

10−

46.093×

10−

41.794×

10−

32.742×

10−

3

18003.104×

10−

74.746×

10−

67.193×

10−

53.558×

10−

41.071×

10−

31.635×

10−

3

20001.781×

10−

72.879×

10−

64.520×

10−

52.189×

10−

46.765×

10−

41.050×

10−

3

TableA

.3.Crosssectionsin

pbforallgenerated

LQ

eventsforthescenario

S3 →

tµ,bν.O

btainedvaluesfrom

MadGraph5_aMC@NLOare

rescaledby

aK

-factorof1.5to

accountforNL

OQ

CD

corrections.Foreachentry,N

=100000

eventsare

produced.

78

ML

Q[G

eV]

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

1.15

3×10

−2

1.53

6×10

−1

6.07

4×10

−1

1.40

1×10

02.

562×

100

3.88

8×10

05.

382×

100

6.80

0×10

08.

393×

100

500

3.63

5×10

−3

4.97

6×10

−2

1.91

6×10

−1

4.62

8×10

−1

8.32

5×10

−1

1.29

2×10

01.

806×

100

2.28

0×10

02.

966×

100

600

1.34

6×10

−3

×10

−3

1.85

0×10

−2

7.27

2×10

−2

1.71

9×10

−1

3.18

2×10

−1

5.30

3×10

−1

7.00

8×10

−1

9.53

0×10

−1

700

5.49

6×10

−4

7.50

0×10

−3

3.00

0×10

−2

7.20

8×10

−2

1.33

2×10

−1

2.14

1×10

−1

3.09

2×10

−1

4.23

8×10

−1

5.64

5×10

−1

800

2.43

6×10

−4

3.41

3×10

−3

1.35

2×10

−2

3.21

6×10

−2

6.28

1×10

−2

9.97

7×10

−2

1.44

7×10

−1

2.07

6×10

−1

2.90

0×10

−1

900

1.16

8×10

−4

1.63

1×10

−3

6.57

3×10

−3

1.59

8×10

−2

3.14

7×10

−2

5.28

6×10

−2

7.78

5×10

−2

1.17

2×10

−1

1.60

8×10

−1

1000

5.83

7×10

−5

8.29

7×10

−4

3.45

2×10

−3

8.57

4×10

−3

1.67

1×10

−2

2.94

5×10

−2

4.58

7×10

−2

6.88

7×10

−2

9.78

3×10

−2

1100

3.10

1×10

−5

4.48

1×10

−5

1.86

0×10

−3

4.89

0×10

−3

9.69

2×10

−3

1.72

4×10

−2

2.79

5×10

−2

4.21

2×10

−2

6.10

1×10

−2

1200

1.77

3×10

−5

2.54

6×10

−4

1.09

3×10

−3

2.85

5×10

−3

5.93

4×10

−3

1.06

0×10

−2

1.75

8×10

−2

2.78

7×10

−2

4.10

1×10

−2

1300

1.06

1×10

−5

1.53

0×10

−4

6.63

2×10

−4

1.80

0×10

−3

3.89

3×10

−3

6.92

7×10

−3

1.20

5×10

−2

1.89

2×10

−2

2.82

8×10

−2

1400

6.63

9×10

−6

9.74

6×10

−5

4.24

4×10

−4

1.18

3×10

−4

2.55

0×10

−3

4.84

8×10

−3

8.13

3×10

−3

1.29

4×10

−2

2.02

1×10

−2

1500

4.16

9×10

−6

6.39

9×10

−5

2.87

1×10

−4

7.85

1×10

−4

1.76

0×10

−3

3.44

7×10

−3

5.82

5×10

−3

9.04

8×10

−3

1.46

9×10

−2

1600

2.90

9×10

−6

4.36

1×10

−5

1.99

2×10

−4

5.77

4×10

−4

1.25

8×10

−3

2.54

0×10

−3

4.38

0×10

−3

7.34

5×10

−3

1.06

2×10

−2

1700

2.00

3×10

−6

3.02

6×10

−5

1.44

5×10

−4

4.26

3×10

−4

9.54

2×10

−4

1.86

2×10

−3

3.43

5×10

−3

5.45

7×10

−3

8.26

1×10

−3

1800

1.47

0×10

−6

2.18

6×10

−5

1.05

3×10

−4

3.24

0×10

−4

7.14

0×10

−4

1.48

7×10

−3

2.65

2×10

−3

4.17

9×10

−3

6.54

0×10

−3

1900

1.03

3×10

−6

1.68

2×10

−5

7.90

5×10

−5

2.51

9×10

−4

5.82

0×10

−4

1.14

1×10

−1.

935×

10−

33.

282×

10−

35.

178×

10−

3

2000

8.22

8×10

−7

1.23

7×10

−5

6.20

6×10

−5

1.88

9×10

−4

4.57

5×10

−4

9.30

3×10

−4

1.68

0×10

−3

2.66

1×10

−3

4.04

0×10

−3

Tabl

eA

.4.

Cro

ssse

ctio

nsin

pbfo

ral

lge

nera

ted

LQ

even

tsfo

rth

ede

cay

scen

ario

S3→

bµ.

Obt

aine

dva

lues

from

MadG

raph

5_aM

C@NL

Oar

ere

scal

edby

aK

-fac

tor

of1.

5to

acco

untf

orN

LO

QC

Dco

rrec

tions

.Fo

rea

chen

try,N

=10

0000

even

tsar

epr

oduc

ed.

ML

Q[G

eV]

λ=

0.25

λ=

0.50

λ=

1.00

λ=

1.50

λ=

2.00

λ=

2.25

400

9.28

5×10

−3

1.28

2×10

−1

1.23

6×10

03.

153×

100

5.01

8×10

05.

717×

100

600

1.47

5×10

−3

2.00

0×10

−2

1.74

5×10

−1

4.36

2×10

−1

6.56

4×10

−1

7.34

9×10

−1

800

2.88

0×10

−4

3.84

8×10

−3

3.28

4×10

−2

7.98

6×10

−2

1.20

2×10

−1

1.36

0×10

−1

1000

6.28

4×10

−5

8.41

1×10

−4

7.24

4×10

−3

1.76

7×10

−2

2.70

2×10

−2

3.04

2×10

−2

1200

−1.

995×

10−

41.

703×

10−

34.

263×

10−

36.

653×

10−

37.

670×

10−

3

1400

3.12

8×10

−6

4.18

1×10

−5

4.02

3×10

−4

9.95

4×10

−4

1.65

2×10

−3

1.99

8×10

−3

1600

5.95

4×10

−7

7.91

6×10

−6

7.59

0×10

−5

2.39

7×10

−4

4.47

3×10

−4

5.80

4×10

−4

1800

5.54

7×10

−8

7.93

7×10

−7

1.16

8×10

−5

5.27

0×10

−5

1.30

8×10

−4

1.99

8×10

−4

2000

2.89

5×10

−8

3.64

2×10

−7

6.54

0×10

−7

1.06

5×10

−5

4.63

2×10

−5

7.78

2×10

−5

Tabl

eA

.5.

Cro

ssse

ctio

nsin

pbfo

ral

lge

nera

ted

LQ

even

tsfo

rth

ede

cay

scen

ario

S3→

tν.

Obt

aine

dva

lues

from

MadG

raph

5_aM

C@NL

Oar

ere

scal

edby

aK

-fac

tor

of1.

5to

acco

untf

orN

LO

QC

Dco

rrec

tions

.Fo

rea

chen

try,N

=10

0000

even

tsar

epr

oduc

ed.

79

Appendix A. Additional Tables

λ observed lower limit on MLQ [GeV]

0.25 –0.50 7000.75 9301.00 10301.25 11401.50 11801.75 11902.00 12202.25 1250

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


0.25 –0.50 6801.00 10301.50 11802.00 12402.25 1250

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


0.25 4200.50 9600.75 12801.00 15201.25 17201.50 19001.75 > 20002.00 > 20002.25 > 2000

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

80

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Danksagung

An dieser Stelle möchte ich mich bei all denjenigen bedanken, die mich auf meinem Weg durchdas 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 Themaeiner phänomenologischen Studie hat mir extrem gut gefallen und mir viele interessante Ein-blicke theoretischer und experimenteller Hinsicht erlaubt. Auch für die vielen hilfreichen Tippsund Kommentare in den wöchentlichen Montagsmeetings bin ich sehr dankbar.

Ganz herzlich bedanke ich mich auch bei Dr. Roman Kogler, nicht nur für die Übernahme desZweitgutachtens, sondern insbesondere für die zahlreichen Gespräche und Ideen, die meinenHorizont 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 fürdas Gelingen dieser Arbeit. Grazie mille!

Um meinen Dank gegenüber Arne Reimers auszudrücken, reichen diese Zeilen definitiv nichtaus. Als designierter Leptoquark-Experte musste er für unzählige Fragen vom ersten bis zumletzten 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 Masterarbeitin Kontakt war, danke ich für die freundschaftliche Arbeitsatmosphäre und die mir entgegenge-kommene Hilfsbereitschaft. Insbesondere sind hier meine “office buddies” Ksenia, Christopherund Nino hervorzuheben, die mich über viele Monate hinweg unterstützt und ertragen haben.Hinzu kommt Jan, der glücklicherweise seine Masterarbeit im selben Zeitraum wie Nino undich absolviert hat, sodass viele Probleme gemeinsam gelöst werden konnten. Die Gemeinschaftund Freundschaft mit euch beiden haben mir das Leben sehr erleichtert. Außerdem möchteich mich noch bei Andrea für viele hilfreiche Tipps und Hinweise sowie das Korrekturlesenbedanken.

Zu guter Letzt bedanke ich mich meiner Familie und bei meinen Freunden, die mich überdie vielen Jahre des Studiums hinweg unterstützt haben. Natürlich sind hier meine Eltern zunennen. Vielen Dank nicht nur für die finanzielle Unterstützung, sondern auch für die Hilfe inverschiedensten Situationen. Bei meiner Freundin bedanke ich mich für die bedingungslose,liebevolle Unterstützung.

Mein Dank gilt selbstverständlich auch den Personen, die hier nicht namentlich erwähnt wur-den. Danke vielmals!

Eidesstattliche Erklärung

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

Ort, Datum, Unterschrift

Constraints of Leptoquark Models with CMS Data...Henrik Jabusch November 2019 Eingereicht am 27. November 2019 1. Gutachter: Prof. Dr. Johannes Haller 2. Gutachter: Dr. Roman Kogler

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