Search for Higgsinos in Final States with a Low-Momentum, Displaced Track

Home , Higgsino

Search for Higgsinos in ﬁnal states with a low-momentum, displaced track

von

Moritz Wolf

geboren am

04. März 1994

Masterarbeit im Studiengang Physik

Universität Hamburg

Institut für Experimentalphysik

2020

1. Gutachter: Prof. Dr. Peter Schleper 2. Gutachter: Jun.-Prof. Dr. Gregor Kasieczka

Abstract

Higgsinos are a class of supersymmetric particles that are of particular interest to searches at the LHC. They are featured in many SUSY models with masses on the order of the electroweak scale. A number of LHC searches targeting charged or neutral Higgsino decays in disappearing track and di-lepton searches, respectively, have set exclusion limits on the SUSY model parameters. However, a region in the parameter space with Higgsino mass diﬀerences between 0.3 and 1.0 GeV remains constrained only by LEP results. This domain is of special interest from a phenomenological point of view as it is realized in natural SUSY scenarios. This thesis presents an analysis that establishes sensitivity to that region. In the examined signal models, the lightest chargino has a decay length in the detector of up to a few millimeters and its decay predominantly gives rise to a single, low-momentum pion. A soft and displaced track created by the pion is the crucial part of this analysis as it is used to enhance the signal sensitivity of a monojet-like analysis. Data corresponding to an integrated luminosity of 35.9 fb−1 collected by the CMS experiment in √ proton-proton collisions at s = 13 TeV are analyzed. The observed event yields are consistent with the expected numbers of background events and exclusion limits are set in the plane of the chargino mass and mass diﬀerence of the Higgsino spectrum. For models with a mass splitting between the lightest chargino and the lightest neutralino of 0.8 GeV, charginos with masses up to 120 GeV are excluded.

i Zusammenfassung

Higgsinos sind supersymmetrische Elementarteilchen, die für Suchen nach neu- en Teilchen am LHC von besonderem Interesse sind. In vielen SUSY-Model- len werden für Higgsinos Massen nahe der elektroschwachen Skala vorherge- sagt. Zahlreiche LHC-Analysen konnten mithilfe von disappearing-track- und Di-Lepton-Suchen weite Teile des SUSY-Parameterraums ausschließen. Eine Region im Phasenraum mit Massendifferenzen der Higgsinos zwischen 0,3 und 1,0 GeV ist bis jetzt jedoch nur durch Resultate von LEP begrenzt. Aus phäno- menologischer Sicht ist dieser Bereich besonders interessant, da er Teil natür- licher SUSY-Szenarien ist. In dieser Arbeit wird eine Analyse vorgestellt, die in diesem Bereich sensitiv ist. Die untersuchten Signal-Modelle zeichnen sich dadurch aus, dass das leichteste Chargino eine mittlere Zerfallslänge von bis zu einigen Millimetern hat und der Zerfall in den meisten Fällen ein einzelnes Pi- on mit wenig Impuls hervorbringt. Wesentlich für diese Analyse ist eine stark gekrümmte und leicht versetzte Spur, die das Pion im Detektor hinterlässt. Sie wird benutzt, um eine Monojet-artige Analyse so zu erweitern, dass sie sensitiv auf den Signal-Prozess wird. Es werden Daten vom CMS-Experiment analysiert, die in Proton-Proton-Kollisionen bei einer Schwerpunktsenergie von √ s = 13 TeV aufgezeichnet wurden und die einer integrierten Luminosität von 35,9 fb−1 entsprechen. Die beobachtete Anzahl von Ereignissen in dieser Analy- se deckt sich mit der erwarteten Anzahl von Untergrundereignissen. Es werden Ausschlussgrenzen in der Ebene der Chargino-Masse und der Massendifferenz des Higgsino-Spektrums festgelegt. Auf diese Weise können für Modelle mit einer Massendifferenz zwischen dem leichtesten Chargino und dem leichtesten Neutralino von 0,8 GeV Charginos mit Massen bis zu 120 GeV ausgeschlossen werden.

ii Contents

1 Introduction1

2 Theoretical Background5 2.1 The Standard Model of Particle Physics ...... 5 2.1.1 Particle Content ...... 5 2.1.2 Mathematical Description ...... 8 2.1.3 Hints of Physics Beyond the SM ...... 14 2.2 Supersymmetry ...... 14 2.2.1 Natural SUSY and Light Higgsinos ...... 16

3 The CMS Experiment 19 3.1 The Large Hadron Collider ...... 19 3.1.1 Overview ...... 19 3.1.2 Proton-Proton Collisions ...... 21 3.2 The CMS Detector ...... 23 3.2.1 Coordinate System ...... 24 3.2.2 Tracking System and Magnet ...... 24 3.2.3 Calorimeters ...... 26 3.2.4 Muon System ...... 27 3.2.5 Trigger ...... 28 3.3 Particle Identiﬁcation and Event Reconstruction ...... 29 3.3.1 Track Reconstruction ...... 29 3.3.2 Particle Flow Algorithm ...... 32

4 Analysis Strategy 35 4.1 Datasets ...... 37

iii Contents

4.2 Event and Track Observables ...... 38

5 Soft and Displaced Tracks 41 5.1 Helix Extrapolation ...... 41 5.2 Track-matching to Generated Particles ...... 42 5.3 Multivariate Classiﬁer ...... 45

6 Analysis 53 6.1 Event Reconstruction and Selection ...... 53 6.2 Soft and Displaced Track Requirement ...... 55 6.3 Background Estimation ...... 63 6.4 Validation ...... 67 6.5 Predicted Event Yields and Uncertainties ...... 70 6.6 Observed Event Yields and Exclusion Limit ...... 72

7 Conclusion and Outlook 75

Appendix 79

List of Figures 81

List of Tables 83

Bibliography 85

iv 1 Introduction

One of the strongest motivations to search for physics beyond the Standard Model (SM) is our current lack of a particle-based explanation for Dark Matter (DM). Mod- els incorporating supersymmetry (SUSY) extend the SM and predict the existence of new elementary particles that are linked to the already known particles. The lightest of those supersymmetric particles is, in numerous models, a viable DM candidate. A particularly interesting class of postulated particles are Higgsinos, supersymmetric partner particles of the SM Higgs boson. Higgsinos generally mix with gauginos to form mass eigenstates but in many cases suitable to explain DM, the lightest mass eigenstates are dominated by the Higgsino component. Many so-called natural SUSY models predict those Higgsinos to be relatively light, i.e. on the order of O (100 GeV). Higgsinos of such mass would be kinematically accessible to experiments at the LHC; however, their detection may prove challenging.

The values of the masses of SUSY particles (the spectrum) in natural SUSY models 0 are typically such that two neutral and one charged Higgsino mass eigenstates, χe1, 0 ± χe2 and χe1 , are nearly degenerate but feature slight mass diﬀerences such that the lightest and heaviest of the three are electrically neutral, and the charged state takes an intermediate mass value. Therefore, when a charged Higgsino or heavier neutral Higgsino is produced, it decays to the lightest neutralino, which itself is invisible to the detector, along with additional low-momentum SM decay products that are possibly visible. To search for Higgsinos, the strategy strongly depends on the size 0 0 0 ± ± 0 0 of the mass diﬀerences, ∆m ≡ ∆m χe2, χe1 and ∆m ≡ ∆m χe1 , χe1 . If ∆m is large enough, say ∆m0 > O (1 GeV), the decay often yields two leptons that can be reconstructed and used as a signal signature [1, 2]. In scenarios with more extreme

1 1 Introduction

± ± degeneracy, ∆m is very small, ∆m . 0.35 GeV, and the chargino becomes semi- stable and leaves a track in the detector before decaying. Disappearing tracks can hence be used to probe the SUSY parameter space with a very compressed mass spectrum [3, 4]. Figure 1.1 shows the current exclusion limits achieved with these ± 0 ± two search strategies in the plane of ∆m χe1 , χe1 versus m χe1 . Also shown is the limit from direct searches conducted at the LHC’s predecessor, LEP. What is striking is that the parameter space with mass splittings between approximately 0.3 and 1 GeV remains constrained only by LEP results, as it is neither accessible to di-lepton searches at the LHC nor to disappearing track searches conducted so far.

Figure 1.1: Current Higgsino exclusion limits obtained by ATLAS soft di-lepton and disappearing track searches and LEP limits. The region with mass splittings between 0.3 and 1 GeV has not yet been probed at the LHC. [5]

In this thesis, a strategy to search for Higgsinos with such a small mass splitting is presented, which targets the region that, so far, is lacking sensitivity. In this regime, the chargino decays predominantly, via on oﬀ-shell W boson, to a single pion [6]. The pion’s transverse momentum is of the order of the mass splitting, thus very soft, but often still reconstructable as a simple track. Notably, the chargino has a lifetime that leads to a decay length of up to a few millimeters and the pion is produced at a

2 vertex that is slightly displaced with respect to the primary interaction vertex. The soft and displaced track associated with the pion, as well as its kinematics, are used as handles to distinguish such events from SM background events. Figure 1.2 shows a Feynman diagram of the considered process with an additional jet from initial state radiation which enhances the sensitivity to the signal.

Figure 1.2: Feynman diagram of a typical signal process. For mass splittings ± ∆m . 1 GeV the chargino decay is expected to yield a single pion. The LSP that is produced along with the chargino can be exchanged with another chargino or the second-lightest neutralino. [7]

This thesis begins with a description of the theoretical background in Chapter 2. The experimental setup, namely, the CMS detector at the LHC, is described in Chapter 3. Chapter 4 summarizes the analysis strategy, while Chapter 5 takes a closer look at low-momentum displaced tracks. An analysis of data collected by CMS in 2016 is described in Chapter 6. Chapter 7 features the conclusions and an outlook.

2 Theoretical Background

2.1 The Standard Model of Particle Physics

The Standard Model of particle physics (SM) describes all known elementary particles, including those that carry three of the four known fundamental forces. El- ementary here means that the particles are, to current knowledge, not composed of other smaller, more fundamental particles and are considered point-like. Since its development in the second half of the twentieth century, the SM has been able to explain almost all particle physics experiments’ results and has also predicted a variety of phenomena that were later discovered experimentally. The most recent discovery was the observation of a new boson consistent with the Higgs boson in 2012 by both the ATLAS and CMS experiments at the LHC [8,9], as well as subsequent observations concerning its properties. The SM is thus a very well established and successful theory describing subatomic particles and their fundamental interactions.

2.1.1 Particle Content

The Standard Model consists of several groups of elementary particles which again can be divided according to other criteria. Figure 2.1 shows all particles with their most important properties and their aﬃliation to those groups.

The twelve fermions with half-integer spin on the left-hand side are sub-divided into quarks and leptons. Both are arranged in three generations with everyday matter being composed of particles of the ﬁrst generation. Within the quarks those are the up

5 2 Theoretical Background

Figure 2.1: All Standard Model particles grouped according to common properties. For each particle, the charge, mass, spin and, if applicable, the color charge are listed. [10]

2 1 and down quarks with an electrical charge of 3 and − 3 , respectively. Additionally, all quarks also carry color charge that can take a value of green, red, blue, or a superposition of the three. The ﬁrst generation leptons are electrons with an electrical charge of 1 and neutral electron-neutrinos. Up and down quarks, in combinations of three, make up protons and neutrons. Those composite particles in turn form atomic nuclei, which, together with electrons, form the atoms.

Particles of the second and third generation have, in general, the same properties as their ﬁrst generation counterparts, but they have larger masses and are unsta- ble. The second and third generation partners of the up (down) quark are the charm and top (strange and bottom) quarks and the electron’s second and third

6 2.1 The Standard Model of Particle Physics generation counterparts are the muon and the tau lepton, respectively. Each of those charged leptons has an associated neutral particle, a neutrino, which, in the context of the SM, is massless. Furthermore, all of the fermions have corresponding antifermions, which have the same mass and quantum numbers, but opposite charge.

The right half of Figure 2.1 shows the particles with integer spin, bosons. The gluon is the carrier of the strong force and couples only to the color-charged quarks and to itself. The electromagnetic force is a factor of 103 weaker than the strong force and is mediated by the exchange of photons, which couple to all electrically charged particles. The weak force is mediated by charged W and neutral Z bosons, and is, for small momentum transfer, a factor of 1016 weaker than the strong force. The W and Z bosons are highly massive, which is the underlying reason for the weak force’s very short range. Both the strong and the electromagnetic force have infinite range but exhibit key differences from each other. Namely, the strength of the strong force does not decrease but increases with increasing distance between the involved particles. A striking consequence of this property of the strong force occurs when two quarks move away from each other. At some point it is energetically favorable that a new quark-antiquark pair is formed. This leads to the formation of colorless composite particles called hadrons. This feature is called confinement and prevents quarks and gluons from being observed in isolation.

A central component of the SM is the Higgs boson, which is connected to electro-weak symmetry breaking and is responsible for generating the masses of the other particles. The mathematics that govern the Higgs boson, as well as the above described particles, is described in the following section.

The graviton, the hypothetical carrier of the gravitational force, is notably not part of the SM. As this force is by far the weakest of all four (1041 times weaker than the strong force), it does not play a detectable role in particle physics experiments.

7 2 Theoretical Background

2.1.2 Mathematical Description

From a mathematical point of view, the SM is a gauge quantum ﬁeld theory based on the symmetry group SU(3)×SU(2)×U(1) [11]. Here, the SU(3) symmetry governs the strong force (quantum chromodynamics) and the SU(2)×U(1) governs electroweak interactions [12]. Analogous to classical mechanics, the dynamics of a system can be described by a Lagrangian density (or just Lagrangian for short). In the case of quantum ﬁeld theory, the system is a set of particles moving in the vacuum. The Lagrangian must be both Poincaré invariant, which includes invariance under translations, rotations, and Lorentz-boosts, and gauge invariant under local SU(3)×SU(2)×U(1) transformations.

Each fermion type is represented not by a vector or scalar but by a 4-component Dirac-spinor ψ. For free fermions, the Lagrangian

¯ µ Lkin = ψ iγ ∂µ − m ψ (2.1) can be inserted into the Euler-Lagrange equation in order to arrive at the well-known Dirac equation, valid for free, relativistic spin-1/2 particles:

µ iγ ∂µψ − mψ = 0.

The 4×4 gamma matrices are connected to the three Pauli matrices σi:   1 0 0 0   i! 0 0 1 0 0  i 0 σ γ =   , γ = i = 1, 2, 3. 0 0 −1 0  −σi 0   0 0 0 −1

Fermion spinors can be decomposed according to the particle’s chirality into left- handed and right-handed components. For ultra-relativistic particles moving with β ≈ 1 the chirality coincides with the helicity, which is the projection of the spin vector onto the momentum direction. For left-handed (right-handed) particles, the

8 2.1 The Standard Model of Particle Physics spin is anti-parallel (parallel) to the momentum. Furthermore, the quark spinors can be split up into components for every color.

The theory of quantum chromodynamics (QCD) is based on invariance under SU(3) transformations and deﬁnes the interactions between color-charged particles, i.e. quarks and gluons. The symmetry is generated by eight linearly independent operators, which can be represented by the matrices Ta that are connected to the Gell- λa Mann matrices λa via Ta = 2 . For local invariance under this symmetry, the derivative in 2.1 has to be replaced by the covariant derivative:

a a ∂µ → Dµ = ∂µ + igsT Gµ.

a Here, gs is the strong coupling constant and G are eight new vector ﬁelds corresponding to eight gluons. Together with the kinetic term for the gluons, this leads to the Lagrangian:

µ µ a a 1 a aµν L = iψγ¯ ∂ ψ − g ψ¯ γ T G ψ − G G . (2.2) QCD µ s µ 4 µν

a abc The ﬁeld strength tensor Gµν is deﬁned with the structure constant f 6= 0 as

a a a abc b c Gµν = ∂µGν − ∂νGµ − gsf GµGν. (2.3)

The second term in 2.2 describes quark-gluon interaction and the third term contains gluon self-coupling with either three or four gluons involved.

For uniﬁed electroweak theory, the underlying symmetry is SU(2)×U(1). The charge related to SU(2) is the weak isospin I3. It is only carried by left-handed particles. Thus, the symmetry is also often denoted as SU(2)L. Left-handed particles 1 are arranged in isospin doublets where the upper entry has I3 = + 2 and the lower

9 2 Theoretical Background

1 entry I3 = − 2 . Right-handed particles in contrast have I3 = 0 and are singlets. In summary, the fermions are represented by ! ! ! ! ! ! νe νµ ντ u c t ψL = , , , , , and e µ τ 0 0 0 L L L d L s L b L

ψR = eR, µR, τ R, uR, dR, cR, sR, bR, tR.

0 0 0 It is noted that the interaction (or ﬂavor) eigenstates d , s , b and νe, νµ, ντ are not the same as the mass eigenstates d, s, b and ν1, ν2, ν3 but superpo- sitions of the respective three. The charge of the U(1) symmetry, on the other hand, is the hypercharge Y linked to the conventional electrical charge Q via Y =

2 (Q − I3).

a σa SU(2) symmetry is with respect to transformations given by the generators T = 2 (where σa are the Pauli matrices). Local invariance under this set of transformations a calls for three new vector ﬁelds Wµ , whereas invariance under U(1) transformation leads to a single U(1) gauge ﬁeld, written as Bµ. With this, the electroweak La- grangian is written

1 1 L = iψ¯ γµD ψ + iψ¯ γµD ψ − W a W aµν − B Bµν. (2.4) EWK L µ L R µ R 4 µν 4 µν

a a The ﬁeld strength tensors Wµν and Bµν are deﬁned analogously to Gµν (see Equation

2.3). However, in case of the Bµ gauge ﬁeld the last term vanishes.

Weak interactions of left-handed particles can be seen as a transition within their isospin doublet; for example, a muon can decay to a muon-neutrino by radiating oﬀ a W boson.

Because right-handed particles do not interact with the SU(2) gauge ﬁelds, the covariant derivatives for left-handed and right-handed particles are diﬀerent:

ig ig0 D ψ = ∂ + σaW a + YB ψ (2.5) µ,L L µ 2 µ 2 µ L ig0 D ψ = ∂ + YB ψ . (2.6) µ,R R µ 2 µ R

10 2.1 The Standard Model of Particle Physics

With the coupling constants g and g0 of the SU(2) and U(1) symmetry groups, the covariant derivative for left-handed particles is

ig ig0 D = ∂ + σaW a + YB (2.7) µ,L µ 2 µ 2 µ ! ! ig W 3 W 1 − iW 2 ig0 B 0 = ∂µ + + Y . (2.8) 2 W 1 + iW 2 W 3 2 0 B µ µ

Because the interaction of left-handed particles to the gauge bosons is given by ¯ µ iψLγ DµψL it can be concluded that the off-diagonal elements in the matrices correspond to interactions in which both particles of the isospin doublet participate. The basis can hence be changed to separate flavor-changing (off-diagonal) and flavor- conserving (diagonal) contributions. By identifying the physical W bosons as W ± = √1 (W ∓ iW ) 2 1 2 one arrives at ! ! ig 0 W + ig0 gW 3 + g0YB 0 Dµ,L = ∂µ + + Y . 2 W − 0 2 0 −gW 3 + g0YB µ µ

W 3 and B apparently interact with the same particles and can be linearly combined to form the physical Z boson and photon by rotation by the Weinberg angle

θW : ! ! ! W 3 cos θ sin θ Z µ = W W µ . Bµ − sin θW cos θW Aµ

It is important to note that up until now, a mass term of the form −mψψ¯ , as seen in the Lagrangian for a free fermion (equation 2.1), is not invariant under SU(2)×U(1) transformations. This means, that particles can not be massive “from the beginning” but rather have to acquire mass through some mechanism. The Higgs mechanism, proposed in 1964 by several independent theorists including Peter Higgs [13], does just that.

11 2 Theoretical Background

The Higgs mechanism postulates a new complex scalar (spin 0) ﬁeld as a weak isospin doublet

+! ! φ φ1 + iφ2 φ = 0 = . φ φ3 + iφ4

This ﬁeld has to fulﬁll the Klein-Gordon equation which leads to the Lagrangian

2 LH = Dµφ − V (φ) . (2.9)

Here, Dµ is the electroweak covariant derivative from equation 2.7. To solve for the potential V, an ansatz is chosen:

V (φ) = µ2 |φ|2 + λ |φ|4 .

For the vacuum to be stable, λ has to be greater than zero. If µ2 were also positive, the ground state would correspond to |φ| = 0, which would not lead to the desired mass terms. Instead, the symmetry is spontaneously broken with µ2 < 0 such that q 2 −µ the minimum lies at |φ| = v = λ 6= 0. v is the vacuum expectation value of the Higgs ﬁeld and has, as the only dimensionful parameter in the SM, units of mass (or energy).

By expanding this ﬁeld around the minimum as ! 1 0 φ = √ , (2.10) 2 v + H(x) excitations H(x) can be interpreted as a particle, the Higgs boson. The potential can now be written as 1 V (φ) = −µ2H2 + λvH3 + λH4. 4 √ p 2 2 This includes the Higgs boson mass in the ﬁrst term mH = 2µ = 2λv and three- and four-vertex Higgs self-couplings in the second and third term.

12 2.1 The Standard Model of Particle Physics

By inserting 2.10 into the Lagrangian 2.9, one arrives at interaction terms coupling the Higgs to the W and Z bosons as well as quadratic terms in Wµ and

Bµ which lead to the W and Z boson masses while the photon remains massless: q 1 1 2 02 mW mW = vg , mZ = v g + g , = cos θW . 2 2 mZ

The fermion masses in turn, can be explained by a Yukawa coupling of the Higgs ﬁeld to the fermion ﬁelds. It is of the form

+! ! ! ¯ ¯ φ ¯ +† 0† ψ1 LYukawa = −cf (ψ1, ψ2)L ψ2,R + ψ2,R (φ , φ ) . φ0 ψ 2 L

By inserting the Higgs ﬁeld expanded around the minimum (equation 2.10), a gauge invariant mass term is obtained along with an interaction term between the Higgs ﬁeld and the fermion: c v c L = − √f ψ¯ ψ − √f Hψ¯ ψ . Yukawa 2 2 2 2 2 2

Here, ψ2 is one of the lower-entry fermions from the isospin doublets. By using the charge conjugate of the Higgs doublet, analogously, also mass terms for the upper- entry quarks can be derived. As mentioned above, in the SM, neutrinos do not have mass because right-handed neutrinos don’t exist. However, experiments observing neutrino oscillations have shown that they must have a non-vanishing mass [14]. This fact can, however, be included into the SM by predicting right-handed sterile neutrinos or by including Majorana mass terms for neutrinos.

c v m = √f Thus, both the fermion masses f 2 and the coupling to the Higgs ﬁeld are proportional to the fermion’s Yukawa coupling constant cf and therefore proportional to each other.

13 2 Theoretical Background

2.1.3 Hints of Physics Beyond the SM

Although being a self-consistent and very successful theory, the SM has a number of shortcomings and can thus be only seen as an approximation to a yet unknown, more fundamental theory. One of these motivations to search for physics that goes beyond the SM is that the SM does not explain the fourth of the known fundamental forces, gravitation, and does not incorporate general relativity.

Furthermore, observations from astrophysical experiments clearly indicate that there has to be Dark Matter which makes up around 27% of the total energy density in the universe [15]. Dark here means that there is no electromagnetic interaction but the impact on a gravitational level is well observable. Another 68% of the universe’s energy density is attributed to Dark Energy. This form of energy is needed to explain why the universe is expanding at an accelerating rate and is also not accounted for in the SM.

Another open question is the so-called hierarchy problem. It refers to the fact that the weak force is many orders of magnitude stronger than gravity or, expressed diﬀerently, that the Higgs vacuum expectation value v ≈ 246 GeV is so much smaller than the Planck mass of 1019 GeV. This requires severe ﬁne-tuning to cancel quadratic radiative corrections to the Higgs mass.

The presented arguments, among others, motivate the search for yet unknown particles that would be part of a theory beyond the Standard Model (BSM). One particularly well-motivated and thoroughly studied extension to the SM is the notion of supersymmetry.

2.2 Supersymmetry

Supersymmetry (SUSY) is a symmetry that extends the SM by predicting for each fermion (boson) in the SM a bosonic (fermionic) superpartner with spin s = 0 1 (s = 2 ) [16–19]. The superpartners to SM fermions are typically denoted sfermions (e.g. selectron) while the superpartners to SM bosons are named with the suﬃx

14 2.2 Supersymmetry

"-ino" (e.g. Higgsino). If this symmetry were not broken, the new particles would have the same quantum numbers as their SM counterparts (except, of course, the spin). However, since such particles therefore would also have the same masses, they should have materialized at current particle collider energies which they have not. Thus, the symmetry must be broken, leading to heavier supersymmetric particles.

There are many supersymmetric theories, one of them being the minimal supersymmetric Standard Model (MSSM). Minimal here means that the MSSM predicts the least possible number of new particles. In the context of the MSSM, a new quantum number called R-parity can be deﬁned as

3B+L+2s PR = −1 .

Here, B is the baryon number, L the lepton number, and s the spin. SM particles have R-parity of +1 whereas all SUSY particles have PR = −1. Therefore, if R-parity is conserved, SUSY particles can only be produced in even numbers. Conservation of R-parity has desirable consequences, including the stability of the proton required by constraints on the proton lifetime [20]. Furthermore, the lightest supersymmetric particle (LSP) cannot decay and is stable which makes it a suitable candidate to explain Dark Matter.

Another problem of the SM that can be resolved by supersymmetry is the hierarchy problem described in section 2.1.3. Essentially, a large degree of ﬁne-tuning can be avoided because positive contributions to the Higgs mass by bosons would cancel out with negative contributions of the corresponding superpartner fermion and vice versa. However, this requires that supersymmetry breaking must be soft, meaning that it occurs around the electroweak scale. Higher-order, and thus smaller, corrections contributing to the Higgs boson mass do not cancel, however. This consideration leads to an expectation that the masses of the SUSY particles, particularly the LSP, are expected to not be signiﬁcantly larger than O (1 TeV) [19].

In the MSSM, the Higgs sector is expanded to contain two Higgs doublets rather than only one in the SM. This extension leads to four additional Higgs bosons that

15 2 Theoretical Background all have R-parity +1: a light scalar particle h0 (which seems to be consistent with the SM Higgs boson), a heavier scalar (H0) and a pseudoscalar (A0) Higgs boson and a pair of charged Higgs particles H±. The superpartners of those Higgs bosons (the Higgsinos) mix with the wino and bino gauge eigenstates to form four neutralino and 0 two chargino mass eigenstates that are labeled in order of ascending mass: χe1,2,3,4 ± and χe1,2. The lightest neutralino is usually assumed to be the LSP because it would ﬁt the assumption of cold dark matter being made up of weakly interacting particles (WIMPs). The electroweakino mixing is determined by the Higgsino mass parameter

µ and by the bino and wino mass parameters M1 and M2. Depending on their values, the neutralinos and charginos can be to diﬀerent extents dominated by the Higgsino-, bino-, or wino-component and thus be referred to as Higgsino-, bino-, or wino-like.

2.2.1 Natural SUSY and Light Higgsinos

The unconstrained MSSM has more than 100 free parameters [19]. This makes in- terpretations in its parameter space very impractical if not impossible. To provide a more convenient framework that also has a strong footing in its physical motivation, natural SUSY models were developed. “Natural” refers to a mild level of ﬁne-tuning in these scenarios, which ensures that the new physics satisfactorily addresses the hierarchy problem, which historically is the basis of the argument for the emergence of supersymmetry at the weak scale and therefore at the LHC.

Naturalness in SUSY models has various implications on the model parameters. However, the most robust result is that Higgsinos should be rather light [21]. The underlying reason is that in the wake of electroweak symmetry breaking, the Higgsino mass parameter µ is in leading order directly connected to the mass of the Z boson mZ :

2 2 2 2 mZ mH − mH tan β − = µ2 − d u . (2.11) 2 tan2 β − 1

16 2.2 Supersymmetry

In this equation, which is a minimization condition for the MSSM Lagrangian, Hd and

Hu are the two supersymmetric Higgs doublets, and tan β is the ratio of their vacuum expectation values. This means that by naturalness arguments, the Higgsino mass can not be much larger than mZ , a condition expressed in terms of the electroweak

ﬁne-tuning parameter ∆EW as

m2 |µ|2 < ∆ Z . EW 2

Here, ∆EW is the maximum value of any term in an expanded version with higher orders of equation 2.11. The condition can be interpreted such that to avoid ﬁne- tuning stronger than 1%, which means ∆EW < 100, Higgsinos can not be heavier than approximately 700 GeV. Meanwhile, the bino and wino mass parameters can be very large:

M1,2 |µ| .

This configuration leads to the lightest three electroweakinos being Higgsino-like with very similar masses as they are barely influenced by M1 and M2. Therefore, the mass differences

0 ± ∆m ≡ m 0 − m 0 , ∆m ≡ m ± − m 0 χe2 χe1 χe1 χe1 are rather small. In this thesis, like in many models, it is assumed that the lightest chargino is the next-to-lightest supersymmetric particle (NLSP) with the relation

∆m0 = 2∆m±.

This relation is also consistent with the limit of large tan β in the simpliﬁed model described in [22].

If R-parity is conserved, direct Higgsino production, like direct production of any SUSY particle, can only occur in pairs. Besides, at the LHC, it has a rather low cross section compared to processes involving colored particles. After being produced, a

17 2 Theoretical Background

(a) (b)

Figure 2.2: Charged Higgsino branching fractions (a) and decay length (b) as a function of the mass diﬀerence to the lightest neutral Higgsino. A MSSM 0 0 ± model with Higgsino-like χe1, χe2 and χe1 is assumed with the neutralinos being mass degenerate. [6]

± 0 χe1 or χe2 will decay to the LSP and a, possibly oﬀ-shell, gauge boson (W or Z, respectively). For this thesis, particularly chargino decays in models with ∆m± < 1 GeV are of interest. In this case, the W boson will decay predominantly into a single pion [6] and the decay width Γ can be parametrized [23] as

 s −1 ± 3 2 −1 14 mm ∆m mπ± Γ ± 0 ± '  1 − ± 2  . χe1 →χe1π ~c 340 MeV ∆m

The chargino branching ratios and decay lengths for diﬀerent mass splittings are shown in Figure 2.2. In these plots, a region labeled “Pure higgsino range” is marked in which the mass splittings are only attributed to radiative corrections as M1,2 → ∞.

18 3 The CMS Experiment

The research for this thesis was performed on simulations for and data recorded by the Compact Muon Solenoid (CMS) detector located at the Large Hadron Collider (LHC). Therefore, this chapter will give an introduction to the experimental setup at hand by brieﬂy describing the collider itself and the detector with its various components, both hardware and software wise.

3.1 The Large Hadron Collider

The Large Hadron Collider is a circular particle accelerator situated at the European Organization for Nuclear Research (CERN) laboratory near Geneva, Switzerland. The hadrons which are accelerated are mostly protons and sometimes heavy ions. However, for this thesis only proton collisions are relevant.

3.1.1 Overview

With its circumference of 26.7 km and its current center-of-mass energy for protons of 13 TeV, the LHC is the world’s largest and most powerful particle accelerator [24]. Such high energies are reached by utilizing several pre-accelerators which are shown in ﬁgure 3.1 along with the rest of the CERN accelerator complex.

The particles are accelerated in radiofrequency (RF) cavities in which electromagnetic ﬁelds oscillate. Due to the way of functioning of these structures there are no

19 3 The CMS Experiment

Figure 3.1: Sketch of the LHC (dark blue line) embedded into the entirety of the CERN accelerator complex [25] continuous beams but bunches of roughly 100 billion particles each which are moving along the ring. They are kept on their circular path by superconducting dipole magnets which have to be cooled to temperatures as low as −271 ◦C to reach the necessary magnetic field strength of 7.74 T [24]. As the deflection of charged particles in magnetic fields depends on the momentum of the particle and the protons in the beams have a certain momentum spread, the beam is being defocused in each dipole magnet. To correct this and to further focus and control the beams, also quadrupole (and higher-order) magnets are deployed.

Protons (or heavy ions) circulate in two beam lines in opposing directions and are brought to collision at four interaction points along the ring. At each of these points, a particle detector is housed in an underground cavern. There are two general- purpose experiments, ATLAS and CMS, and two more specialized detectors: ALICE, which focuses on heavy ion collisions, and LHCb, a forward detector targeting B mesons.

20 3.1 The Large Hadron Collider

3.1.2 Proton-Proton Collisions

When analyzing proton-proton (pp) collisions, it is important that protons are not elementary but rather composed of so-called partons [26] (namely quarks and gluons, see section 2.1). Each of those particles carries a fraction of the total proton energy. Therefore, in pp collisions, the exact energy of the actually colliding particles (i.e. the partons) is unknown. However, the momentum of the partons perpendicular to the beam axis (in the transverse plane) must be very close to zero. This can be exploited in the analysis of collision products because due to momentum conservation, their momenta have to add up to zero in the transverse plane.

At the LHC, with its bunch spacing of around 25 ns, there are approximately 1 billion pp collisions per second [24]. Most of these are soft interactions like elastic scattering, with soft meaning that the amount of transferred energy between the colliding particles is small. In contrary, hard interactions are characterized by large energy transfer such that new particles can be created. Hard interactions are the interactions of interest. Due to the fact that not single protons but bunches collide, they happen simultaneously with multiple soft and sometimes also hard interactions from other proton pairs. The entirety of those additional interactions is called pile- up.

To quantify the probability of a certain process to happen in a particle collision, a cross section σ is given in units of barn with 1 b = 10−28 m2. To get the absolute number of events N per time, this number has to be multiplied by the luminosity L, a measure characterizing the particle collider:

dN = σL. dt

The luminosity depends only on beam parameters. With f being the revolution fre- quency, n1,2 the number of particles per bunch and σx,y characterizing the transverse beam size, it can be expressed as n n L = f 1 2 . 4πσxσy

21 3 The CMS Experiment

(a) (b)

Figure 3.2: (a) LHC delivered integrated luminosity separate for each year in Run 1 and Run 2. Also stated is the corresponding center-of-mass energy. [27] (b) LHC delivered and CMS recorded integrated luminosity for Run 1 and Run 2, cumulative for all years. [27]

The LHC design luminosity is 1034 cm−2 s−1 [24]. By integrating the luminosity R over time Lint = L dt, a number specifying the amount of generated data can be given.

The peak luminosity per day as well as the center-of-mass energy of the LHC grew for each year after its commissioning in 2010 (except for a lower peak luminosity in 2015 compared to the running year before that). Figure 3.2 shows an overview over all running years so far. One has to distinguish the luminosity delivered by the LHC and the luminosity recorded by CMS during times when the detector was fully functioning. The ﬁrst years from 2010 to 2012 during which the center-of-mass energy was 7 and 8 TeV are generally referred to as "Run 1". Afterwards, upgrades during the "Long Shutdown 1" facilitated a center-of-mass energy of 13 TeV for the second running period from 2015 to 2018, called "Run 2". The total luminosity recorded by CMS in 2016 is 36 fb−1 and for the whole of Run 2 it is 140 fb−1.

22 3.2 The CMS Detector

3.2 The CMS Detector

The Compact Muon Solenoid (CMS) detector is one of two general-purpose particle detectors at the LHC. The layers of sub-detectors are built symmetrically around the interaction point like a cylindrical onion. In total, the detector weighs around 14 000 tonnes and is 21 meters long and 15 meters wide and high (a big onion). Figure 3.3 shows an overview of the detector. This chapter will start with a description of the coordinate system used in CMS, then describe its components: the tracking system made out of silicon, the eponymous solenoid magnet, both the electromagnetic and the hadronic calorimeters and the muon system as the outermost part of the detector. Each of those subsystems is divided into three parts: a barrel part cylindrically around the beam line and two endcaps. A detailed description of the detector can be found at [28].

Figure 3.3: Layout of the CMS detector with its diﬀerent components. [29]

23 3 The CMS Experiment

3.2.1 Coordinate System

Within the CMS collaboration a right-handed coordinate system is used which has its origin at the nominal interaction point in the center of the detector. The z-axis points along the beam line in anti-clockwise direction along the accelerator ring. Thus, the x- and y-axes span the transverse plane. The y-axis points upwards, whereas the x-axis points to the center of the LHC.

To deﬁne the direction of momentum of a particle, the azimuthal angle ϕ to the x-axis and the pseudorapidity η are used. The latter variable depends on the polar angle θ to the z-axis and is deﬁned as

θ η = − ln tan . 2

Therefore, it ranges from 0 (orthogonal to the beam axis, θ = 90°) to ±∞ (parallel to the beam axis, θ = 0°, 180°). However, the CMS detector is not able to detect particles arbitrarily close to the beam line. The tracking system, for example, is designed to detect particles with |η| . 2.5 corresponding to a polar angle of θ & 10° or 170° to the z-axis [28]. The rapidity is used because for massless particles, diﬀerences in this quantity are invariant under Lorentz-transformation along the z- axis. p To state the angular distance between particles, ∆R = ∆ϕ2 + ∆η2 is often used.

3.2.2 Tracking System and Magnet

In order to determine the momentum of a charged particle via the curvature of its track, the tracking system has to be located inside a magnetic field. The necessary magnetic field strengths are achieved by using a superconducting coil made of Niobium-titanium cooled to 4.6 K [28]. It sits outside the tracking system and the electromagnetic and hadronic calorimeters (see figure 3.3). The flux is re- turned through a return yoke sitting in between the muon chambers. The mag-

24 3.2 The CMS Detector netic ﬁeld strengths reached in this way are 3.8 T inside the coil and 2 T outside.

The tracking system of the CMS detector has a length of 5.8 m, a diameter of 2.5 m, and is entirely made of semiconducting silicon sensors totaling to around 200 m2 of active silicon area which makes it the largest silicon detector ever built [28]. In the innermost layers the sensors are pixel-shaped and further outwards there are strip sensors. However, the way of functioning is the same: a charged particle travel- ing through the sensor creates electron-hole pairs and due to an applied high voltage the charge can be collected. If it surpasses a certain threshold, a hit is registered.

The pixel detector has been upgraded during the LHC shutdown 2016/2017 from Phase 0 to Phase 1. Both setups are shown in ﬁgure 3.4. The Phase 0 pixel detector consisted of three layers in the barrel part located at radii of 4.4 cm, 7.3 cm and 10.2 cm plus two endcaps at each side. The individual sensors are 285 µm thick and each pixel has a size of 100 µm×150 µm. For the Phase 1 upgrade, a fourth barrel layer was inserted. The layers are now located at distances of 2.9 cm, 6.8 cm, 10.9 cm and 16.0 cm to the beam line. Also, a third endcap layer has been added. The dimensions of the pixel sensors themselves have not changed.

Figure 3.4: Schematic comparing the CMS pixel tracking detector used until and including 2016 (Phase 0, bottom) and afterwards (Phase 1, top). [30]

25 3 The CMS Experiment

The strip detector consists of 9.3 million strips with varying sizes. Their length ranges from 10 cm to 25 cm and their thickness from 320 µm to 500 µm. They are arranged in 10 layers in the barrel region, divided into the Tracker Inner Barrel (TIB) with 4 layers and the Tracker Outer Barrel (TOB) with 6 layers, and 12 disks in the endcaps, divided into the Tracker Inner Disks (TID) with 3 layers each and the Tracker Endcaps (TEC) with 9 disks at each side. Figure 3.5 shows how the diﬀerent subsystems are arranged within the CMS tracker.

Figure 3.5: Schematic cross section through the CMS tracker with the pixel subsys- tem directly around the interaction point and the diﬀerent strip subsystems further outwards. [28]

This setup results in a spatial hit resolution as low as 10 µm in the x/y-plane and 20 µm in z-direction [31].

3.2.3 Calorimeters

Calorimeters are installed outside the tracking system to stop emerging particles and to measure their energy. In contrary to the tracker, where it is desirable that the particles lose as little energy as possible, the energy loss in the calorimeters has to be as high as possible in order to stop the particles completely and capture all of

26 3.2 The CMS Detector their energy. Two types of calorimeters are deployed: an electromagnetic calorimeter (ECAL) for electromagnetically interacting particles like electrons and photons and a hadronic calorimeter (HCAL) for particles that mainly interact via the strong force (hadrons).

The ECAL consists of 80 000 scintillating crystals made out of lead tungstate (PbWO4). They act both as absorber and active material meaning that due to their high density 8.3 g Z of cm3 and high nuclear charge , the entering particles quickly lose energy in electromagnetic showers during which scintillation light is evoked. This light can be detected by attached photodiodes and by measuring the amount of light (number of photons) the energy of the initial particle can be determined. Electromagnetic showers are a result of mainly two processes: electron-positron pair production by high-energetic photons and bremsstrahlung from electrons and positrons. The barrel part of the ECAL covers a range of |η| < 1.479 and the endcaps extend this range to |η| < 3.0 [28].

The HCAL is built as a so-called sampling calorimeter, which means that the absorber material, in which hadronic showers are initiated, alternates with the active scintillating material. This is due to the longer mean interaction length of strongly- interacting hadrons. The absorber in use is made of brass with a chemical com- 8.5 g position of 70% Cu and 30% Zn and a density of cm3 . The HCAL pseudorapidity coverage is extended to |η| < 5.2 by forward hadron calorimeters placed at z = ±11.2 m [28].

3.2.4 Muon System

Muons are, together with neutrinos, the only known particles that are expected to pass through the dense calorimeters without interacting and without being stopped. Since neutrinos are not charged and interact only via the weak force, they escape the detector without a trace. Muons, to the contrary, are charged, leave a track in the silicon tracker and a second tracking detector is installed outside the calorimeters to capture the muon’s signature. The muon system is made up of four layers, called stations, with three diﬀerent working principles: drift-tubes (DT)

27 3 The CMS Experiment in the central region (|η| < 1.2), cathode strip chambers (CSC) in the endcaps (0.9 < |η| < 2.4) and resistive plate chambers (RPC) both in the barrel and endcap (|η| < 1.6) [28].

In all those detectors a volume is ﬁlled with gas which is ionized by the muon. The free charge is then collected by a high voltage applied to anodes and cathodes of diﬀerent forms depending on the type of the detector (wires, strips or plates). The electrical signal is registered and a hit is assigned. The RPC also provides a timing resolution of 1 ns which makes it suitable for triggering (see section 3.2.5).

The muon stations are interspersed with three layers of steel return yoke to guide the magnetic ﬁeld generated by the solenoid magnet. As the magnet sits between the inner tracker and the muon system, a track in the muon system is bent in the opposite direction than in the silicon tracker. The momentum of the muon can also be determined via the curvature of its track in the muon chambers. In fact, the two tracks can be combined to achieve a better momentum resolution (see section 3.3.2).

3.2.5 Trigger

At the LHC up to 1 billion particle collisions per second can take place. Recording all of these events is simply impossible and also not desired because most of the collisions are soft interactions with little energy transfer which are well understood (cf. section 3.1.2). Therefore, a trigger system is needed that can identify possibly interesting events that are then recorded. The CMS trigger system consists of two parts: The Level-1 (L1) trigger reduces the event rate to around 100 kHz and the subsequent High-Level-Trigger (HLT) leads to a further reduction of a factor 100, leading to an event rate of approximately 1 kHz that is recorded.

The L1 trigger is completely implemented in hardware which makes it very fast. It uses information from the muon system and the calorimeters and looks for easy to detect signs of interesting physics like very high-energetic particles. During the decision time of around 3.2 µs [28] the data is temporarily stored in buﬀers. The HLT,

28 3.3 Particle Identiﬁcation and Event Reconstruction on the other hand, uses combined information from multiple detector components and is implemented in software. It categorizes the events into several trigger streams that can then be used in physics analyses.

3.3 Particle Identiﬁcation and Event Reconstruction

To properly analyze a given event it is crucial that all emerging particles are reconstructed as fully as possible. To identify a particle one can make use of the fact that each type of particle leaves a distinct signature in the detector. This is shown in ﬁg- ure 3.6. Muons, for example, leave a trace in the inner tracker and are not stopped in either of the calorimeters which makes them leave another trace in the outer muon system. Electrons, on the other hand, shower in the electromagnetic calorimeter and are stopped there after having left a track in the inner tracker. This track dis- tinguishes them from photons that only deposit energy in the ECAL. Hadrons are stopped and shower in the hadronic calorimeter and if they are charged their tracks are also registered in the inner tracking system.

As mentioned before in section 3.2.4, neutrinos are the only known particles that leave the experiment undetected. However, their presence can be deduced from miss missing energy in the transverse plane pT (see section 3.1.2). This quantity is also important in searches for physics beyond the Standard Model because some of the corresponding new particles are also predicted to leave the detector without a trace.

3.3.1 Track Reconstruction

To reconstruct the path of a charged particle through the detector the ﬁrst step is to reconstruct the hits it left by ionization in detector cells (pixels or strips) of the tracking system. This process is referred to as local reconstruction. Firstly, neighboring cells with collected charges above a certain threshold are clustered into

29 3 The CMS Experiment

Figure 3.6: Transverse slice through the barrel of the CMS detector with its diﬀerent sub-detectors and the signatures of selected particle types [32] hits. Their positions are then determined with the distribution of deposited charge in the cluster taken into account. The hit resolution for tracks with transverse momenta pT > 12 GeV is measured to be 9.4 µm in the rφ-coordinate and between 20 µm and 45 µm in the longitudinal direction depending on the incident angle [31].

Because charged particles in a uniform magnetic field travel along a helical path, in principle a five-parameter helix fit to the reconstructed hits deposited by the charged particle has to be performed in order to determine the particle’s momentum. However, the sheer number of registered hits, inhomogeneities of the magnetic field, the occurrence of fake hits, and energy loss due to scattering can lead to er- rors. Therefore, a more complex and realistic method is applied. The relevant algorithm is referred to as global reconstruction and is a computationally demanding task.

30 3.3 Particle Identiﬁcation and Event Reconstruction

The tracking software is an extended and adapted Kalman ﬁlter that is run in multiple iterations (iterative tracking). Each iteration consists of the same four steps [31]:

1. A track seed is found from only two or three hits that deﬁne the initial estimate of the track’s trajectory.

2. The track ﬁnding is then performed by extrapolating the seed trajectory along the expected ﬂight path. Additional hits are assigned to the track candidate.

3. A ﬁt is performed to get the best possible track parameters and their uncertainties.

4. Tracks are discarded or kept with a quality ﬂag assigned corresponding to speciﬁed criteria.

The iterations mainly differ by the configurations of the seed generation and the track selection and each one is dedicated to a certain type of track. The first iteration aims at reconstructing prompt tracks (originating very close from the interaction point) with relatively high pT. Later iterations try to find displaced tracks, low-momentum tracks, or tracks with one or more missing hits in a detector layer. For each iteration, hits assigned to high-quality tracks found in previous iterations are excluded from the reconstruction which reduces the combinatorial complex- ity.

The track parameterization used in CMS is based on ﬁve parameters that are given at the so-called "reference point" of a track v = (vx, vy, vz) which is deﬁned as the point of closest approach to the center of the detector (0, 0, 0):

1. The signed inverse of momentum q/|~p| [GeV−1]

π 2. The dip angle λ = 2 − θ

3. The azimuthal angle φ

31 3 The CMS Experiment

4. The signed minimal distance in the transverse plane between the straight line

passing through (vx, vy) with angle φ and the point (0, 0):

dxy = −vx sin φ + vy cos φ [cm]

5. The signed minimal distance in the s-z-plane between the straight line passing

through (vx, vy, vz) with angles φ and λ and the point (s = 0, z = 0). Here, the s-axis is deﬁned by the projection of this straight line onto the transverse plane: dsz = vz cos λ − vx cos φ + vy sin φ sin λ [cm].

In this parameterization, the transverse and longitudinal impact parameters can be deﬁned as d0 = −dxy and dz = dsz/cos λ. The magnitude of transverse momentum can be calculated as pT = |~p| sin θ.

3.3.2 Particle Flow Algorithm

In CMS an algorithm known as Particle Flow (PF) is applied. The task of PF is to combine information from all sub-detectors, to identify particles or jets 1 and to provide additional information like missing transverse energy.

Reconstructed tracks are extrapolated to the calorimeters and linked to matching clusters of energy deposition forming a so-called "block". Additionally, energy clusters are linked to a track if they are located along tangents to the track to capture bremsstrahlung photons. Tracks found in the muon system are extrapolated back to the inner tracker and suitable pairs are formed by applying a global fit to the tracks. If the fit returns a reasonable χ2 and if the momenta measured in both sub-detectors agree within three standard deviations, the tracks are regarded as a "particle-flow muon". The used tracks are subsequently excluded from the inter- pretation procedure. Afterwards, blocks made out of tracks and ECAL clusters are

1Collimated ensembles of particles emerging from the fragmentation and hadronization of a quark or gluon that has been produced in the interaction.

32 3.3 Particle Identification and Event Reconstruction defined as "particle-flow electrons" if certain quality criteria are fulfilled. The used elements are again excluded from further consideration. Selected combinations of tracks and HCAL clusters are interpreted as charged hadrons, whereas calorimeter clusters without an assigned track are considered as neutral hadrons or photons depending on whether the concerned cluster was found in the HCAL or ECAL. The vectorial missing transverse energy is then defined as the negative vectorial sum of the transverse momenta of all found particles.

Interaction vertices are reconstructed in order to measure the location of all pp interactions in each event including the main vertex and all other vertices from pile-up interactions. For this task, as a ﬁrst step high-quality tracks are selected from all reconstructed tracks. Those tracks are then clustered into groups of tracks that appear to stem from the same vertex. The positions of the corresponding vertex candidates are measured by ﬁts to the associated tracks and uncertainties are assigned. The vertex with the largest sum of its associated track’s transverse momenta is referred to as the primary vertex (PV).

4 Analysis Strategy

The objective of this analysis is to search for semi-stable charginos decaying to the lightest neutralino, the LSP (see chapter 2.2.1) in events within the 2016 dataset √ collected by the CMS detector in proton-proton collisions with s = 13 TeV. The studied SUSY parameter space is characterized by a small mass splitting between the chargino and the lightest neutralino ∆m± = [0.3, 1.0] GeV, which means that the energy transferred to the visible decay product, typically a pion, is very small. The pion has a transverse momentum on the order of the mass splitting between the involved electroweakinos ∆m± (in the following referred to as the mass splitting if not stated otherwise), which makes it very soft. Additionally, due to the small mass splitting, the chargino has a discernible decay length in the detector of cτ = O (0.01 − 1) cm. Therefore, the pion is produced at a vertex that is displaced with respect to the primary interaction vertex where the chargino originates. The emerging soft and displaced track can thus be used as a handle to distinguish such events from SM background events.

Charginos can either be produced in pairs or along with a neutralino, either the lightest neutralino directly or the second-to-lightest neutralino which also decays to the lightest neutralino. In all cases, the ﬁnal state involves two LSPs that escape the experiment undetected. This leads to a large magnitude of missing transverse momentum which can be further ampliﬁed when the electroweakinos recoil against a high-pT jet from initial state radiation. Therefore, events are selected for analysis if they pass the event selection described in section 6.1 with the main requirement miss being large missing energy in the transverse plane, pT > 250 GeV. Further event selection requirements, apart from the soft and displaced track, are based on the latest CMS monojet analysis [33]. This analysis establishes that the dominant background

35 4 Analysis Strategy processes are Z(ν ν), contributing approximately 60% to the total background, and W(` ν)+jets with a share of roughly 30%. The remaining background is attributed to top quark processes and diboson production.

To identify the soft and displaced signal track among all tracks reconstructed in an event, an initial subset of candidate tracks is deﬁned by requiring tracks satisfying a number of selection criteria. This pre-selection reduces the number of total considered tracks from an average of roughly 500 to only around 100, but accepts nearly 100% of signal tracks. Subsequently, a multivariate classiﬁer in the form of a boosted decision tree (BDT) is employed to identify the most signal-like track in each event. Its implementation is described in chapter 5.3. The BDT is trained to distinguish tracks matched to generated pions emerging from the chargino decay from tracks reconstructed in simulated Z(ν ν) and W(` ν)+jets events. The latter are found to closely resemble the tracks within the signal events not originating from the SUSY particles (in-signal background). The main background sources on single-track level are relatively soft QCD processes, e.g. from pile-up or the underlying event, secondary 0 interactions like KS-decays, and fake tracks (cf. [23]).

The BDT is trained with the known mass splitting for the signal tracks as an input variable such that it can make use of different signal characteristics for different mass splittings in the considered range of ∆m± = [0.3, 1.0] GeV. For the background training sample, mass splittings are assigned based on a random sampling of the distribution of ∆m± from the signal sample. In this way, when evaluating the BDT, a specific mass splitting can be targeted optimally.

To incorporate the soft and displaced track requirement into the event analysis, an event-level quantity is deﬁned as the maximal track-level BDT score in the event. The BDT is evaluated for two mass splittings, 0.3 GeV and 1.0 GeV, and two orthogonal signal regions are deﬁned in the plane of the two maximal track-level BDT scores.

In order to estimate the expected number of background events in the signal regions, a data driven method is used which is brieﬂy described in the following and in more detail in chapter 6.3. Firstly, a "cleaned" Drell-Yan (DY) sample is obtained by selecting events with two opposite sign, isolated muons with an invariant mass

36 4.1 Datasets around the Z-mass. The muons are then removed from the event and their momenta miss are added to the ~pT . This procedure, referred to as Drell-Yan cleaning, has the purpose to create an event sample which is a good proxy for events with a Z boson that decays invisibly. The cleaning procedure is further described in section 4.1. The maximum BDT score distributions for cleaned DY events can then be used to model the SM background processes in the events to be analyzed. This is done by scaling the cleaned DY distributions in a control region.

To validate this procedure, a closure test is performed where both the cleaned DY and the background Z(ν ν) and W(`ν)+jets events are taken from simulated Monte Carlo (MC) events. Deviations are taken as systematic uncertainties.

± ± Exclusion limits are then set in the ∆m − m(χe1 ) plane by evaluating a likelihood based on the numbers of expected signal, background and observed events in the signal regions, along with various systematic uncertainties.

4.1 Datasets

For the signal MC samples, diﬀerent model points are used with chargino masses ± m(χe1 ) ∈ {100, 115, 140, 160, 180, 200, 225, 250, 275, 300, 400, 500} GeV and mass splittings ∆m± ∈ {0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1.0, 1.3, 1.8, 2.3, 3.3, 4.3, 5.3, 6.3} GeV with decay lengths based on [22]. The events are generated using Pythia8 [34] with LO precision and processed using the CMS Fast Simulation (FastSim) described in [35]. The branching ratio of the chargino decaying to a single pion and the LSP is assumed to be 1 and the signal cross sections are computed at NLO plus next-to-leading-log 0 ± 0 (NLL) precision in a limit of mass-degenerate Higgsinos χe1, χe1 and χe2 [36,37]. The cross sections for the considered chargino masses are shown in Table 4.1. Back- ground MC samples (Z(ν ν), W(` ν)+jets and Drell-Yan) are generated with Mad- graph [38] and Pythia8, and are further processed by a full detector simulation based on Geant4 [39]. The data DY control sample is taken from the Run2016 SingleMuon datastream.

37 4 Analysis Strategy

± m(χe1 ) [GeV] 100 115 140 160 180 200 cross section [fb] 16797 10833 5166 3109 2041 1336

± m(χe1 ) [GeV] 225 250 275 300 400 500 cross section [fb] 860.6 577.3 400.1 284.9 88.74 33.85

Table 4.1: The signal cross sections for the sum of all relevant production processes for diﬀerent chargino masses in the case of fully degenerate Higgsinos.

The Drell-Yan cleaning is performed in the following way: muons, identified by the PF-algorithm (see sec. 3.3.2) are selected if they fulfill pT > 10 GeV and are inside the pseudorapidity acceptance range of |η| < 1.4442 or 1.566 < |η| < 2.4. P −1 Additionally, they have to be isolated with P F Cs ∆R<0.2 pT × pT, muon < 0.2 to only allow for well reconstructed muons. If there are two opposite charge muons with an invariant mass of 75 GeV < mµµ < 105 GeV, i.e. consistent with the Z boson mass, their momentum vectors are added to the missing transverse momentum vector and the PF-candidates themselves and tracks (jets) matched via ∆R < 0.05 (< 0.2) are excluded from further consideration. With this procedure a sample resembling the main background, Z(ν ν), is obtained as there is no intrinsic difference between this process and the process of a Z boson decaying to two charged leptons. Muons are chosen instead of electrons because their momentum resolution is better due to additional hits in the muon chambers.

4.2 Event and Track Observables

All event-level observables used in this analysis are listed in Table 4.2 and Table 4.3 summarizes all track-level quantities. The reasoning for these observables will be described in the following chapters.

38 4.2 Event and Track Observables

Event-level

miss ~pT Negative vector sum of all PF candidates (PFCs) in an miss event; the magnitude is denoted as pT 100 Njets Number of jets with pT > 100 GeV and |η| < 2.5 ∆ϕ ~p miss, ~p miss T jets1,2,3,4 min Minimal azimuthal angle between T and the four leading jets with pT > 30 GeV and |η| < 2.5 miss miss mT ~pT , jet1 Transverse mass of ~pT and the leading jet deﬁned with the azimuthal angle between the two ∆ϕ as 2 miss miss jet1 mT ~pT , jet1 = 2pT pT (1 − cos ∆ϕ) b-tagged Njets Number of jets with pT > 30 GeV, |η| < 2.5 and a b- tag value assigned by the CSVv2-algorithm higher than 0.8484, corresponding to the medium working point.

Nleptons Number of electrons and muons with pT > 10 GeV and |η| < 1.4442 or 1.566 < |η| < 2.4 and isolated with P −1 P F Cs ∆R<0.2 pT × pT, lepton < 0.02

Nphotons Number of photons with pT > 15 GeV and |η| < 2.5 and P −1 isolated with P F Cs ∆R<0.2 pT × pT, photon < 0.02

Table 4.2: Table of event-level observables.

39 4 Analysis Strategy

Track-level

pT Transverse momentum and its error η Pseudorapidity PV |dxy | Distance in the transverse plane between a track and the primary vertex, using linear approximations. Plus, the error on this quantity. closest |dxy | Distance in the transverse plane between a track and the closest vertex in xy, using linear approximations. PV |dz | Distance along the z-axis between a track and the primary vertex, using linear approximations. Plus, the error on this quantity. closest |dz | Distance along the z-axis between a track and the closest vertex in z, using linear approximations. jets ∆Rmin Minimal ∆R to jets with pT > 30 GeV tracks PV ∆Rmin Minimal ∆R to tracks with pT > 1 GeV, |dxy | < 0.15 cm PV and |dz | < 0.15 cm

∆ηleading jet, ∆ϕleading jet Distance in pseudorapidity and azimuthal angle between the track and the jet with the highest pT miss ∆ϕMET Azimuthal angle between the track and ~pT

Table 4.3: Observables used in the track pre-selection as well as in the BDT.

40 5 Soft and Displaced Tracks

This section describes the analysis related to the soft and displaced tracks. It begins with the description of a track helix extrapolation tool that is, among other things, used for matching simulated particles to reconstructed tracks. Subsequently, the method to classify a soft and displaced track with a BDT is described in section 5.3.

5.1 Helix Extrapolation

Tracks with charge q, transverse momentum pT, pseudorapidity η, and azimuthal angle ϕ0 are extrapolated from their reference point v = (vx, vy, vz) along a helix with parameter t and constant r = 87.78 cm. Here, r is the radius of the path of a particle with pT = 1 GeV in a magnetic ﬁeld of 3.8 T, and so pT has to be given in GeV:

x(t) = vx + r · q · pT · [sin ϕ0 − sin (ϕ0 + t)]

y(t) = vy − r · q · pT · [cos ϕ0 − cos (ϕ0 + t)] −η−1 z(t) = vz − r · q · pT · t tan 2 · arctan e .

Along this path, both the curvature (and therefore pT) and the pseudorapidity are constant. The azimuthal angle changes according to ϕ (t) = ϕ0+t.

This parameterization assumes a constant magnetic ﬁeld, which is certainly not true when looking at the whole detector but is a very good approximation in the concerned region within a few millimeters around the beam line. In this close vicin-

41 5 Soft and Displaced Tracks ity to the beam line, also multiple scattering eﬀects along the track are negligible.

5.2 Track-matching to Generated Particles

To facilitate the analysis of tracks left by the soft and displaced pions, as a first step, there has to be a matching of the generator-level particle (the pion) to the reconstructed object (the track). In most analyses this is done by finding the reconstructed p object closest in ∆R = ∆ϕ2 + ∆η2 and matching if this distance is smaller than a certain threshold. However, for this analysis it is found that this technique fails when dealing with very soft and/or displaced objects. The reason lies in the defini- tion of the azimuthal angle ϕ for reconstructed tracks. As explained in section 3.3.1, all track parameters are given at the reference point, which is the point of closest approach to the center of the CMS detector. Figure 5.1 shows that the corresponding value of ϕ differs from the pion azimuthal angle and that this difference is sensitive to the difference between the true decay vertex and the reconstructed track reference point. Therefore, the ∆R matching criterion fails. Obviously, this becomes more important, the more the track is bent (the lower the pT) and the more it is displaced.

To overcome this issue, a new matching procedure is developed using the helix extrapolation described in chapter 5.1: For each simulated pion, a subset of tracks is defined with all tracks that have been assigned the pion’s charge and feature a relative pT difference to the pion |pT,pion − pT,track|/pT,pion < 0.2, as well as satisfying |ηT,pion − ηT,track| < 0.1 and |ϕT,pion − ϕT,track| < 1.57. This is done to reduce the number of considered tracks without a loss of matching efficiency. Among these tracks, the track with the minimal spacial distance ∆xyz to the pion’s origin vertex is identified. This is done by extrapolating the tracks along their helices and evaluating the points and corresponding distances of closest approach to said vertex. A track’s azimuthal angle can be extrapolated to the point of closest approach

42 5.2 Track-matching to Generated Particles

Figure 5.1: Sketch showing the different definitions of azimuthal angle for generated pion and reconstructed track. Here, it is assumed that the pion is radiated off in the direction of flight of the chargino. and a new ∆Rextrapolated can be computed. If the track with the minimal distance fulfills ∆xyz < 0.2 cm and ∆Rextrapolated < 0.05, it is matched to the pion. The new matching procedure is validated by comparing the ∆xyz versus ∆Rextrapolated distributions for pions and tracks with the same charge and with opposite charge. The distribution with the wrongly charged track does not show any accumulation in the matching region, indicating that the matching criteria effectively identify the correct tracks and reject random pairings. This can be seen in Figure 5.2.

Figure 5.3 shows a comparison of the pion matching efficiencies for the standard ∆R < 0.02 matching procedure (“old matching”) with the newly developed matching. The matching efficiencies are plotted for different chargino transverse decay lengths and pion transverse momenta. The improvement for transverse decay lengths of the chargino larger than approximately 1 cm and pion transverse momenta lower than roughly 2 GeV are clearly visible.

43 5 Soft and Displaced Tracks

Figure 5.2: Distributions of ∆xyz vs. ∆Rextrapolated for simulated pions and tracks with same charge (left) and opposite charge (right). The z-axis shows the (for each plot individually) normalized number of entries on a logarithmic color scale. A matching is performed if ∆xyz < 0.2 cm and ∆Rextrapolated < 0.05. It is shown that the contamination from random combinations in this region is negligible.

Figure 5.3: Pion matching efficiency for the new matching procedure using the track with the minimal spacial distance (left) and the standard ∆R < 0.02 matching (right) plotted versus chargino transverse decay length and pion pT. Note that particles with transverse momentum smaller than pT ≈ 150 GeV have a small reconstruction efficiency which also con- tributes to the matching efficiency shown here.

44 5.3 Multivariate Classiﬁer

5.3 Multivariate Classiﬁer

To identify the soft and displaced signal track in an event, a boosted decision tree (BDT) is trained, using the Toolkit for Multivariate Data Analysis with ROOT (TMVA) [40]. For the training, tracks matched to generated pions from the chargino decay in samples with a mass splitting in the range ∆m± = [0.2, 1.3] GeV are used as signal tracks. Background tracks are taken from simulated Z(ν ν) and W(` ν)+jets events, weighted to a ratio of Z(ν ν):W(` ν)+jets = 2:1 which corresponds to the ratio of expected background events, see section 4. Tracks from simulated events are used as background tracks instead of tracks from data to avoid training on artifacts from possible mismodeling of soft tracks in MC. In order to train the BDT with tracks from events that also pass the ﬁnal event selection, all events have to pass the event selection described in section 6.1, with the main feature being a large magnitude of missing transverse momentum. All tracks are required to pass a very loose pre-selection:

PV jets pT < 5 GeV and |dz | < 1 cm and ∆Rmin > 0.4.

In total, 700 000 signal and 2 000 000 background tracks are used. Each sample is divided into a training and a testing sample with a 2:1 ratio. The BDT is trained with 1 000 trees with a maximal depth of 6 using AdaBoost boosting with a learning rate of 0.3. These settings were optimized to yield a large integral under the ROC1 curve and high signal eﬃciency at low background eﬃciency while avoiding overtraining.

Additionally to the track observables listed in Table 4.3, three variables are deﬁned using the helix extrapolation described in chapter 5.1, namely:

PV, PCA 1. |dxy |: Distance in the transverse plane between a track and the primary vertex, evaluated at the point of closest approach (PCA) in 3D between the track’s helix extrapolation and the primary vertex;

1receiver operating characteristic

45 5 Soft and Displaced Tracks

PV, PCA 2. |dz |: Distance along the z-axis between a track and the primary vertex, evaluated at the PCA;

PCA 3. ∆ϕMET: Azimuthal angle between the vector pointing from the primary vertex miss to the PCA and ~pT .

miss The event-level magnitude of ~pT is also used as an input variable because signal miss events have a harder pT spectrum than background events. Furthermore, the BDT is trained with the known mass splitting for the signal tracks in order for it to be able to exploit the changing signal characteristics, for example by focusing more on displacement-related variables for lower mass splittings with longer chargino decay lengths or by learning the expected range of track-pT corresponding to the mass splitting. Figure 5.4 shows the distributions of four important input variables for background tracks and signal tracks with ∆m± ≈ 0.3 GeV and ∆m± ≈ 1.0 GeV. The distributions for the remaining variables can be found in Figures 5.5 and 5.6 and a ranking of the input variables, provided by TMVA, is included in Table 5.1.

Figure 5.7 shows the BDT response for signal and background tracks, each divided into a training and a testing sample. A Kolmogorov-Smirnov test yields a p-value of 0.741 (0.964), meaning that the null hypothesis that the signal (background) test and training sample distributions are drawn from the same distribution can not be rejected, which indicates no overtraining. The integral under the ROC curve amounts to 0.940.

When evaluating the BDT performance for different mass splittings, different structures resulting in different shapes of the BDT classifier output become apparent. Figure 5.8 shows the BDT response in narrow ranges around ∆m± = 0.3 GeV and ∆m± = 1.0 GeV. The two-peak structure for the higher mass splitting can be attributed to the rejection of tracks from pile-up that can easily be separated out due to PV higher values of the longitudinal impact parameter |dz | (see Figure 5.4a). For signal tracks with a lower mass splitting, however, this differentiation is not as easy as they themselves tend to be more displaced from the PV.

46 5.3 Multivariate Classiﬁer

(a) (b)

Figure 5.4: Normalized distributions of four BDT input variables that distinguish background tracks from signal tracks. Signal tracks are shown for two mass splittings indicating the large value ranges within the diﬀerent model points.

47 5 Soft and Displaced Tracks

Figure 5.5: Normalized distributions of BDT input variables for background tracks and for signal tracks with ∆m± = 0.3 GeV and ∆m± = 1.0 GeV - Part 1

48 5.3 Multivariate Classiﬁer

Figure 5.6: Normalized distributions of BDT input variables for background tracks and for signal tracks with ∆m± = 0.3 GeV and ∆m± = 1.0 GeV - Part 2 49 5 Soft and Displaced Tracks

Rank Variable Importance

1 ∆m± 0.09258 PV 2 log10 |dz | 0.08130 PV, PCA 3 log10 |dxy | 0.07437 PV 4 log10 error on |dxy | 0.07067

5 pT 0.06886 closest 6 log10 |dz | 0.06534 PV 7 log10 |dxy | 0.05580 PV 8 log10 error on |dz | 0.05554 PV, PCA 9 log10 |dz | 0.05501

10 ∆ϕMET 0.05321 closest 11 log10 |dxy | 0.05274 miss 12 pT 0.05016 PCA 13 ∆ϕMET 0.04860 jets 14 ∆Rmin 0.04130

15 ∆ηleading jet 0.03968 tracks 16 ∆Rmin 0.03783 17 η 0.02861

18 ∆ϕleading jet 0.02839

Table 5.1: Ranking of BDT input variables.

50 5.3 Multivariate Classiﬁer

Figure 5.7: BDT response for training and testing samples for signal and background tracks with linear and logarithmic y-axis cumulative of all mass splittings.

(a) ∆m± = 0.3 GeV (b) ∆m± = 1.0 GeV

Figure 5.8: BDT response for training and testing samples for signal and background track limited to two signal mass splittings.

6 Analysis

6.1 Event Reconstruction and Selection

A set of event and object selection criteria are established to obtain signal regions with high significance. The tracks used in this analysis are reconstructed as described in section 3.3.1 and are required to pass basic quality criteria rejecting tracks that have been assigned zero valid hits, zero degrees of freedom, or a charge of zero. Electrons, muons, and photons are reconstructed by the Particle Flow (PF) algorithm illustrated in section 3.3.2. Jets are constructed from the PF candidates by the anti-kt algorithm with distance parameter R = 0.4. Charged particles from pile-up are removed before the clustering. Jet quality criteria are applied to the neutral and charged energy fractions and the number of jet constituents; events with a bad jet inside |η| < 2.5 are rejected. In addition, various event filters are employed to reduce the number of events with mismeasurements leading to a flawed reconstruction of the missing transverse momentum. Jet energy corrections are applied and propagated to the missing transverse momentum (Type-I MET correction).

Signal region events are selected using selection criteria that are very similar to the ones used in the latest CMS monojet analysis [33]. To gain sensitivity to the signal process, these event selection cuts are then extended with the requirement of the presence of a soft and displaced track as described in the following chap- miss miss ter. Triggers with a threshold of 120 GeV on both pT,trig and HT,trig are used. miss Here, HT,trig is the magnitude of the vectorial sum of the transverse momenta of jets with pT > 20 GeV and |η| < 5. A further oﬄine selection requirement of miss pT > 250 GeV is applied and the trigger eﬃciency in this regime is found to

53 6 Analysis be larger than 97%. Figure A.1 in the appendix shows the trigger eﬃciency as a miss function of pT . Furthermore, a leading jet with pT > 100 GeV and |η| < 2.5 is required. A veto on events with an electron, muon, isolated photon, or b-tagged b-tagged jet is applied: Nleptons < 1,Nphotons < 1,Njets < 1. The exact deﬁnitions of these observables are given in Table 4.2. QCD multijet background is rejected by miss requiring the minimal azimuthal angle between ~pT and the four leading jets with p > 30 GeV |η| < 2.5 ∆ϕ ~p miss, T and , denoted T jets1,2,3,4 min, to be larger than 0.5 radians. To further reduce the background from W(` ν)+jets events, a threshold is set on the transverse mass of the missing transverse momentum and the leading jet: miss mT ~pT , jet1 > 300 GeV.

∆ϕ ~p miss, The distributions of missing transverse momentum and T jets1,2,3,4 min for data, MC Z(ν ν), MC W(` ν)+jets, and two signal model points are shown in Figure 6.1 after these event selection cuts. It has to be noted that only the two most important background processes, Z(ν ν) and W(` ν)+jets, are included. Also, in the simulated Z(ν ν) and W(` ν)+jets samples, cuts on the pT of the Z boson and the vectorial sum of all neutrinos, respectively, are applied which slightly inﬂuences the miss pT spectrum at lower values. As this analysis relies on a data driven background estimation method, the depicted data to MC agreement is assessed to be suﬃciently good.

54 6.2 Soft and Displaced Track Requirement

(a) (b)

miss Figure 6.1: Data to MC comparison in two variables: pT and ∆ϕ ~p miss, T jets1,2,3,4 min. Only the two most dominant background processes, Z(ν ν) and W(` ν)+jets, are shown. Also included are the distributions for two signal model points.

6.2 Soft and Displaced Track Requirement

Additionally to the event selection described above, in each event, the presence of a soft and displaced track is required to gain sensitivity to the signal process. This requirement is implemented using the multivariate classiﬁer described in chapter 5.3. Per event, all tracks are assigned two BDT scores; with the BDT evaluated for ∆m± = 0.3 GeV and for ∆m± = 1.0 GeV. These two mass splittings are chosen because the respective BDT scores are not correlated for suﬃciently large values and, like this, the whole range of considered mass splittings can be covered. Subsequently,

55 6 Analysis

(a)Z( ν ν) (b) Signal

Figure 6.2: The signal and control regions are orthogonalized with a diagonal cut in the plane of the two maximal BDT scores. (a) The distribution for Z(ν ν) events is underlaid. (b) The distributions for two signal model ± ± points are underlaid: m(χ1 ) = 115 GeV, ∆m = 0.27 GeV (orange) and ± ±e m(χe1 ) = 115 GeV, ∆m = 0.97 GeV (blue). two event-level quantities are deﬁned as the maximal BDT scores obtained for each of the mass splittings. In the two-dimensional plane of these observables, a diagonal cut is applied such that each event is either assigned to the ∆m± = 0.3 GeV domain (if the maximal BDT score for an evaluation at ∆m± = 0.3 GeV is bigger than the maximal BDT score for an evaluation at ∆m± = 1.0 GeV) or vice versa. This is done to orthogonalize the two signal regions and to establish two independent bins for the limit setting.

This is visualized in Figure 6.2 along with the signal regions and control regions used for the background estimation in the plane of the two maximal BDT scores. Also shown is, in Figure 6.2a, the two-dimensional distribution for Z(ν ν) events and in Figure 6.2b for two signal model points. The exact deﬁnitions of the signal and control regions are described later in this chapter.

To validate that in signal events, this procedure is actually sensitive to the sought- after signal track and does not depend on in-signal background tracks, a matching of the tracks with the highest BDT scores to the simulated particles is per- ± formed. Figure 6.3 shows, for diﬀerent signal model points with m(χe1 ) = 115 GeV

56 6.2 Soft and Displaced Track Requirement and ∆m± ∈ {0.17, 0.27, 0.57, 0.97} GeV and for the two BDT implementations, the fraction of the highest-scoring tracks that are matched to the pion from the chargino decay, or to a neutralino decay product, versus the maximal BDT score. It can be seen that generally, in events with high maximal BDT scores, the highest-scoring track is connected to a SUSY particle, mostly to the chargino. Also, as expected, this eﬀect is enhanced if the signal mass splitting is close to the mass splitting for which the BDT was evaluated. But also signal tracks in events with an intermediate mass splitting, ∆m± = 0.57 GeV, are seen to obtain high BDT scores, especially for the ∆m± = 1.0 GeV BDT. For lower signal mass splittings, where the reconstruction of the soft and displaced signal track from the chargino decay becomes increasingly 0 ± 0 diﬃcult, also tracks connected to χe2 decays in events with χe1 χe2 production play a role. Owing to the assumed Higgsino spectrum with ∆m0 = 2∆m±, those tracks have slightly higher transverse momenta and evidently additional properties that lead them to be assigned a high BDT score.

Figure 6.4 shows the maximal BDT score distributions for Z(ν ν) and W(` ν)+jets ± MC background events and for two selected signal model points: one with m(χe1 ) = ± ± ± 115 GeV and ∆m = 0.27 GeV and the other with m(χe1 ) = 115 GeV and ∆m = 0.97 GeV. All distributions are scaled to the corresponding cross sections. It can be seen that signal events generally have a higher maximal BDT score than background events and also that within the signal model points, the one with the mass splitting closer to the mass splitting for which the BDT was evaluated performs better. In the tails of the W(`ν)+jets distributions the limited MC statistics become apparent.

For each mass splitting, a signal region is deﬁned by computing the signal signiﬁ- cance S σ = q 2 B + δBsyst

2 for diﬀerent cuts on the maximal BDT score. In this equation, δBsyst is the systematic uncertainty associated to the background estimation method (see chapter 6.3) and is composed of two contributions, added in quadrature: A constant term of 10%

57 6 Analysis relative uncertainty and a term depending on the signal region cut taking into account the increasing statistical uncertainty for higher cut values. The number of signal ± events surviving a cut S is taken from a signal model with m(χe1 ) = 140 GeV and a mass splitting matching the mass splitting for which the BDT is evaluated. The number of background events after a cut B is taken from the cleaned DY data sample which is used for the background estimation. A cut at 0.44 (0.43) yields the highest signiﬁcance for the ∆m± = 0.3 (1.0) GeV BDT, as can be seen in Figure 6.5.

Furthermore, two sideband control regions are established that are later used for scaling the cleaned DY distributions as part of the background estimation method. The control regions are deﬁned close to the signal regions in order to enable a pre- cise background prediction; while avoiding signal contamination of more than 3% for the signal model point with the highest cross section that is not yet excluded ± ± ± by LEP results, m(χe1 ) = 100 GeV. For ∆m = 0.3 GeV (∆m = 1.0 GeV), the control region is chosen to range from 0.3 (0.25) to 0.4 (0.35), cf. Figure 6.6.

58 6.2 Soft and Displaced Track Requirement

Figure 6.3: Maximal BDT score distributions for signal events (gray) and with the requirements that the highest-scoring track is matched to the signal pion (red) or to a neutralino decay product (orange). In the left column, the BDT is evaluated at ∆m± = 0.3 GeV and in the right column for ∆m± = 1.0 GeV. Diﬀerent signal model points are arranged with ascending ∆m± from top to bottom: 1. row: ∆m± = 0.17 GeV, 2. row: ∆m± = 0.27 GeV, 3. row: ∆m± = 0.57 GeV, 4. row: ∆m± = 0.97 GeV. ± All signal model points have m(χe1 ) = 115 GeV. 59 6 Analysis

(a) (b)

Figure 6.4: Maximal BDT score distributions with the BDT evaluated at (a) ∆m± = 0.3 GeV and (b) ∆m± = 1.0 GeV. The distributions for MC Z(ν ν), W(` ν)+jets, and two signal model points are shown.

60 6.2 Soft and Displaced Track Requirement

(a) ∆m± = 0.3 GeV (b) ∆m± = 1.0 GeV

Figure 6.5: Distributions of the maximal BDT scores with the signal signiﬁcance in the lower panels for diﬀerent cuts on the observables. On the left (right) hand side, the BDT output evaluated at ∆m± = 0.3 GeV (∆m± = 1.0 GeV) is shown. In the lower panels, also the relative error due to changing statistics in the signal regions for the closure test and the number of cleaned DY events (labeled B) for each cut value is shown.

61 6 Analysis

(a) ∆m± = 0.3 GeV (b) ∆m± = 1.0 GeV

Figure 6.6: Quantities used to optimize the sideband control regions for both the ∆m± = 0.3 GeV BDT (left) and the BDT evaluated at ∆m± = 1.0 GeV (right). The upper panels show how much the ratio of MC Z(ν ν) to cleaned DY MC events in the signal regions differ from 1 for different definitions of the control regions. The corresponding signal contamination ± is shown in the lower panels as the ratio of the number of m(χe1 ) = 100 GeV signal events to the number of events in data.

62 6.3 Background Estimation

6.3 Background Estimation

To estimate the number of expected SM background events in the two signal regions, a data driven method is applied. It uses a cleaned Drell-Yan (DY) sample where the momenta of two muon candidates with an invariant mass consistent with the Z boson mass are added to the missing transverse momentum and the corresponding candidates and tracks are removed from the event. A more detailed description of this procedure is given in section 4.1. The cleaned DY sample is now expected to be a good proxy to the most important background process, Z(ν ν). In addition to that, soft tracks from pile-up vertices or the underlying event are naturally also contained in the cleaned DY sample and their inﬂuence does not need to be estimated from possibly not well modeled MC simulations.

The distributions of the maximal BDT scores (evaluated at ∆m± = 0.3 GeV and ∆m± = 1.0 GeV) for the cleaned DY sample can thus be used as templates. By scaling them to the data event yield in a sideband control region, the appropriate normalization is achieved. The deﬁnition of the control regions and signal regions is documented in section 6.2.

The method is validated with the means of a closure test by applying it to MC Z(ν ν) events with also the cleaned DY sample taken from MC Drell-Yan events. Fig- ure 6.7 shows the corresponding distributions, the distribution for Z(ν ν) is scaled to the corresponding cross section and the distribution for the cleaned DY events is scaled to the Z(ν ν) distribution in the control region. It can be seen that, for both mass splittings, a good agreement is achieved in broad ranges containing the signal regions. There is, however, a trend visible to underpredict the event yield the lower the maximal BDT scores are. This effect can be attributed to the circumstance miss that the pT distribution of the cleaned DY sample is biased due to the pT depen- dence of the muon acceptance. In other words, the lower the muon pT, the lower the miss reconstruction efficiency and therefore events with lower pT are underrepresented in the cleaned DY samples. Because the BDT score is positively correlated to the miss magnitude of ~pT , this effect is propagated to the shown maximal BDT score dis- miss tributions. However, in the signal-like region of the BDT with high pT , this bias

63 6 Analysis does not play a role since the muon acceptance reaches a plateau for high transverse momenta.

(a) ∆m± = 0.3 GeV (b) ∆m± = 1.0 GeV

Figure 6.7: The closure test for MC Z(ν ν) events (a) for the ∆m± = 0.3 GeV BDT and (b) for the ∆m± = 1.0 GeV BDT shows good agreement in the signal regions. In the lower panels, the ratio between the Z(ν ν) and the cleaned DY sample is shown. The control regions (CR) are marked in gray and the signal regions (SR) in red.

The cleaned DY template is used to estimate the entirety of SM background events including W(` ν)+jets and other events. When looking at W(` ν)+jets events sepa- rately, it is important to note that this process has key diﬀerences with respect to the DY process. Firstly, as there is only one neutrino present at tree-level, in general, miss a softer pT spectrum and therefore more events with lower maximal BDT scores are expected. Also, the occurrence of electrons, muons and especially tau leptons from the W boson decay plays a role. While electrons and muons mostly do not pass

64 6.3 Background Estimation

the pT < 5 GeV requirement, it is found that low-momentum particles from the tau decay are a background source. This is expected due to the lifetime of the tau leading to a slightly displaced decay vertex and due to the soft spectrum of the charged pions in tau decays. Especially the maximum BDT score distribution for the BDT evaluated at ∆m± = 1.0 GeV is contaminated by such events and exhibits a slightly enhanced tail. However, the statistical uncertainties in this region are large. The distributions for the W(` ν)+jets MC sample are shown in Figure 6.8 along with the distribution for the cleaned DY events from MC scaled to W(` ν)+jets in the control regions. It can be seen that in the signal regions, the prediction from the cleaned DY MC sample agrees with the actual yield from W(` ν)+jets MC events within the statistical uncertainties.

(a) ∆m± = 0.3 GeV (b) ∆m± = 1.0 GeV

Figure 6.8: The background estimation method tested for MC W(` ν)+jets events. In the lower panels, the ratio between the W(` ν)+jets and the cleaned DY sample is shown. The control regions (CR) are marked in gray and the signal regions (SR) in red.

65 6 Analysis

To quantify the systematic uncertainty associated to the background estimation method, the method is applied to Z(ν ν) and W(` ν)+jets MC events combined; each sample scaled to its respective cross section. Figure 6.9 shows that the ratio exhibits the expected trend towards lower maximal BDT scores and that the prediction and actual MC event yields in the signal regions agree. The systematic uncertainty is taken to be the maximum of the deviation to 1 in the signal regions and the statistical uncertainty in these bins, i.e. for the ∆m± = 0.3 GeV BDT 30% and for ∆m± = 1.0 GeV 38%.

(a) ∆m± = 0.3 GeV (b) ∆m± = 1.0 GeV

Figure 6.9: The background estimation method tested for MC Z(ν ν) and W(`ν)+jets events combined. In the lower panels, the ratio between the Z(ν ν) and W(` ν)+jets event numbers and the cleaned DY event yields is shown. The control regions (CR) are marked in gray and the signal regions (SR) in red.

66 6.4 Validation

6.4 Validation

To validate the analysis beyond the simulation-based closure test, control region distributions are compared. This is done for two pairs of datasets: The cleaned DY sample from data is compared to the MC cleaned DY sample and the data events are compared to events of the data cleaned DY sample. Two of the variables are PV shown in Figures 6.10 and 6.11: log10 |dz | and ∆ϕMET of the highest scoring tracks; all distributions are normalized.

The ﬁrst comparison is done to assess the simulation of the soft and displaced track in MC events. It is expected that the simulation of such tracks from pile-up or the underlying event may not be optimized and the agreement with data may be rather poor. However, for this analysis the MC samples are only used for the closure test of the background estimation method and for the determination of the associated uncertainty. It is assumed that the extent of mis-modeling is the same for all MC samples and therefore the observed closure for MC can be transferred to data. Nonetheless, the comparison in Figure 6.10 shows that the agreement between cleaned DY from data and from MC generally is within ±10%.

By comparing the track-related distributions for data versus cleaned DY data, it is determined if tracks obtaining a BDT score in a particular range also exhibit the same kinematic distributions in both samples. Figure 6.11 shows that this is the case within small uncertainties on the percent-level. Thus, the general approach to use the BDT score distributions of cleaned DY events as templates is supported.

67 6 Analysis

(a) (b)

PV Figure 6.10: Normalized distributions of log10 |dz | (top) and ∆ϕMET (bottom) of the highest scoring track in the ∆m± = 0.3 GeV (left) and ∆m± = 1.0 GeV (right) control regions for cleaned DY MC and cleaned DY data. “Max. Track ∆m=X” refers to the track with the highest BDT value in a given event, where X is the mass splitting for which the BDT was evaluated. 68 6.4 Validation

(a) (b)

PV Figure 6.11: Normalized distributions of log10 |dz | (top) and ∆ϕMET (bottom) of the highest scoring track in the ∆m± = 0.3 GeV (left) and ∆m± = 1.0 GeV (right) control regions for data and cleaned DY data. “Max. Track ∆m=X” refers to the track with the highest BDT value in a given event, where X is the mass splitting for which the BDT was evaluated. 69 6 Analysis

6.5 Predicted Event Yields and Uncertainties

The systematic uncertainty of the data driven background estimation is taken from the MC closure test in section 6.3. It amounts to 30% in the ∆m± = 0.3 GeV signal region and 38% for ∆m± = 1.0 GeV. As the ﬁnal predicted event counts depend on the event yields for data and cleaned DY in the control regions, as well as the event yields for cleaned DY in the signal regions, see equation 6.1, the respective statistical uncertainties are also included. Especially the latter are signiﬁcant as the unscaled event numbers for cleaned DY in the signal regions are as low as 14 (11) for ∆m± = 0.3 GeV (∆m± = 1.0 GeV). The resulting total number of expected SM background events are 393 ± 158 for ∆m± = 0.3 GeV and 355 ± 172 for ∆m± = 1.0 GeV. This is shown in Figure 6.12, blinded in the signal regions, where the statistical uncertainties are shown as blue shaded areas in the upper plots and as error bars in the ratio plots; and the systematic uncertainties are visualized as gray shaded areas in the ratio plots.

N(data in CR) expected background = × N(cleaned DY in SR) (6.1) N(cleaned DY in CR)

For the expected signal event yields, systematic uncertainties associated to various sources are included:

• cross section prediction: 4%,

• luminosity measurement: 2.5%,

• jet energy scale: 4%,

• b-jet and lepton veto: 6%.

Additionally, the statistical MC uncertainties are added in quadrature.

70 6.5 Predicted Event Yields and Uncertainties

(a) (b)

Figure 6.12: Maximum BDT score distributions for data and cleaned DY scaled to data in the control regions for (a) the ∆m± = 0.3 GeV BDT and (b) the ∆m± = 1.0 GeV BDT. In the lower panels, the ratio between the data event numbers and the cleaned DY event yields is shown. The control regions (CR) are marked in gray and the signal regions (SR) in red. In the signal regions, the gray shaded areas indicate the systematic uncertainty adding to the statistical uncertainty shown as error bars. The signal regions are blinded.

71 6 Analysis

6.6 Observed Event Yields and Exclusion Limit

The expected event yields with their total uncertainties for four benchmark signal model points and for the total expected background are shown in Table 6.1. Unblind- ing the signal regions for data leads to 385 (495) observed events for ∆m± = 0.3 GeV (∆m± = 1.0 GeV). Figure 6.13 shows the whole range of the maximal BDT score distributions for data and cleaned DY (scaled to data in the control regions). The numbers of observed events in the signal regions are consistent with the number of predicted background events.

± ± ± ∆mBDT m(χe1 ) = 115 GeV m(χe1 ) = 140 GeV Total Observed ± ± ± ± expected ∆m = ∆m = ∆m = ∆m = bkg. 0.27 GeV 0.97 GeV 0.28 GeV 0.98 GeV

0.3 GeV 41.2 ± 6.7 11.7 ± 3.0 27.5 ± 4.0 6.2 ± 1.6 393 ± 158 385 1.0 GeV 26.5 ± 5.1 80.9±10.6 12.3 ± 2.4 60.7 ± 7.1 355 ± 172 495

Table 6.1: Expected event yields for four signal model points with total uncertainties (systematic and MC statistics) in both signal regions; as well as the total numbers of expected SM background events with total uncertainties (systematic and due to statistics in the signal regions for cleaned DY and in the control regions for cleaned DY and data). Also stated are the observed event counts in the two signal regions.

± ± To establish an exclusion limit in the plane of ∆m and m(χe1 ), the Higgs Combine Tool [41] is used. Figure 6.14 shows the 95% conﬁdence level upper limit on the production cross section and the corresponding expected and observed limits that are in agreement within 1 σ throughout the whole range. The analysis is most sensitive in the region of ∆m± ≈ 0.8, where chargino masses up to 120 GeV are excluded. But also for lower mass splittings as low as 0.6 GeV, the current exclusion limits can be extended.

72 6.6 Observed Event Yields and Exclusion Limit

(a) (b)

Figure 6.13: Maximum BDT score distributions for data and cleaned DY scaled to data in the control regions for (a) the ∆m± = 0.3 GeV BDT and (b) the ∆m± = 1.0 GeV BDT. In the lower panels, the ratio between the data event numbers and the cleaned DY event yields is shown. The control regions (CR) are marked in gray and the signal regions (SR) in red. In the signal regions, the gray shaded areas indicate the systematic uncertainty adding to the statistical uncertainty shown as error bars.

73 6 Analysis

Figure 6.14: Expected (dashed, red) and observed (solid, black) exclusion limits with their respective 1 σ contours along with the 95% conﬁdence level upper ± ± limit on the production cross section in the plane of ∆m and m(χe1 ). The signal model is a natural SUSY model with the three lightest electroweakinos being Higgsino-like. The mass splitting between the two lightest neutralinos is assumed to be twice as large as the mass splitting between the lightest chargino and the lightest neutralino. Also, the chargino is assumed to decay exclusively to the LSP and a single pion.

74 7 Conclusion and Outlook

In this thesis, a search for Higgsinos has been presented using events with a large magnitude of transverse momentum pmiss recorded by the CMS detector in proton- √ T proton collisions at s = 13 TeV. In the examined SUSY parameter space, the ± mass diﬀerence between the lightest charged Higgsino χe1 and lightest neutral Hig- 0 gsino χe1, which is assumed to be the lightest supersymmetric particle (LSP), is very small: ∆m± = [0.3, 1.0] GeV. This scenario is motivated by a small level of ﬁne-tuning in so-called natural SUSY models. The chargino thus has a decay length of up to a few millimeters and predominantly decays to the LSP and a single pion. This pion has transverse momentum on the order of the mass splitting ∆m± and is slightly displaced with respect to the primary interaction vertex due to the chargino’s lifetime. The corresponding soft and displaced track that the pion leaves in the detector is used as a handle to distinguish signal events from SM background events.

It is established that for the matching of a simulated pion with such properties to its reconstructed track, a dedicated method is needed. A helix extrapolation tool is developed for this purpose. Moreover, to identify the signal track among the in total hundreds of tracks reconstructed in an event, a multivariate classiﬁer in the miss form of a BDT is employed. The BDT uses event-level observable such as pT and several track variables exploiting, for example, the fact that signal tracks have large transverse and longitudinal impact parameters to the primary vertex and are miss ± generally found pointing into the direction of ~pT . The mass splitting ∆m is also used as an input to the BDT in order to facilitate that, when evaluating the BDT, a particular mass splitting can be targeted.

75 7 Conclusion and Outlook

To use the soft and displaced track classifier in the event analysis, two event-level observables are defined as the maximum BDT scores of all tracks in an event with the BDT evaluated at ∆m± = 0.3 GeV and ∆m± = 1.0 GeV, respectively. By applying cuts on these quantities, in addition to event selection cuts corresponding to a monojet-like analysis, two signal regions are defined. The number of expected background events, dominated by the Z(ν ν) process, in each signal region is obtained by a data driven background estimation method that uses a cleaned Drell-Yan sample as a proxy to all SM background processes. Cleaned here means that Z(µ− µ+) events are selected for which the two muons are removed in order to resemble Z(ν ν) events.

For data corresponding to an integrated luminosity of 35.9 fb−1, no signiﬁcant ex- cess above the expected number of events is found and exclusion limits are set in ± ± the plane of ∆m versus m(χe1 ). The search can extend the current exclusion limits in the range of ∆m± = [0.6, 0.9] GeV. The highest sensitivity is reached for ∆m± ≈ 0.8 GeV where charginos with masses up to approximately 120 GeV are excluded.

By extending this analysis to the full Run 2 dataset, its sensitivity range can be enlarged. Figure 7.1 shows an extrapolation of the expected exclusion limit to a luminosity of 137 fb−1. It can be seen that charginos with masses up to 160 GeV could be in reach.

Also, the sensitivity to the signal process could be improved by taking into account the charge of the soft and displaced track as signal tracks are expected to be more often positively charged while for background tracks charge parity is expected.

The accuracy of the background prediction method could be increased by extending the cleaned DY sample to contain both muons and electrons. Furthermore, a dedicated treatment of the W(` ν)+jets background could help to reduce the systematic uncertainty connected to the background estimation method. For example, correction factors to the cleaned DY sample could be derived to account for additional contributions by soft leptons from the W boson decay or tau decay products. Another option would be to employ a MC based background estimation method. However,

76 Figure 7.1: Expected exclusion limit of this analysis extrapolated to a luminosity corresponding to the full Run 2 dataset recorded by CMS. for this to be reliable, the simulation of soft tracks from pile-up, the underlying event and fake tracks would have to be validated thoroughly.

Besides that, cornering Higgsinos by extending the reaches of disappearing track searches, targeting charginos with decay lengths of a few centimeters, and di-lepton searches, targeting decays of the second lightest neutralino to two leptons, and com- bining their results with this analysis will be crucial. Soft tracks can be of use for both of these analysis strategies. The signature of a disappearing track with an attached soft track could be used to enhance the sensitivity in those searches. Also, substituting identiﬁed leptons by tracks in di-lepton searches could prove most help- ful in extending the reach to smaller mass splittings. When entering the regime in which the second lightest neutralino has a discernible lifetime before decaying to the LSP and a soft lepton pair, the appearance of a displaced vertex with two soft tracks

77 7 Conclusion and Outlook assigned, analogous to the single displaced track in this analysis, could serve as a promising handle to suppress SM background events.

More generally, this analysis shows the importance and the capability to access dark matter related signatures which previously were inaccessible at the LHC. Any discovery of such signatures would change our view on both particle physics and cos- mology.

78 Appendix

CMS s = 13 TeV

efficiency 2016 (35.9 fb-1) 1.4 denom. trigger: single-el efficiency 2017 (41.5 fb-1) 250 cuts: H >300 GeV, n(j)>1 1.2 T efficiency 2018 (59.2 fb-1) Events/GeV 200 1 trigger efficiency 0.8 150

0.6 100 online Hmiss>120 GeV, Emiss >120 GeV (2016) 0.4 T T measurement sample (2016) 50 0.2

0 0 100 200 300 400 500 600 700 800 900 1000 miss HT /GeV

Figure A.1: Trigger eﬃciency for the HLT PFMET120 PFMHT120 trigger. By Samuel Bein.

List of Figures

1.1 Current Higgsino exclusion limits ...... 2 1.2 Signal process Feynman diagram ...... 3

2.1 Standard Model particles ...... 6 2.2 Chargino branching ratios and decay length ...... 18

3.1 CERN accelerator complex ...... 20 3.2 LHC luminosity plots ...... 22 3.3 CMS detector layout ...... 23 3.4 CMS pixel detector Phase 0 vs. Phase 1 ...... 25 3.5 CMS tracker cross section ...... 26 3.6 CMS detector transverse slice ...... 30

5.1 Different definitions of azimuthal angle for generated pion and reconstructed track ...... 43 5.2 Distributions of ∆xyz vs. ∆Rextrapolated for simulated pions and tracks with same charge and opposite charge ...... 44 5.3 Pion matching efficiency for the new matching procedure and the standard ∆R < 0.02 matching ...... 44 5.4 Four important BDT input variables ...... 47 5.5 BDT input variables - Part 1 ...... 48 5.6 BDT input variables - Part 2 ...... 49 5.7 BDT response cumulative for all mass splittings ...... 51 5.8 BDT response for different mass splittings ...... 51

pmiss ∆ϕ ~p miss, 6.1 Data to MC comparison in T and T jets1,2,3,4 min ..... 55

81 List of Figures

6.2 Two-dimensional distribution of the two maximal BDT scores with the signal and control regions ...... 56 6.3 Signal samples with matched tracks ...... 59 6.4 Maximal BDT score distributions ...... 60 6.5 Distributions of the maximal BDT scores with the signal signiﬁcance 61 6.6 Quantities used to optimize the sideband control regions ...... 62 6.7 Closure test for MC Z(ν ν)...... 64 6.8 Background estimation method for W(` ν)+jets ...... 65 6.9 Background estimation method for Z(ν ν) and W(` ν)+jets combined 66 PV 6.10 Normalized distributions of log10 |dz | and ∆ϕMET of the highest scoring track for cleaned DY MC and cleaned DY data ...... 68 PV 6.11 Normalized distributions of log10 |dz | and ∆ϕMET of the highest scoring track for data and cleaned DY data ...... 69 6.12 Background estimation in data (blinded) ...... 71 6.13 Background estimation in data (unblinded) ...... 73 6.14 Expected and observed exclusion limits ...... 74

7.1 Expected exclusion limit extrapolated to 137 fb−1 ...... 77 A.1 Trigger eﬃciency ...... 79

82 List of Tables

4.1 Signal cross sections ...... 38 4.2 Table of event-level observables...... 39 4.3 Table of track-level observables ...... 40

5.1 Ranking of BDT input variables...... 50

6.1 Expected and observed event yields in the signal regions ...... 72

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Eidesstattliche Erklärung

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

Ich bin damit einverstanden, dass die Masterarbeit veröﬀentlicht wird.

Moritz Wolf - Hamburg, 08. Juni 2020