Measurement of the Standard Model Higgs Boson Produced in Association with a W Or Z Boson and Decaying to Bottom Quarks

MEASUREMENT OF THE STANDARD MODEL HIGGS BOSON PRODUCED IN ASSOCIATION WITH A W OR Z BOSON AND DECAYING TO BOTTOM QUARKS

By DAVID CURRY

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2017 ⃝c 2017 David Curry Dedicated to my Mother for always supporting me ACKNOWLEDGMENTS First and foremost, thank you to the Univeristy of Florida for the oppurtunity to study physics and for providing a thriving research environment. Thank you to my advisor, Ivan Furi´c,for continued support through the ups and downs of graduate research. Thank you to all my colleagues at CERN and at UF for whose help was necsessary to get this far: Pierluigi Bortignon, Michele de Gruttola, Jaco Konigsberg, Darin Acosta, Gael Perrin, Luca Perozzi, Stephane Cooperstein, Chris Palmer, and Sean-Jian Wang.

4 TABLE OF CONTENTS page ACKNOWLEDGMENTS ...... 4 LIST OF TABLES ...... 7 LIST OF FIGURES ...... 8 ABSTRACT ...... 10

CHAPTER 1 INTRODUCTION AND OPENING REMARKS ...... 11 2 THEORETICAL FOUNDATIONS ...... 13 2.1 Historical Development ...... 13 2.2 The Standard Model ...... 14 2.3 Quantum Electrodynamics ...... 15 2.4 Quantum Chromodynamics ...... 16 2.5 Weak Interactions ...... 19 2.6 The Higgs Mechanism ...... 21 2.7 The Higgs Boson ...... 24 3 THE CMS EXPERIMENT ...... 27 3.1 LHC ...... 27 3.2 CMS Detector ...... 30 3.3 Tracker ...... 31 3.4 Calorimeters ...... 32 3.5 Muon Systems ...... 34 3.6 Trigger ...... 35 4 PARTICLE IDENTIFICATION ...... 38 4.1 Energy Losses by Particles in Matter ...... 38 4.2 Electrons ...... 39 4.3 Muons ...... 42 4.4 Jets ...... 45 4.5 Lepton Isolation ...... 47 4.6 b-Jet Identiﬁcation ...... 47 4.7 Neutrinos ...... 48 4.8 Jet Energy Regression ...... 49 5 THE VHBB ANALYSIS ...... 52 5.1 Backgrounds ...... 53 5.1.1 Drell-Yan ...... 55

5 5.1.2 t¯t ...... 56 5.1.3 Diboson ...... 57 5.1.4 Single Top ...... 57 5.2 Data and Simulation ...... 57 5.2.1 Data ...... 57 5.2.2 Simulation ...... 58 5.2.3 Simulated Event Reweighting ...... 59 5.3 Triggers ...... 60 5.4 Analysis Object Selections ...... 64 5.4.1 Pile-Up and Primary Vertex Selection ...... 64 5.4.2 Electrons ...... 68 5.4.3 Muons ...... 69 5.4.4 Jets ...... 70 5.4.5 Missing Energy ...... 71 5.5 Multivariate Strategy ...... 71 5.6 Control Regions ...... 72 5.7 Systematics ...... 76 6 RESULTS ...... 87 6.1 Signal and Control Regions ﬁts ...... 87 6.2 Signal Strength Calculation ...... 87 6.3 Blinding ...... 90 6.4 Results VH ...... 90 6.5 Next Steps ...... 91 6.6 Conclusions ...... 93 REFERENCES ...... 94 BIOGRAPHICAL SKETCH ...... 97

6 LIST OF TABLES Table page 2-1 Higgs Boson Branching Ratios ...... 25 3-1 LHC luminosity terms and deﬁnitions ...... 29 √ 5-1 Signal cross sections and branching ratios for Mhiggs = 125 at s = 13...... 53 5-2 List of 2016 data samples used for the SingleMuon dataset...... 58

5-3 Signal Monte Carlo samples with Mhiggs = 125 ...... 59 5-4 List of Monte Carlo diboson samples ...... 59 5-5 List of Monte Carlo V + jets leading order samples ...... 60 5-6 List of Monte Carlo V + jets leading order samples ...... 61 5-7 List of Monte Carlo V + jets next-to-leading order samples ...... 61 5-8 Top and QCD Monte Carlo samples ...... 62 5-9 List of L1 and HLT triggers used for the 2016 data set ...... 63 5-10 Variables used in the BDT training...... 73 5-11 Preselection cuts for each channel to deﬁne the signal region...... 75 5-12 Deﬁnition of control regions for the Z(ℓℓ)H channel...... 76 5-13 Control Region Scale Factors ...... 83 6-1 Signal Region Event Yields ...... 87 6-2 Expected and Observed Event Yields ...... 91

7 LIST OF FIGURES Figure page 2-1 Visual representation of the fundamental particles of the Standard Model ...... 14 2-2 Feynman diagram for Compton Scattering ...... 15 2-3 Fundamental QCD Feynman diagram ...... 17 2-4 Gluon-Gluon Coupling ...... 18 2-5 Z boson neutral current decay...... 19 2-6 W boson decay ...... 19 2-7 Higgs Potential Energy ...... 22 2-8 Higgs production at the LHC ...... 25 2-9 SM Higgs boson production cross sections ...... 25 3-1 An overview of the LHC ...... 28 3-2 One quarter view of the CMS detector ...... 35 3-3 Overview of the Run 2 Upgraded Level 1 Trigger ...... 36 4-1 Output of the electron-identification BDT ...... 42 4-2 Electron Reconstruction Efficiency ...... 43 4-3 Tag-and-probe Results for Muon Efficiency ...... 45 4-4 Distributions of dijet invariant mass ...... 51 5-1 Feynman diagrams for VHbb production ...... 53 5-2 Feynman diagram for the Drell-Yan background process ...... 56 5-3 Feynman diagram for the t¯t background process...... 56 5-4 Feynman diagram for the ZZ diboson background process...... 57 5-5 Single Electron Trigger Efficiencies (WP80) ...... 64 5-6 Double Electron Trigger Efficiencies (WP90) ...... 65 5-7 Double Muon Trigger Efficiencies (Runs BCDEFG) ...... 66 5-8 Double Muon Trigger Efficiencies (Run H) ...... 66 5-9 MET Trigger Efficiency ...... 67

8 5-10 BDT Output for Signal and Background ...... 74 5-11 Eﬃciency and background reduction in the Signal Region ...... 75

5-12 Z + udscg control region plots (low V pT) ...... 77

5-13 Z + udscg control region plots (high V pT) ...... 78

5-14 t¯t control region plots (low V pT) ...... 79

5-15 t¯t control region plots (high V pT) ...... 80

5-16 Z + bb control region plots (low V pT ...... 81

5-17 Z + bb control region plots (high V pT ...... 82 5-18 Systematic Impact and Pulls ...... 86 6-1 Post-fit BDT Output ...... 88 6-2 Post-fit Control Region Distributions ...... 89 6-3 Best-fit Signal Strength Parameter ...... 92 6-4 Signal over Background Log Distribution ...... 93

9 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy MEASUREMENT OF THE STANDARD MODEL HIGGS BOSON PRODUCED IN ASSOCIATION WITH A W OR Z BOSON AND DECAYING TO BOTTOM QUARKS By David Curry December 2017 Chair: Ivan K. Furic Cochair: Jaco Konigsberg Major: Physics A search for the standard model Higgs boson decaying to bottom quark pairs when produced in association with a W or Z vector boson is presented. Data samples corresponding √ to an integrated luminosity of 35.9 fb−1 at s = 13 TeV recorded by the CMS experiment at the LHC during Run 2 in 2016 have been analyzed in 5 channels: Z(µµ)H, Z(ee)H, Z(νν)H, W(µν)H, W(eν)H. An excess of events is observed in data when compared to the background only hypothesis (absence of a H → b¯b signal process). For a Higgs boson of 125 GeV the measured signal significance is 3.3 standard deviations, which crosses the 3.0 standard deviation evidence threshold, while the expected signal significance is 2.8. The measured signal

strength is found to be µ = σ/σSM = 1.19 0.35.

10 CHAPTER 1 INTRODUCTION AND OPENING REMARKS The Standard Model (SM) has long predicted the existence of a Higgs Field that is responsible for breaking the electroweak symmetry and giving mass to the W and Z vector bosons, as well as the other massive particles of the Standard Model(1)(2)(3). Detection of the quanta of this field, the Higgs boson, has been a goal of experiments from LEP (the Large Electron-Positron Collider at CERN), the Tevatron at Fermilab, and currently the LHC along with CMS at CERN. In the summer of 2012 observations of a resonance at 125 GeV were announced by the ATLAS and CMS experiments at the LHC. The main decay modes of the Higgs boson that fueled its discovery were the ZZ and γγ channels(4). The exact manner in which the Higgs boson couples to quarks, and whether this coupling is in agreement with current Standard Model predictions, still remains unresolved. The goal of this thesis is a complete description of the measurement of the unobserved decay of the Higgs boson to bottom quark pairs (b¯b), and whether this decay rate is consistent with Standard Model predictions. The detection of this bottom quark decay mode has been a considerable challenge due to the final decay states of the Higgs boson existing within an overwhelming sea of events that are topologically similar. At the Large Hadron Collider there exists an abundance of proton-proton collisions that lead to final states that contains bottom quark pairs. To aid in reducing background contamination arising from b¯b final states, we require that the b-quark pair be produced in conjunction with a W or Z vector boson. In Section 1 we start with a summary of the theoretical background of the Standard Model, the various forces fundamental to particle interactions in the Large Hadron Collider, and the Higgs mechanism. Section 2 will provide an overview of the Large Hadron Collider (LHC) and the Compact Muon Solenoid (CMS). The various sub-detectors of CMS and their roles in indentifying Higgs boson signatures will be discussed.

11 Reconstructing particles from measurements made in the sub-detectors is the goal of Section 3. Muons, electrons, jets, and neutrinos are discussed. Techniques to identify different types of quarks through a method called b-tagging are presented. Section 4 will cover the analysis strategy used in the measurement of the Higgs coupling to b-quark pairs. Selections of all physics objects are also given in this section. Control regions are described in detail and plots showing the level of data to simulation agreement are provided. Lastly, section 5 describes the results of this thesis: for a Higgs boson mass of 125 GeV, we find evidence for an excess of signal events with a local significance of 3.3 standard deviations.

12 CHAPTER 2 THEORETICAL FOUNDATIONS 2.1 Historical Development

Today we have a concise model of all experimentally verified fundamental particles and the forces that govern them However, this was not the case as the physics world moved into the 1970’s. It was suspected that there lurked a more fundamental set of particles (what we now know as quarks) that make up the proton and neutron, but definitive evidence for a particular quark model had not yet been found. A theoretical model of quarks was proposed in 1964 by Murray Gel-Mann and George Zweig independently. Experiments from the Stanford Linear Accelerator (SLAC) in the late 1960’s in which electrons were scattered off hydrogen and deuterium brought forth strong evidence that the proton was not fundamental and that it was composed of point-like objects with charges +2/3 and -1/3(5). These experiments where much like the Rutherford scattering experiments in the early 20th century in which it was found that the atom was not fundamental and contained positive charge localization (ie., a nucleus). By 1969 the up, down, and strange quarks had been discovered at SLAC and the quark model of Gel-Mann and Zweig appeared to describe nature accurately. The final nail in the coffin which cemented the quark model as the best descriptor of nature was the discovery of the J/ψ in 1974 by two independent groups: the Burton Richter led group at SLAC, and the Samuel Ting led group at Brookhaven National Labratory(6). The J/ψ is also refered to as charmonium, as it is a bound-state of a charm quark and an anti-charm quark, with a rest mass of 3.097 GeV. It has a much longer lifetime than expected due to the suppression of its hadronic decay modes and as result has a very narrow dilepton resonance. This clear experimental signature is now used in the LHC and other modern particle detectors as a calibration point. Until the Richter-Ting discovery the theorized charm quark had remained elusive, and the sea of heavy particles (pions, kaons, etc.) and quarks previously discovered remained part of a disorganized ordering system. The discovery of the J/ψ took part in what is now known as the

13 November Revolution in physics: the development of the Standard Model that was spurred on by the J/ψ discovery. 2.2 The Standard Model

Figure 2-1. A visual representation of the fundamental particles of the Standard Model.

The Standard Model of particle physics (visually represented in Figure 2-1) is a concise description of all experimentally observed particles and their interactions. To date there have been no experimental results that contradict the predictions of the Standard Model. It has been a resounding success in describing testable phenomena and the last undiscovered fundamental particle predicted by the Standard Model, the Higgs boson, was discovered in 2012(7). Three generations of quarks and leptons describe the fermionic components (fermions

14 have 1/2 integer spin and obey Fermi-Dirac statistics), while the remaining particles are gauge bosons (integer spin and obeying Bose-Einstein statistics). The gauge bosons are the mediators of the electromagnetic (photon), strong (gluon), and the weak (W,Z) forces. These forces are described by the theory of quantum gauge symmetry and belong to the gauge group: SU(3) x SU(2) x U(1) (2–1)

SU(3) describes the interaction of gluons through color charge, and contains 8 gauge bosons arising from linear combinations of the three color charges and their anti-charges: red, blue, and green. SU(2) describes the three bosons of weak isospin (W+,W-,Z). U(1) describes the hypercharge and its associated gauge boson, the photon. The combination of SU(2) and U(1) create the theory of the ElectroWeak force(6). An introduction to each of these forces will now be given. 2.3 Quantum Electrodynamics

Interactions between charged particles occur due to the electromagnetic force, which is described as the exchange of a photon. A fundamental Feynman diagram for this process is given in Figure 2-2, in which two electrons interact by exchange of a photon. e− e−

e− e− Figure 2-2. Feynman diagram for the QED interaction of two charged particles by virtue of photon exchange (Compton Scattering).

Within the Feynman diagrams of QED, electric charge must be conserved at each vertex(8). In Figure 2-2 an electron enters and leaves at each vertex, making the total charge before and after equal to negative one(the photon with zero electric charge does not violate

15 conservation of electric charge). The QED Lagrangian describes the interaction between a spin-1/2 ﬁeld and an electromagnetic ﬁeld and is given by

1 L = ψ¯(iγuD − m)ψ − F F µv . (2–2) µ 4 µv The kinetic energy term in the QED Lagrangian is the last term where

µ ν ν µ Fµν = ∂ A − ∂ A , (2–3)

Aµ = (ϕ, A¯), (2–4)

and

1 1 D = ∂µ + ig τ¯ · W¯ + ig′ YB . (2–5) µ 2 µ 2 µ Gauge invariance of the U(1) symmetry group requires this kinetic term to be invariant under transformations of the form

Aµ(x) → Aµ(x) −µ η(x), (2–6)

for any η(x)(8). This transformation holds for a massless gauge boson, which the photon is, but does not hold for cases where the gauge boson does have mass. This point is highlighted in order motivate the fundamental problem that is solved by the Higgs Mechanism: allowing the W and Z vector bosons, force carries of the EWK SU(2) group, to acquire mass without violating the gauge symmetry of the QED Lagrangian and by extension the ElectroWeak Lagrangian of section 2.5. Before we turn to further discussions of EWK theory and the Higgs Mechanism, an introduction to Quantum Chromodynamics (QCD) is given. 2.4 Quantum Chromodynamics

QCD describes the interactions between quarks and gluons and, analagous to QED and charge, will involve the absorption or emission of a gluon. Gluons, like the photon, are

16 q(blue) q(green)

q(green) q(blue) Figure 2-3. Feynman diagram for the QCD interaction of two quarks by virtue of gluon exchange.

massless and have spin 1, but also possess combinations of two color charges(red, green or blue and antired, antigreen or antiblue), which leave the total colro charge of the gluon to be zero. Quarks can have one of three colors: red, green, blue, while the anti-quarks have anti-red/green/blue. Again, analogous to QED, we have a fundamental QCD Feynamn diagram in Figure 2-3, in which two fermions interact by exchange of a massless vector boson(9). Unlike the QED reaction, the initial and final state particles have been slightly altered due to the additional QCD degree of freedom: color. In QCD a new conservation associated with color is introduced: just like with electric charge in QED, color must be conserved at each vertex. Since the mediator of the strong force carries a color charge, it is possible for quarks to enter and leave a reaction in a different state (color) and color conservation will still be met (Figure 2-3). Coupling between gluons is also possible and can lead to gluon emission by a gluon (Figure 2-4). This process can occur before or after the primary interaction and is called ISR or FSR: intial or final state radiation. Another very important phenomenon that results from gluon self-coupling, as well as the fact that gluons carry color “charge”, is QCD anti-screening. In order to make sense of anti-screening one can first look at the QED analogy: electron screening. In vacuum a charged particle will exist in a sea of virtual electron-positron pairs that couple to the charged particle through virtual photon interactions. To an observer some distance away from the lone particle,

17 the charge that he/she would measure will be lower than the particle’s actual charge value. The particles charge appears smaller than it actually is and we say that the particles true charged is screened, or diminished. This very same screening effect also happens for quarks (particles with color “charge”). For a quark in vacuum there also exists a sea of quark-antiquark pairs that couple to it through gluon interactions and the effect is to diminsh the observed color charge, or strength of the strong force, as observed from a distance. However, because of the gluon color charge and ability to self-couple there also exists a sea of gluon self interactions surrounding the quark. The overall effect of the the gluon self-couplings is to make the color appear stronger than it actually is. This is called anti-screening. Since the gluon-gluon couplings are less suppressed than quark-antiquark couplings at low energies, anti-screening will dominate. As the energy of an incoming particle increases, so does its ability to probe smaller length scales. What this means is that for higher energies one is able to measure the true charge, either electric or color, of the source particle. For the case of electromagnetism this means the observed charge strength will increase with energy, as it was orignally diminished, or screened. For particles that carry color this means that the observed color strength goes down with energy, since their color stength was originally inflated, or anti-screened. This results in the

strong coupling constant(αs ) decreasing with increasing energy. For proton-proton collsions at high energies within experimental particle colliders this means the amount of quark-antiquark pairs within the proton increases at high energy(9). It is exactly this large fraction of qq¯ pairs that make proton-proton colliders feasible for studying qq¯ initiated process, such as the associated production Higgs channel this thesis is focused on. 2.5 Weak Interactions

Weak interactions are characterized by the emission or absorption of W and Z bosons: the mediators of the weak force. All quarks and leptons interact through two types of weak interaction: charged, mediated by the W+/W−, and neutral, mediated by the Z. Examples of charged and neutral weak interactions are shown in Figures 2-5-2-6(9).

18 g

g Figure 2-4. Gluon-Gluon Coupling e−

Z 0

e+ Figure 2-5. Z boson neutral current decay.

The neutral current process depicted in Figure 2-5 is a Z boson decaying into a lepton and its anti-particle. A similar diagram exists for a Z boson decaying into a quark-anti-quark pair. The charged current reaction depicted in Figure 2-6 is a negatively charged W boson decaying into an electron and anti-electron nuetrino. A similar diagram exists for the postive current reaction where the electron becomes an anti-electron and the anti-electron nuetrino becomes a non anti-type. A fundamental concept in knowing which types of weak interactions are allowed is that of lepton number conservation. Each generation of lepton (electron, muon, tau, and their e−

W −

v¯e Figure 2-6. W boson decay. The example here depicts the minus charged current weak reaction.

19 associated neutrino) has a unique lepton number: +1 is assigned to the non-anti variety and -1 for anti-type. The mediators of the weak force, the W/Z bosons, are given a lepton number of zero. As shown in Figures 2-5-2-6 the lepton number is conserved at each vertex (zero before and after). Branching fractions for the W boson can be derived by considering all possible quark and leptonic decays. For positive W bosons decaying into leptons we have the following possible modes:

+ + W → e + ve, (2–7)

+ + W → µ + vµ, (2–8)

+ + W → τ + vτ . (2–9)

And the hadronic decay modes are:

W + → u + d¯/¯s/b¯, (2–10)

W + → c + d¯/¯s/b¯. (2–11)

Thus there are 9 possible decay modes for the W, where 2/3 of the time the W decays hadronically and the other 1/3 to leptons. Experimentally determined values for W branching ratios are 67.60% for hadronic modes, and 10.80% for the possible leptonic decays. The Z boson experimentally determined branching ratios are 69.1% to hadrons, 20.0% to all neutrino decays, and 3.6% for each other leptonic (electron, muon, tua) decay mode(10). Weak interactions combined with the electromagnetic interactions of section 2.3 give us the SU(2) x U(1) EWK group of the Standard Model. The kinetic energy term of the EWK Lagrangian is given by

1 1 L = W W µv − B Bµv , (2–12) kin 4 µvi i 4 µv

20 where µv µ ν − ν µ ν Wi = ∂ Wi ∂ Wνi + gϵijk Wj Wk , (2–13)

Bµv = ∂µBν − ∂νBν. (2–14)

ν Wi are the three guage bosons of SU(2) and Bν the gauge boson of U(1) that we have seen previously, the photon. Due to the necessities of gauge theory all four EWK gauge bosons are massless, yet the W and Z bosons have experimentally veriﬁed non-zero masses(9). A new mechanism is thus required that gives rise to the massive W and Z bosons that we observe, while leaving the photon massless. 2.6 The Higgs Mechanism

Invariance of the EWK Lagrangian (eq. 2-12) under rotations prevents a mass term from simply being added to it. Instead, we have to add a new system or ﬁeld (Φ) which satiﬁes the following:

• It must be a complex,scalar ﬁeld - to preserve Lorentz invariance of the vacuum state

• It must give rise to three massive bosons belonging to the SU(2) group

• It must keep the photon massless A complex, scalar doublet is deﬁned:    ϕ+  Φ =   , (2–15) ϕ0 and a new term involving this doublet is now added to the Lagrangian:

† µ LHiggs = (DµΦ) (D Φ) − V (Φ), (2–16) where V (Φ) = µ2Φ†Φ + λ(Φ†Φ)2, (2–17)

and

′ DµΦ = (∂µ − 1/2igτ · µ − 1/2ig Bµ)Φ. (2–18)

21 Figure 2-7. Plot of the Higgs Potential Energy when λ > 0 and µ2 < 0.

In order to ensure a non-zero vacuum expectation value for Φ we take λ > 0 and µ2 < 0. This choice for λ and µ create a “mexican hat” potential ﬁeld, as can be seen in Figure 2-7. Massless gauge bosons (ie., the photon) occupy the minimum states of the potential energy ﬁeld, while the weak vector bosons spontaneously break the symmetry by moving out of the minumum potential well. Pertubations about this non-zero minumum vacuum state create excitations in the Higgs Field which are the Higgs Bosons sought after in this thesis. We now choose an orientation of Φ in the SU(2) space that breaks the symmetry of SU(2), and thus giving mass to the W and Z bosons, while leaving the U(1) symmetry unbroken:   1  0  Φ = √   , (2–19) 2 ν

A gauge transformatinon of this scale doublet is also deﬁned:   1  0  Φ → U(χ)Φ = √   (2–20) 2 ν + H

22 where

( ) χ · τ U(χ) = exp i . (2–21) ν .

µ Additionally, the gauge bosons of SU(2), Wi , are also aﬀected by this transformation, while the photon is left unchanged:

Bµ → Bµ, (2–22)

while

( ) ( ) τ · W τ · W i µ → U(χ) µ U−1(χ) − (∂ U(χ))U−1(χ). (2–23) 2 2 g µ Substituting back into the EWK Lagrangian yields the following for the kinetic term:   ( ) 2 0 2 1 1 1 ′ 1   |DµΦ| = √ (0 ν) gτ · Wµ + g Bµ √   . (2–24) 2 2 2 2 ν

Lastly, the physical bosons (i.e. those that have mass for the case of the W and Z) that are observed are deﬁned as complex, linear combinations of the massless gauge bosons:

W 1 + −iW 2 W +− = µ √ µ , (2–25) µ 2

3 ′ gW − ig Bµ Z = √µ , (2–26) µ g2 + g′2

′ g W3 +igB A = √ µ µ . (2–27) µ g2 + g′2 The kinetic term of the EWK Lagrangian now yields

23 ( ) ( ) g2ν2 1 (g2 + g′2 |D Φ|2 = W +W u− + Z Z µ + ... (2–28) µ 4 µ 2 4 µ where all non-mass terms have been dropped. The potential term of the EWK yields

1 V (Φ) = (2µ2)H2 + ... (2–29) 2 The W and Z bosons have now aquired a mass given by

√ g g2 + g′2 √ M = v; M = v; M = 2µ, (2–30) W 2 Z 2 H where v is the vacuum expectation value (VEV) and can be written as

µ2 v = . (2–31) λ v is extracted for measurments of muon decay using the Fermi relation

G g2 1 √f = = ; v 2 = (246GeV )2. 2 2 (2–32) 2 8MW 2ν The Higgs mass now depends only on the choice of lambda, which is not determined uniquely by the Standard Model and must be determined experimentally. 2.7 The Higgs Boson

The Higgs ﬁeld described in previous section can be detected by measurment of its excitation, the Higgs boson. On July 4th, 2012 the two general-purpose detectors (CMS and ATLAS) at the Large Hadron Collider (LHC) announced the discovery of the Higgs boson. The Higgs boson was observed with a mass of 125 GeV with standard deviations between 5 and 6 each(4). Proton-Proton (pp) collisions occuring at the Large Hadron Collider will be the relevant method of Higgs production. Quark-antiquark pairs and gluons within the proton will be responsible for initiating the Higgs production mechanisms. These mechanisms for Higgs creation are shown in Figures 2-8(11). The most abundant production mechanisms are

24 Figure 2-8. Higgs production at the LHC. (a)gluon-gluon fusion, (b)vector boson fusion, (c)associated vector boson production, (d)associated top quark production.

Figure 2-9. The SM Higgs boson production cross sections as a function of center of mass energy for pp collisions. gluon-gluon and vector boson fusion (VBF), followed by associated production with a vector boson (VH), and associated production with a top quark pair (ttH). This thesis will focus on the associated production channel and motivations for this choice will be discussed in chapter 5. Cross-sections for these production mechanisms are shown in Figure 2-9. The Standard Model is able to predict the branching ratios of the Higgs (sumamrized in Table 2-1 for a mass of 125 GeV(11)). The Higgs branching ratios in fermionic decays get larger as the fermion masses increase. The behavior of the Higgs coupling to fermions is to increase as the square of the fermion mass (7). This feature of the Higgs having higher coupling to more massive particles is a

25 √ Table 2-1. Higgs Boson branching ratios for a mass of 125 GeV at s = 13 TeV. Decay Channel Branching Ratio Rel. Uncertainty H → γγ 2.28 ∗ 10−3 5% H → ZZ 2.64 ∗ 10−2 4.2% H → W +W − 2.15 ∗ 10−1 4.2% H → τ +τ − 6.32 ∗ 10−2 5.7% H → b¯b 5.7 ∗ 10−1 3.2% H → µ+µ− 2.19 ∗ 10−4 6.0%

consequence of how the theory is built and we are testing whether this is true or not by measuring the Higgs coupling to b quarks. For a Higgs decaying to ZZ/WW, coupling to higher masses is not followed. As summarized in the latest Particle Data Group Higgs Boson Review (12) the Z boson aquires an extra factor of two in the denominator of its coupling to the Higgs boson. This causes the lighter W boson to have a stronger coupling to the Higgs than the heavier Z boson. The aforementioned discovery of the Higgs Boson at the LHC was done at an operating √ center of mass ( s) energy of 7 and 8 TeV. The LHC has now entered a new period of √ increased energy, called run 2, of s = 13 TeV. With this increase in center of mass collision energy there is an associated increase in the cross-sections and their uncertainties for various ﬁnal states as shown Figure 2-9(7). This increase in cross-section is a result of more quark-antiquark pairs and gluons having a high enough energy in order to initiate their respective production mechanisms. Also, as the proton energy increases so does the abundance of quark-antiquark pairs and gluons, which will increase the rate of Higgs production. Now that the theoretical foundations for the Higgs boson have been introduced and its main production modes discussed, we now turn to a discussion of the experimental methods and apparati used to detect the Higgs boson.

26 CHAPTER 3 THE CMS EXPERIMENT The Compact Muon Solenoid (CMS) is a multipurpose general detector capable of detecting all well known particles. CMS exists within the Large Hadron Collider (LHC) in Geneva, Switzerland. The European Organization for Nuclear Research (CERN) employs thousands of scientists from around the world and operates the LHC. Within the LHC two beams of protons are accelerated in adjacent, circulating rings in opposite directions. Collisions between these beams happen at four diﬀerent points along the ring: ATLAS and CMS (general-purpose detectors), ALICE (QCD measurements in dense, heavy ion environments), and LHCb (dedicated to b-quark physics). This chapter will give brief descriptions of the LHC and CMS detector and motivations for their design. 3.1 LHC

The LHC is a proton-proton collider with a radius of 27 km and a current operating center √ of mass energy of s = 13 TeV. To achieve this energy protons are accelerated through a chain of linear and circular accelerators, of which the LHC is the last stage of acceleration(13). This chain of linear and circular accelerators is referred to as the CERN accelerator complex and is comprised of older accelerators from the previous generation of high energy experiments at CERN. The chain begins with LINAC2, a linear accelerator, which serves as the source of protons and inital stage of acceleration. In LINAC2 bottles of hydrogen gas feed the initial chambers which ionize the hydrogen atoms yielding clusters of protons. Radio-Frequency (RF) cavities then create electric ﬁelds which then accelerate the proton clusters to an initial energy of 50 MeV. The next stage of boost is the Proton Synchrotron Booster (PSB) which splits the incoming proton cluster into four diﬀernet circular paths, which now boost the protons to 1.4 GeV. These 1.4 GeV protons then make it to another synchrotron, the Proton Synchrotron (PS), and then lastly before the LHC comes the Super Proton Synchrotron (SPS) where an energy of 450 GeV is achieved.

27 Figure 3-1. An overview of the LHC

Once the cluster of protons reach the LHC they are split into two beam pipes (one cluster moving clockwise and the other counter-clockwise) that traverse the full circumference of the LHC (27 km). RF cavities are stationed at four points along the LHC beam pipes that serve two main functions: one, to further increase the proton energy from 450 GeV to 6.5 TeV, and two, to maintain the clusters of protons in tight packets, or bunches. Having tight proton bunches is crucial for obtaining high luminosity collisions and for modelling pile-up. Each colliding proton bunch is separated in time by 25 nanoseconds. When bunches collide there are multiple proton-proton interactions that occur in addition to rare events, such as the Higgs decay this analysis aims to study. These additional collisions are referred to as pile-up. Pile-up can be in-time, when the collisions come from the same bunch, or out-of-time, when collisions come from the preceding or following bunch. The ability to model pile-up depends on the LHC’s ability to maintain tightly clustered bunches, and is achieved through the use of oscillating electric fields in the RF cavities. The frequency of the RF cavity is tuned to the circular frequency of the circulating proton bunches. As a result, when a bunch arrives at an RF cavity the forward protons who arrive slightly early feel a slowing down effect from the RF cavity electric field which is has not been fully flipped.

28 The protons which are lagging behind at the rear of the bunch will arrive after the electric field has been flipped and points in the same direction of the protons movement and will thus experience an acceleration. The protons in the middle of the bunch feel no acceleration because the electric field is perpendicular to its trajectory. The end result is a self-correcting tightening of each proton bunch. Additionally, each bunch is kept in a circular orbit by a 3.8 Tesla superconducting magnet. Finally, collisions will take place between bunches of protons in two main points of the LHC ring: ATLAS and CMS, two general purpose detectors that are currently searching for new physics. One measure of a colliders performance is its luminosity: the rate of particles colliding, and is often thought of as the operating time of an experiment, or the amount of data collected. The LHC was designed with having high luminosity in mind and currently has an instantaneous luminosity of 1034cm−2s−1(14). The formal expression of instantaneous luminosity at the LHC is given by:

2 γkbfN L = p (3–1) ϵ

Variable Definition γ Lorentz factor kb number of bunches f frequency of revolution 2 Np number of protons per bunch ϵ effective collision area Table 3-1. LHC luminosity terms and definitions

At this luminosity the CMS detector would be saving many terabytes of data per second, which is very impractical to record and store. Instead dedicated triggers are employed that serve to only record those events which are deemed interesting to physics analyses (see section 3.6 for further discussion of the CMS trigger).

29 3.2 CMS Detector

The CMS detector is located in Cessy, France, 100 meters below the surface. A typical high energy pp collision will produce a wide variety of particles, each with different properties. Identyfing these particles, or their decays, and measuring their energies and momenta is a design goal of CMS. At a length of 21.6 meters and a diameter of 15 meters, CMS is composed of many subdetectors that each specialize in detecting and measuring a subset of the particles produced in collisions. The inner detector meausures the paths of charged particles and is only a few radiation lengths thick in order to not impede movement to the next layer of detectors. Surrounding the inner detector are the calorimeters: the electromagnetic calorimeter measures the energy of charged particles and photons, and the hadron calorimeter measures the energy of particles that interact by the strong force. The outer layers of CMS are composed of dedicated muon detectors in both the barrel and endcap regions. From the intial stages of CMS design the detection of isolated leptons (electrons and muons) and isolated photons have been a central design goal. Detection of these isolated particles are key components in Higgs and Beyond Standard Model (BSM) searches(15), as evidenced by the two key analyses that contributed to the Higgs boson discovery: ZZ decays which result in 4 isolated leptons, and the diphoton decay mode. For case of BSM searches, high energy muon detection is key for heavy Z boson decays to µ+µ− . The key component of CMS that allows for precise momentum measurements is its extremely strong magnet that enables curved trajectories of particles traversing the detector. In sections 3.2 and 3.3 the CMS detection of muons and electrons is discussed further. The CMS coordinante system is defined with the z-axis pointing along the beam line, x-axis towards the center of the LHC, and y-axis upwards. Two new variables, pseudo-rapidity (η) and rapidity (y), are useful in colliders and are given by the following equations:

[ ( )] θ η = −ln tan . (3–2) 2

30 [( )] 1 E + p c y = ln z . (3–3) 2 E − pz c Where θ is the polar angle with respect to the z-axis (along the beam line), E is the total energy of the particle and pz the particles momentum along the z-axis. Under large boosts where the colliding protons and its constituents can be considered relativistic, η is a very good approximation of the rapidity (y). This approximation is very valuable because it is often difficult to get an accurate measurement of a particles total energy and beam line momentum. When this approximation can be made the difference in η between two particles is Lorentz invariant under a boost in the z direction. Again, for hadron colliders this becomes very important as the composite nature of colliding protons means that parton interactions carry different boosts along the z-axis. The variable η ranges from zero, when a particle is travelling along the beamline, and to infinity when a particle is parallel to the beamline. A particle that has an absolute pseudo-rapidity greater than 2.4 will be refered to as forward and elsewhere refered to as being central. These limits relate to the geometry and spatial extent of the sub-detectors, as will be described in the following sections. 3.3 Tracker

The first detector encountered by particles produced in collisions will be the tracker. Composed almost entirely of silicon pixels, the tracker’s aim is path reconstruction of high energy particles, as well as detection of short lived particles which may only live long enough to interact in the tracker. A challenge of the tracker is the high flux of partciles due to its proximity to the beam line: roughly 10 million particles per square centimeter per second(16). The silicon layers in the tracker act as reverse-biased p-n junctions which produce electrical signals when a charged particle passes through them. Since the goal of the tracker is path reconstruction and not energy measurement, the tracker will not impede the particle and only record its path. One notable feature of the tracker is its ability to accurately measure momentum in different regions of the detector. In fact, the following discussion will also hold for

31 momentum measurements anywhere in the CMS detector. The tracker will attempt to provide a momentum measurement based on a particles measured trajectory: charged particles follow a curved path in the presence of a magnetic ﬁeld and this curvature is higher for lower momentum particles. A key geometrical quantity that relates a particles curvature and the tracker’s ability to assign momentum is the sagitta (s): the distance on a circular arc from the center of the arc to its base.The relationship between momentum resolution, s, and the magnetic ﬁeld (B) is given by

δp p ∝ . (3–4) p sB As can be seen from this equation for momentum resolution, an increase in the magnetic ﬁeld and/or the saggitta results in a smaller uncertainty on momentum measurements. Electrical signals detected in the diﬀerent layers of the tracker are used to reconstruct a charged particles path into an object called a track. Tracks are crucial in determining the momentum and trajectory of charged particles, in addition to where the primary interaction vertices are located. A primary vertex is the most likely coordinate of where the initial collision took place. Reconstruction of a primary vertex is done by requiring a minumum number of high-quality tracks and having the largest squared transverse momentum sum associated to it. Primary vertices can be measured with a resolution of better than 50 µm(17). Such high spatial resolution becomes instrumental in identifying long lived particles, such as the b quarks in this analysis, that decay within the tracker and will be described further in Section 3.6. 3.4 Calorimeters

After the inner tracker the next sub-detectors for a particle to interact with are the electromagnetic calorimeter (ECAL) and then the hadronic calorimeter (HCAL). Their design is such that a particle, and all of its decay products, are completely absorbed within the medium of the calorimeters, allowing for an energy measurement of the particle. Both calorimeters are situated before the magnetic solenoid in order to ensure that a portion of a particles energy

32 would not be lost in interactions with the solenoid material and throw off the calorimeter energy measurement. The ECAL is scintillating calorimeter made of 15,000 lead tungstate crystals in the endcaps, while the barrel contains 61,200. Unlike calorimeters that have a separate absorber and collector, the CMS ECAL is homogenous. Lead tungstate was choosen as the homogenous material because it can produce light in fast, well-defined bursts that allow for precise measurements. Incident charged particles produce electromagnetic showers as the particle traverses the crystal. Lead tungstate can produce roughly 30 photons per MeV of an incoming particle. These photon signals are amplified and detected by silicon avalanche photodiodes in the barrel and vacuum phototdiodes in the endcaps(16). A side effect of having many individual photodiodes is the ability to provide spatial resolution in addition to an energy measurement. The average energy lost by electrons can be divided into two main regimes which are significant: energies more than 10 MeV where brehmstrahlung dominates, and below 10 MeV where energy losses through ionization becomes dominant. As a consequence of this energy dependence, high energy electrons and photons will produce secondary photons by brehmstrahlung, or secondary electrons by pair production. These secondary particles then continue this electromagnetic cascade until there is insufficient energy to continue. This process of electromagnetic cascading creates a spread of energy in the calorimeters refered to as a cluster. Associated clusters can be grouped together to form super-clusters. The measurement of energy with an electromagnetic calorimeter is based on the principle that the energy released in the detector material by the charged particles of the shower, mainly through ionization and excitation, is proportional to the energy of the incident particle. ECAL resolution will improve as a particle’s energy increases as shown in the following formula:

σ S N ( E )2 = (√ )2 + ( )2 + C 2 (3–5) E E E

33 Where S is the stochastic term, N is the noise term due to electronic noise in the detector, and C is a constant term which does not depend on energy. This latter term is caused by instrumental effects that can originate from imperfections in the detector material, the electronic readout system, and from physical wear and radiation damage. The HCAL is composed of alternating layers of a dense absorber, made of brass, and tiles of plastic scintillators. Brass was choosen as the absorber due to its short interaction length and because it is relatively easy to produce. When a particle traverses the aborbing brass layer strong interactions occur with the nucleui of the brass causing a cascade of particles at lower energies. Within each layer of tiles optical fibers called wavelength-shifting fibers of diameters less than 1 mm absorb the light produced in the absorber. The resolution for the HCAL follows the same form as the ECAL (Formula 3-5). 3.5 Muon Systems

The outermost sub-detectors are the muon systems: drift tubes (DT) in the barrel region, cathode strip chambers (CSC) in the endcap, and resistive plate chambers (RPC) in both barrel and endcap(16). The DT and CSC systems have efficient spatial resolution, while the RPC system excels at timing measurements. Since muons only interact electroweakly, their interactions in the HCAL are neglible and their larger mass also makes energy losses due to bremsstrahlung and ionization in the ECAL minimal. As such the muon systems can be placed outside the magnet without fear of affecting muon energy measurements. DTs are composed of 4 cm wide gas filled tubes with a single wire in the center. When a charged particle passes through the tube it will ionize the gas and cause electrons to flow onto the wire, creating a current. This signal along with the known drift velocity of the ionized electrons allows for a two-dimensional spatial measurement. CSCs are arrays of gas filled chambers enclosing a positively charged anode wire and a negatively charged cathode copper strip that passes perpendicular to the anode. Ionized electrons move toward the anode, while positive ions are attracted to the cathode. In this way two perpendicular coordinates are assigned to passing particles.

34 RPCs consist of alternating layers of a positively-charged anode plate and a negatively-charged cathode plate. A gas volume sits between the anode and cathode and much like the CSC and DT systems, use ionization to detect particles.

Figure 3-2. One quarter view of the CMS detector. DT, CSC, and RPC systems are shown.

Within both the CSC and DT systems there exist multiple stations that a muon will deposit energy into. Hits from successive stations can then be combined to form a path the muon had taken and thus assign a momentum to the muon. Eﬀective range in eta of the CSCs is 0.9-2.4, while the RPCs currently stop at η = 1.6. Information is currently shared between the DT, RPC, and CSC systems in order for muons to be detected that pass through both the barrel and endcap. 3.6 Trigger

Unlike the sub-detectors discussed in the previous chapters, which have a deﬁnite physical location within the detector, the CMS trigger system has no single, physical location. One of the challenges of any CMS analysis is to record and select relevant physics collisions out of the overwhelming number of collisions that occur within CMS. For the LHC designed instantaneous

35 luminosity of 1.5 ∗ 1034 cm−2 sec−1, there are 23 collisions for every beam crossing, which occurs with a frequency of 25 nanoseconds. This results in an input rate of 109 events that occur every second. The goal of the CMS trigger is to reduce this input rate (109 Hz) by a factor at least 106 to create an input rate of 1 kHz, which is the limiting rate of the CMS storage farm. The trigger is split into two online levels: Level 1 (L1), reducing the input rate to 100 kHz; Level 2, the High Level Trigger (HLT), recieves the output of the L1 trigger and further recudes the input rate to 1 kHz. The L1 trigger was upgraded for run two (shown in 3-3) and is divided into three main categroies: L1 muon trigger, L1 calorimeter trigger, and L1 global trigger (18).

Figure 3-3. Overview of the Run 2 Upgraded Level 1 Trigger

The main technology upgrade to the L1T is the use of Advanced Mezanine Cards (AMC) which ﬁts into the microTCA telecommunications standard. The boards of the L1 system communicate via optical serial links with a bandwidth of 10 gigabytes per second. The L1 Muon trigger is further divided into three subcategoires corresponding to the muon sub-detectors discussed in section 3-5: Drift Tube Trigger in the barrel, Cathode Strip Chamber Trigger in the endcap, and Resistive Plate Chamber Trigger in the overlap region. Whether or not the decision to trigger was sent by one of the muon sub-systems, all trigger objects found are sent upstream. Trigger Timing and Control system (TTC), which

36 is responsible for synchronous timing between all the trigger subcomponents. As mentioned previously, the L1 trigger has been upgraded in order to handle the higher luminosity and resulting pile-up that is expected from the increased collision energy. All subsystems have deployed improved reconstruction algorithms for the objects needed in Level 1 triggef decisions. The L1 Calorimeter Trigger is responsible for trigger decisions based on measurements of primitives in the HCAL and ECAL sub-detectors. Trigger tower energy sums in both the HCAL and ECAL are accompanied by a bit representing the transverse extent of the electromagnetic energy deposit in the ECAL case, and a bit representing the presence of minimum ionizing energy for the HCAL case. An intermediate Regional Calorimeter Trigger (RCT) recieves the ﬁrst stage of trigger information from the ECAL and HCAL and is responsible for forming the following primitives: electrons, photons, taus, and jets. Additionally, the RCT is responsible for identifying isolated or non-isolated electrons and muons. The main tasks of the L1 Global Trigger (GT) is to synthesize information from the L1 Muons and Calorimeter Triggers and to pass a Level-1 trigger decision upstream. Additionally, the L1 Global Trigger stores the coordinates in (η, ϕ) space for all trigger objects. The ﬁnal output of the L1 GT is a decision to accept, called L1A, or reject each bunch crossing.

37 CHAPTER 4 PARTICLE IDENTIFICATION The CMS sub-detectors record energy and raw hit information from particles passing through the detector. The main technique within CMS for particle reconstruction is the particle flow (PF) algorithm(19), whose aim is identifying and reconstructing all the particles from the initial collision by combining information from the different sub-detectors. A simplified description of the PF algorithm can be described as follows. Tracks from the tracker are extrapolated through the ECAL and HCAL, and if they pass within specified boundaries of the calorimeter super-clusters, a charged particle is associated to them. Electrons are assigned from super-clusters in the ECAL to curved trajectories in the tracker, and similar processes occur in the HCAL to create charged hadron candidates. Once all the tracks have been dealt with, the remaining clusters in the ECAL are associated to photons and the neutral hadrons to clusters in the HCAL. Muons will be reconstructed from charged tracker tracks that have no associated energy deposits in the calorimeters, and with energy deposits in the CSCs or DTs. Reconstruction of electrons, muons, jets, and neutrinos (in the form of missing energy) from the information recorded in the sub-detectors will be summarized in this section. 4.1 Energy Losses by Particles in Matter

Identification of different particles will depend on the different ways they interact with matter and loose energy. The main processes for energy loss are ionization and radiation. Ionization is the process by which charged particles interact with electrons bound to atoms, resulting in an energy transfer. Other than electrons and positrons energy loss due to ionization will dominate over radiation loss for all but the highest attainable energies. The expression for energy loss due to ionization by a particle as it travels through a medium is given by:

[ ( ) ] dE Dq2n 2m c 2β2γ2 δ(γ) − = e ln e − β2 − , (4–1) dx β2 I 2 where x is the distance travelled through the medium, D is a constant (5.1 ∗ 10−25 MeV cm2),

v − 2 −1/2 me is the electron mass, β = c , γ = (1 β ) , ne is the medium electron density, I is

38 the mean ionization potential of the atoms averaged over all electrons, and δ is a dielectric screening correction for relativistic particles. Charged particles will also lose energy due to the bremsstrahlung (translated from German as braking radiation) mechanism. The electric ﬁeld of a nucleus will accelerate and decelerate passing particles, causing them to radiate photons. For electrons and positrons this will be the dominant mechanism of energy loss. The rate of energy loss due to bremsstrahlung is given by:

dE E − = , (4–2) dx LR

where LR is the radiation length and is given by:

( ) ( ) 1 ℏ 2 183 = 4 Z(Z + 1) 3n . α aln 1/3 (4–3) LR mc Z The most important characteristic of Formulas 4-1 and 4-3 are the 1/m2 dependence, where m is the mass of any charged particle. Since ionization losses are only weakly dependent on the charged particle mass, bremsstrahlung will dominate for the case of low mass particles such as the electron. For muons, whose mass is roughly 200 times that of the electron, any energy loss due to radiation is suppressed by the 1/m2 dependence. Ionization losses will dominate for muons and due to the fact that that they do not interact by the strong force will penetrate the the detector more than the other charged particles. 4.2 Electrons

Electron reconstruction is done through a combination of tracker and ECAL measurements. As an electron passes through the inner silicon tracker it will radiate photons as its trajectory is curved due to the magnetic ﬁeld. The amount of brehmstrahlung from the electron will

depend on its pT and will spread out in ϕ (also proportional to pT ). This spray of energy from the electron will be recorded by the ECAL as clusters along a ϕ path. Combining these clusters creates a super-cluster, whose energy weighted mean is then propagated back into the tracker. Matching a curved trajectory from the tracker to a super-cluster in the ECAL will also diﬀerentiate electrons from photons, where the latter will not leave behind a curved trajectory

39 in the tracker. By combining tracker and ECAL measurements we utilize the low momentum efficiency of the tracker with the high momentum quality of the ECAL, creating an electron whose energy resolution is optimized across a wide range of energies(20). It is necessary to employ advanced reconstruction techniques that classify supercluster patterns into distinct categories based on track reconstruction. The current electron track reconstruction algorithm used in CMS is a Gaussian Sum Filter (GSF). Due to brehmsstrahlung losses from electrons propagating in a highly non-Gaussian way, a Kalman Filter which relies on Gaussian probabilty density functions may not be ideal. The GSF algorithm models brehmsstrahlung energy losses by treating each observable sensitive to brehmsstrahlung as a Guassian and building a “mixture” or sum of Guassians. The GSF algorithm aids in supercluster identification and the creation of the aftormentioned electron categories. These supercluster pattern categories are used to differentiate between “well-measured” and “poorly measured” electrons and, in general, imply different energy-momementum measurements and different electron identification performance. The four electron categories are:

• Golden Electrons. This class represents those electron candidates which are associated with low brehmsstrahlung, with a reconstructed track well matching the supercluster and a well behaved supercluster pattern.

– a supercluster formed by a single cluster (i.e. without observed bremsstrahlung sub-cluster) – a measured bremsstrahlung fraction below 0.2 – a matching between the supercluster position and the track extrapolation from last point within 0.15 rad

– an Esc /pin value in excess of 0.9, where Esc is the measured supercluster energy and pin is the momentum measured at the primary vertex.

• Big Brem Electrons. This class shares most of the characteristics with the Golden electron class - well behaved supercluster pattern(i.e. the bremsstrahlung photons are merged inside the single cluster), no evidence of energy loss through photon conversion- and diﬀers only in that Big Brem electrons radiate all their brehmsstrahlung in a single step when crossing the tracker silicone layers. This is class is deﬁned by

– a supercluster formed by a single seed cluster

40 – a measured bremsstrahlung fraction above 0.5

– an Esc /pin value between 0.9 and 1.1 The last two electron categories are those with good energy-momentum matching and measurement, but fail to be classiﬁed as Golden of Big Brem, are deﬁned by the following class.

• Narrow Electrons. This class has a large bremsstrahlung fraction, but not as large as the Big Brem class, and a well behaved supercluster pattern. Its charachteristics are

– a supercluster formed by a single seed cluster

– an Esc /pin value between 0.9 and 1.1 – a measured bremsstrahlung fraction and/or a ϕ matching outside the range of Golden and Big Brem electrons. The last class constitutes the remaining electrons that are thought of as the “bad” electons:

• Showering Electons.

– a supercluster pattern identiﬁed with several bremsstrahlung sub-clusters.

– energy-momentum (Esc /pin) matching which fails one of the three deﬁnitions used in the previous classes. Electons used in this analysis are further categorized by the output (MVAID) of a Multivariate discriminator, in this case a Boosted Decision Tree (BDT) algorithm(21). A set of discriminating variables, selected to have the highest correlations between electron and non-electron like events, used in the CMS electron MVAID BDT are

• SuperCluster energy / track momentum at vertex

• ∆η between SuperCluster position and track direction at vertex extrapolated to ECAL assuming no radiation

• ∆ϕ between SuperCluster position and track direction at vertex extrapolated to ECAL assuming no radiation

• Ratio of energy in HCAL behind SuperCluster to SuperCluster energy

• Energy in 3x3 crystals / energy in 5x5 crystals

• Energy of closest BasicCluster to track impact point at ECAL / outermost track momentum

41 • Energy of closest BasicCluster to track impact point at ECAL / innermost track momentum

• ∆Φ between track impact point at ECAL and closest BasicCluster

• 1 − 1 E(SuperCluster) p(trackatvertex)

• Brem fraction = (track momentum at vertex - track momentum at ECAL)/ (track momentum at vertex)

• RMS width of the shower in η

• RMS width of the shower in ϕ

Figure 4-1. Output of the electron-identiﬁcation BDT for electrons from Z e+e data (dots) and simulated (solid histograms) events, and from background-enriched events in data (triangles), in the ECAL a) barrel, and b) endcaps(20).

Performance of the electron MVAID discriminator was tested on Z and J/Ψ decays into e+e− pairs in Data and simulated Drell-Yan events(22). The output of the MVAID BDT is presented in Figure 4-1, and electron track reconstruction eﬃciency presented in Figure 4-2. 4.3 Muons

Due to their large mass and inability to interact through the strong force, muons will traverse the inner sub-detectors with minimal energy loss and reach the outer muon sub-detectors in relative isolation. Within CMS, muon tracks are ﬁrst constructed independently in the inner tracker (tracker track) and in the outer muon systems (standalone muon track)(23).

42 Figure 4-2. Eﬃciency as a function of electron pT for dielectron events in data (dots) and DY simulation (triangles)(20).

Standalone muon tracks are constructed soley from information from the outer muon systems: CSC, DT, and RPC. The “base” primitives measured are hits in the muon chambers, which are then used to build segments or “track stubs”. During offline reconstruction these segments are used to generate “seeds” consisting of position and direction vectors and an estimate of the muon transverse momentum. These initial estimates are used as seeds for the track fits in the muon system, which are performed using segments and hits from DTs, CSCs and RPCs and are based on the Kalman filter technique. The resulting object is a standalone muon.

Tracker muon tracks are required to have pT > 0.5 GeV and are constructed soley from energy deposits in the inner tracker. Once muon tracks have been assigned there are two approaches that CMS uses to build muon objects from muon tracks:

• Global Muon Reconstruction. Starting with a standalone muon track , a corresponding tracker muon track is found by comparing parameters of the two tracks. The resulting object is a global muon track, which is fitted by a Kalman-filter technique. At large transverse momenta, pT > 200 GeV, the global muon track improves on the energy resolution of the tracker muon only fit due to inefficiencies in tracker track reconstruction at high momenta.

• Tracker Muon reconstruction. In this case tracks are ﬁrst identiﬁed in the tracker which satisfy the following momentum criteria: pT > 0.5 GeV and total momentum pT > 2.5

43 GeV. Next these candidate muon tracks are extrapolated to segments in the outer muons sub-systems by taking into account the magnetic ﬁeld, the average expected energy losses, and multiple Coulomb scattering in the detector material. The extrapolated track and the segment are considered matched if their local distance is less than 3 cm or if the value of the pull (diﬀerence in local positions of the extrapolated track and the segment, divided by their combined uncertainty) is less than 4.

At low momenta (pT < 5GeV ) tracker muon reconstruction is more efficient than global muon reconstruction due to only one muon segment being required on the outer muon sub-systems, whereas as the typical global muon reconstruction requires more than one muon segment in different stations of the muon sub-systems. Standalone muons, comprised of only standalone muon tracks, are typically not used in physics analyses due to their worse momentum resolution and higher contamination rates from cosmic rays. After a muon object has been reconstructed there exists different algorithms for muon selection depending on the needs of individual analyses: identification efficiency versus purity. The three most common muon selection categories are:

• Soft Muon selection. This category requires the muon to be a Tracker Muon, with the additional requirement that a muon segment is matched in both x and y coordinates with the extrapolated tracker track, such that the pull for local x and y is less than 3.

• Tight Muon selection. This category requires the muon to be a global muon with the χ2/d.o.f of the global muon track fit less than 10 and at least one muon chamber hit included in the global muon track fit. The tracker muon track is required to be matched to at least two muon segments from the muon sub-systems, in addition to using more than 10 inner tracker hits (including at least 1 pixel hit), and have a transverse impact parameter |dxy| < 2mm with respect to the primary vertex. In flight muon decays (muons not originating from primary interactions) are greatly reduced with this selection.

• Particle-Flow Muon selection. Muons from this category are an extension of tracker and global muons. Information from the various CMS sub-detectors are used in adjusting selecton criteria, such as the energy deposition in the calorimeters. The goal of this category is to optimize the selection of muons within jets with high efficiency, while preventing the misidentification of charged hadrons as muons. Momentum assignment efficiencies for the three muon categories are show in Figure 4-3

+ − + − using J/Ψ → µ µ events for pT < 20 GeV and Z → µ µ events for pT > 20 GeV(24).

44 Figure 4-3. Tag-and-probe results for the muon eﬃciency as a function of muon pT in data compared to simulation. Muons (left), Particle-Flow Muons (middle), and Tight Muons (right) in the barrel and overlap regions (top), and in the endcaps (bottom).

4.4 Jets

Individual quarks have never been observed alone in nature. Only those objects that are color neutral have been observed. When quarks are created they must combine with other quarks to create color neutral objects. This process is called hadronization and leads to the formation of objects called jets. In the high energy collisions of the LHC quarks will have large momenta and thus the particles created during hadronization will be collimated in a cone-like structure (jet) from the quark that induced the hadronization(25). The basic constituents of jets are tracker tracks and clusters in the ECAL and HCAL. Approximately 90% of the measured jet energy will come from charged hadrons and photons measured in the tracker and ECAL, while the remaining 10% will come from neutral hadron energy deposits in the HCAL. Many algorithms to identify and classify jets have been developed. The most widely used alogrithm is the “anti-kt” algorithm, which uses the relative transverse momenta of the particle ﬂow objects(26).

For every two PF objects pi and pj , two quantities are calculated for them:

45 ∆R2 d = ij min(p−2 , p−2 ), (4–4) ij R2 T ,i T ,j and

−2 di = pT ,1. (4–5)

∆ R is the distance in the ϕ/η plane, and R is the desired size of the jet cone. If dij is less than di the anti-kt algorithm will combine objects i and j into a jet. This is repeated until no more PF objects remain. The eﬀect of the algorithm is to combine higher pT jet

constitiuents first and then lower pT objects with a wider angle. The result is a cone-like structure in the rapidity-azimuthal(y, ϕ) plane. CMS also employs a suite of corrections to the measured jet energies -Jet Energy Corrections (JEC)- which seek to offset imperfections in the jet energy measurements and jet reconstruction techniques. Energies of the reconstructed jets are related to the jet energies at particle level and three factorized corrections are applied to the raw (uncorrected) jet energy measurement. The first factorized JEC correction accounts for the presence of energy originating from pile-up jets that are erroneously added to a jets energy measurement. A subtraction to the jet energy is made from a quantity derived from ρ, the average energy density per event, and the

jet area(27). The second JEC correction accounts for the pT and η response of jets due to non-linearities in the calorimeters. The third correction is to the average response per jet, or the jet energy scale (JES). An additional hurdle in jet reconstruction is seperating jets that arise from the primary interaction vertex and those that arise from pile-up (PU) collisions. PU collisions can cluster and form energy deposits in the ECAL and HCAL; these reconstructed objects are refered to as PU jets. On average PU jets tend to be soft (low pT), but multiple PU jets can overlap and form a high pT jet that could be used by the VHbb analysis. Additionally, as the rate of PU jets increases the rate of high pT PU jets increases quadratically(27). Approximately 50% of

46 all 30 GeV jets are PU jets. CMS employs a likelihood discriminator used to identify and reject PU jets. The discriminating inputs used in the likelihood discriminator include 12 variables related to jet shape and vertex related quantities. A high PU-jet rejection eﬃciency is achieved of up to 90 to 95% for central jets with |η| < 2.5, while retaining 99% of the non-PU jets from high pT interactions. 4.5 Lepton Isolation

One of the challenges of lepton identiﬁcation in the VHbb channel is distinguishing leptons whose origin is the the W/Z boson versus leptons that were created in the decay of a jet. The technique developed to help in this process is called lepton isolation(28). Lepton isolation seeks to measure the total energy in a region around the lepton and assign a value to the lepton that is representative of its probability to be born in a jet decay. The higher the energy of tracks around a lepton, the higher the probability for it to have been created during the decay of a jet. Each sub-detector employs unique techniques to measure lepton isolation. The tracker, for example, uses the following equation to isolate lepton tracks:

∑ tracks i i pT Isolation = lepton . (4–6) pT The summation is over all tracks detected in a cone in ϕ − η space: acceptance < √ ϕ2 + η2, and typical cone of acceptance is 0.2. The full particle ﬂow lepton isolation will take pT information from the ECAL, HCAL, and tracker and is deﬁned by the following:

∑ i i i [pT (charged and neutral hadrons) + pT (photons)] PF Isolation = lepton . (4–7) pT

4.6 b-Jet Identiﬁcation

Of particular interest to the VHbb analysis in this thesis is the identiﬁcation of b-quarks. Jets arising from b-quark hadronization will have unique characteristics related to their large lifetimes (τ ≈ 1.5 ps, cτ ≈ 450 µm), large mass, and hard momentum spectrum of the b-hadrons. An algorithm called the Combined MVA v2 (cMVAv2) algorithm exploits this fact

47 to distinguish jets arising from b-quarks from the other quark ﬂavors(25). A secondary vertex is the point at which the b-hadron decays. This point will be displaced with respect to the primary vertex (point of initial b-quark hadronization). Secondary vertex candidates must satisfy the following criteria:

• secondary vertices must share less than 65% of their associated tracks with the primary vertex.

• invariant mass associated with the secondary vertex must be less than 6.5 GeV.

• the flight direction of each candidate has to be within a cone of ∆R < 0.5 around the jet direction. The CMVAv2 algorithm provides a continuous discriminator output, ranging from -1 to 1, combining in an optimal way the information about track impact parameters and identified secondary vertices within jets and information of any soft lepton present in the jet. A boosted decisison tree (BDT) algorithm is the discriminating tool of choice for b-jet identification within CMS, which provides an output score in the range of -1 to 1. Calibration of the CMVAv2 discriminator is achieved by using a tag-and-probe method(29) to generate a set of weights used to correct the simulated CMVAv2 distribution with respect to the distribution observed in data. This procedure involves creating a binned CMVAv2 distribution of the “probe” jet in data and additionally a binned distribution from simulation. Each bin in the two distributions are compared and the simulated bin adjusted to match the observed bin contents.

This procedure is carried out for various bins in pT, η, and for light and heavy hadron ﬂavour jets, where the end result is a jet-by-jet weight used to reweight all jets. 4.7 Neutrinos

Neutrinos occur in the decay of W bosons and jets. Jet energy assignment and associated production Higgs decays rely on the ability to record the presence of a neutrino. Because of their stability, neutral charge, weakly-interacting nature, and low mass, neutrinos will pass through CMS without registering in any of the sub-detectors. Instead, the presence of missing energy in the transverse plane will serve as an indicator of a neutrino. Particles in the

48 LHC collide head-on (along the z-axis) and have zero transverse(x-y plane) momentum. Conservation of energy therefore requires the ﬁnal state to also have zero transverse momentum.

A collision is characterized by an initial total energy and momentum (Ei , p⃗i ) of the initial state particles. In the ﬁnal state we have n particles with total energy and momentum given by:

∑n ∑n E = Ei , ⃗p = p⃗i . (4–8) i i

When E < Ei and ⃗p ≠ p⃗i , this is indicative of a ﬁnal state particle escaping detection. 4.8 Jet Energy Regression

Despite all previous techniques described in this chapter to mitigate errors in jet reconstruction, significant differences in measured jet energy compared to theoretical predictions still exist. Inefficiencies in the tracker, ECAL, and HCAL, as well as missing energy arising from neutrino decays can be difficult to detect due to the low energy signature of neutrinos. In the case of jets containing a neutrino, this will lead to reconstructed jets that have lower assigned energy than they actually possess due to incorrect neutrino energy measurements. Corrections to the jet energy assignment can be made to account for neutrino presence and overall jet reconstruction inefficiency. A machine learning approach using boosted decision trees is utilized to improve the the jet energy resolution. By targeting the jet energy at the generator level in simulation (which contain energy due to neutrinos) a corrected jet energy measurement is given by the BDT output. The complete set of variables used in the regression training are:

• pT – transverse momentum of the jet after corrections

• MT – transverse mass of the jet after corrections

• η – pseudorapidity of the jet

• ptLeadTrk – transverse momentum of the leading track in the jet

49 • vtx3dL – 3-d ﬂight length of the jet secondary vertex

• vtx3deL – error on the 3-d ﬂight length of the jet secondary vertex

• vtxPt – transverse momentum of the jet secondary vertex

• vtxNtrk – number of tracks associated with the jet secondary vertex

• neEmEf – fraction of jet constituents detected in the ECAL that have neutral charge

• neHEF – fraction of jet constituents detected in the HCAL that have neutral charge

• nPVs – number of primary vertices

• SoftLeptPtRel – relative transverse momentum of soft lepton candidate in the jet

• SoftLeptPt – transverse momentum of soft lepton candidate in the jet

• SoftLeptdR – distance in η − ϕ space of soft lepton candidate with respect to the jet axis By correcting the jet energy, the invariant mass of the Higgs boson candidate jets are also corrected (see Figure 4-4). Both the resolution and the scale biases improve after the regression. The ﬁt used in all dijet mass plots is a combination of a crystal ball function (for signal modelling) and a Bernstein polynomial (for background modelling).

50 CMS Preliminary 13 TeV CMS Preliminary 13 TeV 2500 M = 125 GeV M = 125 GeV 6000 H H

Regressed Regressed 2000 5000 Raw Raw PEAK = 120.5 PEAK = 123.8 4000 FWHM = 37.4 FWHM = 30.3 PEAK = 111.0 1500 PEAK = 119.6 Events / 2.5 GeV Events / 2.5 GeV FWHM = 40.9 FWHM = 31.5 3000 1000 2000

500 1000

0 0 50 100 150 200 250 50 100 150 200 250 Mjj (GeV) Mbb (GeV) CMS Preliminary 13 TeV

10 MH = 125 GeV

Regressed 8 Raw PEAK = 122.8 FWHM = 34.3 6 PEAK = 115.6

Events / 2.5 GeV FWHM = 35.8

0 50 100 150 200 250 Mbb (GeV)

Figure 4-4. Distributions of dijet invariant mass in signal Z(ℓℓ)H(top left), Z(νν)H(top right), and W(ℓν)H(bottom) events before and after the regression is applied.

51 CHAPTER 5 THE VHBB ANALYSIS Now that the framework for detection and reconstruction of physics objects has been described in general detail in the previous chapters, we now turn to the specifics of my thesis topic: the VHbb analysis. As mentioned in the introduction, the goal of the VHbb analysis is the measurement of the Standard Model Higgs boson coupling to bottom quark pairs. Due to the overwhelming rate of final states that contain b-quark pairs relative to b-quark pairs that arise from Higgs decays, the additional requirement of the presence of a vector boson (W or Z) is imposed on the final state selection, refered to in this thesis as the VHbb channel or the Higgsstrahlung (Higgs radiation) process. Table 5-1 summarizes the cross sections and branching fractions for the main Higgs production mechanisms. The cross sections are computed at NNLO for a Higgs mass of 125 GeV(30; 31; 32). Although the WH and ZH Higgsstrahlung channels have a much lower cross section than the gluon fusion or vector boson fusion channels, the lack of an additional handle, such as an associated vector boson, makes them much more difficult when attempting to isolate signal events. Three final states, or channels, are defined in the VHbb analysis: Z(ℓℓ)H(the focus of my contributions to the analysis), W(ℓν)H, and Z(νν)H. All have the common trait of a pair of bottom quarks recoiling against the associated vector boson and are uniquely defined by the decay mode and type of associated vector boson:

• Z(ℓℓ)H: A boosted Z boson decays into a Z boson and a Higgs boson, where the Higgs decays into bottom quark pairs and the Z decays into electron or muon pairs.

• Z(νν)H: A boosted Z boson decays into a Z boson and a Higgs boson, where the Higgs decays into bottom quark pairs and the Z decays into neutrino pairs.

• W(ℓν)H: A boosted W boson decays into a W boson and a Higgs boson, where the Higgs decays into bottom quark pairs and the W decays into an electron or muon and a neutrino. The generalized associated Higgs production processes are shown in Figure 5-1, where the incident particles are either quark or gluon pairs. In Run 1, with a lower center of mass energy of 7 and 8 TeV, the gluon initiated VHbb channel was not considered due to its high

52 √ Table 5-1. Signal cross sections and branching ratios for Mhiggs = 125 at s = 13. process σ (pb) QCDScale PDF ggH 44.14 +7.6-8.1% 3.1% VBF H 3.782 +0.4-0.3% 2.1 % WH 1.373 (0.840+0.533) +0.5 -0.7% 1.9 % ZH 0.8839 +3.8 -3.1% 1.6 % decay BR Uncertainty H → b¯b 58.24% +0.72-0.74% activation energy associated with a top quark loop. However, with the current Run 2 center of mass energy of 13 TeV there are sufficient amounts of gluon pairs with high enough energy to produce top quark loops that contribute in a significant way to the final VHbb signal region. Approximately two-thirds of the events in the signal region are from quark initiated processes and one-third from gluon initiated processes.

Figure 5-1. Feynman diagrams for the quark (left) and gluon (right) induced Higgs Strahlung process.

What follows in this chapter is a thorough description of each critical component in the VHbb analysis, building on the generalized CMS reconstruction techniques given in the previous chapter. 5.1 Backgrounds

Final states that possess the same experimental signature as our signal process -two bottom quarks with an invariant mass near 125 GeV recoiling from a vector boson- are refered to as backgrounds. Identfying these background processes and their charachteristics that distinguish them from signal processes is a main task of this analysis, and furthermore all

53 analyses at CMS engaged in measurements or searches of fundamental particles. VHbb signal events are characterized by:

• two b-jets with an expected invariant mass very close to 125 GeV based on current experimental data.

• b-jet pair pT spectrum that is harder and falls less gradually than main background sources.

• isolated leptons not arising from the associated vector boson are not expected.

• b-jet pair is expected to recoil back-to-back to the vector boson in the transverse plane (ie., azimuthal opening angle of π). Additonally the following variables have potential usefullness, depending on the signal channel, in signal versus background separation and whose abreviations will be used in the tables and ﬁgures throughout this thesis:

• M(jj): dijet invariant mass; it peaks at Mhiggs for signal and MZ for diboson events, falls sharply for V+jets, and peaks broadly over the region 100–160 for t¯t events.

• pT(jj): transverse momentum of the Higgs candidate. • pTj : transverse momentum of the Higgs candidate daughters.

• pT(V): vector boson transverse momentum, which is highly correlated with pT(jj) for signal and most backgrounds.

• CMVA: continuous output of the CMVA discriminant, optimized separately for the jet with the higher value (CMVA1), and the one with the lower value (CMVA2).

• Mt: the top mass reconstructed in events with a leptonic decaying W and one of the b-jets.

• ∆ϕ(V, H): azimuthal opening angle between the momenta of the vector boson and the Higgs candidate.

• ∆η(J1, J2): distance in pseudorapidity between the two jets comprising the Higgs candidate.

• ∆R(j, j): distance in η–ϕ space between the two jets comprising the Higgs candidate.

• Naj: number of additional jets in the event apart from the Higgs candidate. Only central jets with |η| < 2.5 are considered, but the pT threshold and number of additional jets

54 to allow are parameters to be optimized separately for each channel. In practice, the optimal threshold was found to be pT > 20 in all channels where a jet veto is applied.

• Nal: number of additional isolated leptons, apart from those associated with the W or Z decay. Only leptons satisfying pT > 20 and |η| < 2.5 are considered in the count.

• pfMET: missing transverse energy calculated with particle-ﬂow objects.

• ∆ϕ(pfMET, J): azimuthal opening angle between the pfMET vector direction and the transverse momentum of the closest central jet in azimuth. Only jets satisfying pT > 30 and |η| < 2.5 are considered. This variable helps in reducing residual QCD background in the Z(νν)H channel, where the source of the missing transverse energy is typically from ﬂuctuations in the measured energy of a single jet.

• ∆φ(pfMET, lept.): azimuthal opening angle between the pfMET vector direction and the leading lepton direction. This variable helps in reducing events of fully leptonic decay of t¯t in Z(νν)H analysis.

• min∆R(H, aj): minimum distance between an additional jet and the Higgs candidate. This variable helps in reducing ttbar background in the Z(νν)H and W(ℓν)H channels.

• soft N5 : number of additional soft track-jets with pT > 5. Given these signal characteristics and variable deﬁnitions we now turn to a discussion of each background source and their distinguishing characteristics. 5.1.1 Drell-Yan

The Drell-Yan process, also refered to as V + jets, is the dominant background contaminant for all three VHbb channels and is shown in Figure 5-2. Here one or more jets from the decay of a radiated gluon is accompanied by a W or Z vector boson in the ﬁnal state. The main challenge of the V+jets background is the identical ﬁnal state object list: two b-jets and two isolated leptons. However, the dijet pair can be distinguished from a signal dijet

pair by its softer pT spectrum and invariant mass spectrum that peaks lower than for signal. Additionally, the dominant contribution to the Drell-Yan process comes from V+light (udscg) jets -jets formed from the hadronization of up, down, strange, charm quarks, or gluons- and can be seperated out by use of b-tagging on both Higgs daughter jets. In the most sensitive regions of the signal phase space it is the V+b¯b contributions that dominate.

55 q¯ ℓ− Z ℓ+

g ¯b

q b Figure 5-2. Feynman diagram for the Drell-Yan background process.

5.1.2 t¯t

Top quark pair production presents a significant background challenge at the higher Run 2 center of mass energy, where the t¯t production cross section has increased by a factor of three compared to the Run 1. The t¯t decay chain is shown in Figure 5-3 where one can see a final state which contains two W boson decays and at least two b-jets. The experimental signature of two isolated leptons and two b-jets is reproduced here, but can be mitigated by the following t¯t topological conditions: the presence of additional jets (jet multiplicity) well beyond final state jet multiplicities, which occurs mainly due to a fully hadronic decay of one of the W bosons; the azimuthal opening angle is not peaked as sharply near π and is more broadly distributed; and lastly, in the case, a top mass reconstruction is utilized in order to reject jets with mass similair to the top mass. b

q / ℓ+

t ′ W+ ¯q / νl

¯t ¯b W− ℓ+ / ¯q′

ν¯l / q Figure 5-3. Feynman diagram for the t¯t background process.

56 5.1.3 Diboson

Vector boson pair production is also a relevant background due the dijet mass resonance overlapping with the signal dijet resonance. Althouth the invariant W/Z mass peaks much lower at 80/91 GeV respectively, significant overlap of the resonances still occurs due to jet reconstruction inefficiencies that lead to a broad dijet mass spectrum. The dominant background contribution arises from diboson final states where one boson decays leptonically and the other into a b-jet pair. Good dijet mass resolution is key to distinguishing this process from signal. Three vector boson decay mode are possible: ZZ (shown in Figure 5-4), WW, and WZ. q¯ ℓ− Z ℓ+

Z ¯b

q b Figure 5-4. Feynman diagram for the ZZ diboson background process.

5.1.4 Single Top

The single top background arises from three channels: tW, t-channel, and s-channel. Single top events are more diﬃcult to reject relative to signal, but the cross section is such that it typically represents only 10-20% of the total background in W(ℓν)H and even less in Z(ℓℓ)H and Z(νν)H. For Z(ℓℓ)H rejection of single top events is made easy due to the typical absence of two isolated leptons, a dijet mass that does not peak near the Higgs mass, and an azimuthal opening angle that is not peaked as sharply near π. 5.2 Data and Simulation

5.2.1 Data

The data used in this thesis was collected in 2016 from the CMS detector with total integrated luminosity of 35.9 fb−1. The proton-proton collisions were recorded with a 25 nanosecond bunch spacing. In the Z(ℓℓ)H channel double muon and electron datasets were

57 used, while W(ℓν)H used the single muon and electron datasets and Z(νν)H used the MET dataset. Table 5-2 summarizes the luminosity breakdown per dataset collected during 2016 and is representive of luminosity breakdown for the other datasets in the VHbb analysis.

Table 5-2. List of 2016 data samples used for the SingleMuon∫ dataset. Dataset L () SingleMuon Run2016B-03Feb2017-v1 ∼5.9 SingleMuon Run2016B-03Feb2017-v2 ∼5.9 SingleMuon Run2016C-03Feb2017-v1 ∼2.7 SingleMuon Run2016D-03Feb2017-v1 ∼4.3 SingleMuon Run2016E-03Feb2017-v1 ∼4.1 SingleMuon Run2016F-03Feb2017-v1 ∼3.2 SingleMuon Run2016G-03Feb2017-v1 ∼3.8 SingleMuon Run2016H-03Feb2017-v1 ∼11.8 Total Lumi 35.9

5.2.2 Simulation

Monte Carlo generated samples (simulation) that reproduce expected CMS data are a vital component of the VHbb analysis. These simulated samples are used to model expected Standard Model processes and allow control regions to be constructed that validate detector operation and theoretical modeling. The Monte Carlo samples used were taken from the CMS RunIISummer16 productions re-miniAODv2 with the Asymptotic 25ns conditions. Tables containing the number of events, cross sections, and integrated luminosity are given for Higgs boson signal events (Table 5-3), di-vector boson production (Table 5-4), vector boson plus jets (Table 5-5), and with QCD multi-jet (Table 5-8). Simulated event creation is achieved through use of one or more of the following event generators: 8(33; 34), (35), (36), 5(37) with MLM merging(38), or aMC@NLO(39) with FxFx merging scheme(40). Parton shower and hadronisation are performed with 8(34) using the CUETP8M1 tune(41). The NNPDF3.0 parton distribution functions (PDF)(42) are used for all samples. Additionally, trigger and object reconstruction emulators from each CMS sub-system are used in the ﬁnal physics objects and trigger bits within the simulated samples.

58 The production cross sections for W+jets and Z+jets are rescaled to next-to-next-to-leading-order (NNLO) cross sections calculated using the 3.1 program(43; 44; 45). The t¯t and single top quark samples are also rescaled to their cross sections based on NNLO calculations(46; 47).

Table 5-3. Signal Monte Carlo samples with Mhiggs = 125 ∫ 2 Sample Generator mH (/c ) σ (pb) events L () /WplusH HToBB WToLNu M125 13TeV powheg pythia8 POWHEG+PYTHIA 8 125 0.840 * 0.108535 * 0.5824 1 317 467 8039.05 /WminusH HToBB WToLNu M125 13TeV powheg pythia8 POWHEG+PYTHIA8 125 0.533 * 0.108535 * 0.5824 1 290 538 12410.58 /ZH HToBB ZToLL M125 13TeV powheg pythia8 POWHEG+PYTHIA8 125 (0.8839 - 0.1227) * 0.10974 * 0.5824 4 926 620 102213.80 /ZH HToBB ZToNuNu M125 13TeV powheg pythia8/ aMC@NLO+PYTHIA8 125 (0.8839 - 0.1227 ) * 0.20103 * 0.5824 1 205 831 13661.96 /ggZH HToBB ZToLL M125 13TeV powheg pythia8 POWHEG+PYTHIA8 125 0.1227 * 0.10974 * 0.5824 2 998 600 192975.96 /ggZH HToBB ZToNuNu M125 13TeV powheg pythia8 POWHEG+PYTHIA8 125 0.1227 * 0.20103 * 0.5824 2 396 838 168136.79

Table 5-4. List of Monte Carlo diboson samples∫ Sample Generator σ (pb) events L () /WW TuneCUETP8M1 13TeV-pythia8 PYTHIA8 118.7 993 640 8.37 /WZ TuneCUETP8M1 13TeV-pythia8 PYTHIA8 47.13 1 000 000 21.22 /ZZ TuneCUETP8M1 13TeV-pythia8 PYTHIA8 16.523 985 600 59.65

5.2.3 Simulated Event Reweighting

Despite much work and advances, the event generators and detector simulations described in the previous section still create simulated event distributions that contain discrepencies with observed data. The VHbb analysis employs a suite of data driven event reweighting procedures in order to mitigate diﬀerences between simulation and data. The diﬀerent reconstruction challenges mitigated by reweighting techniques are

• Pile Up

• b-tagging

• Lepton trigger and identiﬁcation

• NLO to NNLO corrections

59 Table 5-5. List of Monte Carlo V + jets leading order samples∫ Sample Generator σ (pb) events L () /DY1JetsToLL M-10to50 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 725 39 800 000 54.5 /DY2JetsToLL M-10to50 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 394.5 19 400 000 50.2 /DY3JetsToLL M-10to50 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 96.47 4 960 000 52.2 /DYJetsToLL M-50 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 4960*1.23 49 100 000 9.9 /DYJetsToLL M-50 HT-100to200 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 147.40*1.23 10 610 000 72 /DYJetsToLL M-50 HT-200to400 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 40.99*1.23 9 652 000 235.4 /DYJetsToLL M-50 HT-400to600 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 5.678*1.23 10 010 000 1759 /DYJetsToLL M-50 HT-600to800 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 1.367*1.23 8 290 000 6111 /DYJetsToLL M-50 HT-800to1200 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 0.6304*1.23 2 670 000 4280 /DYJetsToLL M-50 HT-1200to2500 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 0.1514*1.23 596 000 3940 /DYJetsToLL M-50 HT-2500toInf TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 0.003565*1.23 399 000 109000 /DYBJetsToLL M-50 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 71.77*1.23 1 470 000 20.9 /DYBJetsToLL M-50 Zpt-100to200 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 3.027*1.23 4 080 000 1320 /DYBJetsToLL M-50 Zpt-200toInf TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 0.297*1.23 2 110 000 6670 /ZJetsToNuNu HT-100To200 13TeV-madgraph MADGRAPH5+PYTHIA8 280.35*1.23 5 240 199 15.20 /ZJetsToNuNu HT-200To400 13TeV-madgraph MADGRAPH5+PYTHIA8 42.75*1.23 5 032 927 95.7

• EWK signal theory corrections

• t¯t pT modeling 5.3 Triggers

Each channel in the VHbb analysis uses a unique trigger set in order to collect events that are consistent with the signal hypothesis. The Z(ℓℓ)H triggers will be described first, followed by the Z(νν)H trigger summary. The W(eν)H and W(µν)H channels utilize single lepton triggers, while the Z(ee)H and Z(µµ)H channels employ di-lepton triggers which are more efficient for the expected di-lepton final state signature. Table 5.3 summarizes the triggers used in this analysis. In order to validate and correct any discrepancies between simulated

60 Table 5-6. List of Monte Carlo V + jets leading order samples ∫ Sample Generator σ (pb) events L () /ZJetsToNuNu HT-400To600 13TeV-madgraph MADGRAPH5+PYTHIA8 10.73*1.23 954 435 72.32 /ZJetsToNuNu HT-600ToInf 13TeV-madgraph MADGRAPH5+PYTHIA8 4.116*1.23 9 645 493 1905.21 /WJetsToLNu TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 61526.7*1.21 86 700 000 1.72 /WJetsToLNu HT-100To200 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 1345*1.21 79 300 000 58.9 /WJetsToLNu HT-200To400 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 359.7*1.21 39 650 00 110.1 /WJetsToLNu HT-400To600 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 48.91*1.21 7 760 000 159.2 /WJetsToLNu HT-600To800 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 12.05*1.21 18 680 000 1543 /WJetsToLNu HT-800To1200 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 5.501*1.21 6 200 000 1130 /WJetsToLNu HT-1200To2500 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 1.329*1.21 6 875 000 5174 /WJetsToLNu HT-2500ToInf TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 0.03216*1.21 2 634 000 82200 /WBJetsToLNu Wpt-100to200 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 6.004*1.21 3 979 072 662.7 /WBJetsToLNu Wpt-200toInf TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 0.8524*1.21 2 892 981 3393.3 /WJetsToLNu BGenFilter Wpt-100to200 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 26.1*1.21 6 690 000 256.3 /WJetsToLNu BGenFilter Wpt-200toInf TuneCUETP8M1 13TeV-madgraphMLM-pythia8 MADGRAPH5+PYTHIA8 3.545*1.21 11 650 000 3286.3

Table 5-7. List of Monte Carlo V + jets next-to-leading order samples∫ Sample Generator σ (pb) events L () /DYJetsToLL Pt-50To100 TuneCUETP8M1 13TeV-amcatnloFXFX-pythia8 5+ 8 369.3 2.19E+07 8.23E+00 /DYJetsToLL Pt-100To250 TuneCUETP8M1 13TeV-amcatnloFXFX-pythia8 5+ 8 81.2 499 000 7.87 /DYJetsToLL Pt-250To400 TuneCUETP8M1 13TeV-amcatnloFXFX-pythia8 5+ 8 2.99 1 609 000 73.6 /DYJetsToLL Pt-400To650 TuneCUETP8M1 13TeV-amcatnloFXFX-pythia8 5+ 8 0.388 1 626 000 628 /DYJetsToLL Pt-650ToInf TuneCUETP8M1 13TeV-amcatnloFXFX-pythia8 5+ 8 0.03.74 1 629 000 7360 /DYToLL 0J 13TeV-amcatnloFXFX-pythia8 5+ 8 4760 49 600 000 6.98 /DYToLL 1J 13TeV-amcatnloFXFX-pythia8 5+ 8 /DYToLL 2J 13TeV-amcatnloFXFX-pythia8 5+ 8 341 42 300 000 10.5

61 Table 5-8. Top and QCD Monte Carlo samples ∫ Sample Generator σ (pb) events L () /TT TuneCUETP8M1 13TeV-powheg-pythia8 + 8 831.76 187 626 200 + 97 994 442 343 /ST tW top 5f inclusiveDecays 13TeV-powheg-pythia8 TuneCUETP8M1 + 8 35.6 1 000 000 28.09 /ST tW antitop 5f inclusiveDecays 13TeV-powheg-pythia8 TuneCUETP8M1 + 8 35.6 999 400 28.07 /ST t-channel top 4f leptonDecays 13TeV-powheg-pythia8 + 8 136*0.325 999 400 22.6 /ST t-channel antitop 4f leptonDecays 13TeV-powheg-pythia8 + 8 81*0.325 1 695 400 64.4 /ST s-channel 4f leptonDecays 13TeV-amcatnlo-pythia8 + 8 10.32 998 400 96.74 /QCD HT100to200 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 5+ 8 27990000 82 095 800 0.003 /QCD HT200to300 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 5+ 8 1712000 18 784 379 0.011 /QCD HT300to500 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 5+ 8 347700 54 267 650 0.16 /QCD HT500to700 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 5+ 8 2.94e4 19 542 847 0.66 /QCD HT700to1000 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 5+ 8 6831 45 100 675 6.60 /QCD HT1000to1500 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 5+ 8 1207 15 193 645 12.59 /QCD HT1500to2000 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 5+ 8 119.9 3 939 077 32.85 /QCD HT2000toInf TuneCUETP8M1 13TeV-madgraphMLM-pythia8 5+ 8 25.42 1 961 774 77.2 and observed trigger behavior, trigger emulation is required for all events used in the VHbb analysis. Correction scale factors are derived using the tag-and-probe method, which utilizes di-lepton events from Z bosons. The trigger efficiencies are measured after the application of offline lepton identification and isolation selections. For Z(ℓℓ)H , which utilzes a di-lepton trigger, each leg of the trigger must have the efficiency calculated separately due to different selections for the leptons associated with each leg. For both single and di-lepton triggers, the computed date/MC correction scale factors are very close to one. The correction scale factor and their uncertainties for electron triggers are shown in Figures 5-5 and 5-6 as a function of electron pT and η.

62 Table 5-9. List of L1 and HLT triggers used for the 2016 data set, and the channels to which they apply.

Channel L1 Seeds HLT Paths

W(eν)H L1 SingleMu20 HLT IsoMu24 OR HLT IsoTkMu24

Z(µµ)H L1 SingleMu20 HLT Mu17 TrkIsoVVL Mu8 TrkIsoVVL v* OR HLT Mu17 TrkIsoVVL TkMu8 TrkIsoVVL v* OR HLT Mu17 TrkIsoVVL Mu8 TrkIsoVVL DZ v* OR HLT Mu17 TrkIsoVVL TkMu8 TrkIsoVVL DZ v*

W(eν)H L1 SingleIsoEG22er OR HLT Ele27 WPTight Gsf L1 SingleEG25

Z(ee)H L1 SingleEG30 OR HLT Ele23 Ele12 CaloIdL TrackIdL IsoVL DZ L1 SingleIsoEG22er OR L1 SingleIsoEG24 OR L1 DoubleEG 15 10

Z(νν)H L1 ETM50 —— L1 ETM60 —— L1 ETM70 —— L1 ETM80 HLT PFMET110 PFMHT110 IDTight OR HLT PFMET120 PFMHT120 IDTight OR HLT PFMET170 NoiseCleaned OR HLT PFMET170 HBHECleaned OR HLT PFMET170 HBHE BeamHaloCleaned

Additonally, reconstruction inefficiencies for muons in the tracker, which vary in time throughout the 2016 collection time period, are accounted for. The double muon trigger efficiencies for data and MC are studied separately for runs B, C, D, E, F, G and for run H. The corresponding scale factors are shown in Figures 5-7- 5-8. For the Z(νν)H channel, which does not trigger on leptons but rather on missing energy, a different trigger approach is needed. The main trigger for Z(νν)H is HLT PFMET110 PFMHT110 IDTight, which is seeded at L1 by an OR of L1 ETM triggers. The overall trigger efficiency has been measured using the data collected by the single-muon and single-electron triggers and requiring the presence of two jets in the tracker acceptance in the event. In order to avoid bias from the L1 MET (calo-MET), the lepton is required not to be back to back with the reconstructed MET. The measured efficiency is then applied on the simulation. Figure 5-9 shows the trigger efficiency for various triggers and the OR as function of the offline min (MET,MHT)

63 distributions obtained in data in the single-electron (right) datasets. The top plots have been obtained on the full dataset.

Figure 5-5. Distributions of HLT Ele27 WPTight Gsf efficiency as function of pT and η for 2016 data. The efficiencies are measured after applying WP80 in the general purpose electron MVA IDs plus isolation selection. The turn-on can be seen as rising efficiency in pT above 27 GeV.

5.4 Analysis Object Selections

In this section speciﬁc selections for all physics objects used in the VHbb analysis - electrons, muons, jets, b-jets, and missing energy- will be discussed. Additionally, a treatment of pile-up and primary vertex selection will also be given. 5.4.1 Pile-Up and Primary Vertex Selection

As described in Section 3.1 pile-up (PU) refers to additonal collisions per bunch crossing. PU can be either in-time or out-of-time. In-time PU refers to collisions occuring in the same bunch crossing as the signal vertex. Out-of-time PU refers to collisions that occur in neighboring bunch crossings, which are spaced 25ns apart.

64 [][Leg 1]

[][Leg 2]

Figure 5-6. Distributions of HLT Ele23 Ele12 CaloIdL TrackIdL IsoVL DZ efficiency as function of p T and η for 2016 data. The efficiencies are measured after applying WP90 in the general purpose electron MVA IDs plus isolation selection. 65 l h rmr etxcniae ycosn h etxwt h largest the the amongst of with selected sum vertex is squared the vertex the choosing signal by The candidates freedom. vertex primary of the degrees all four exceeding fit vertex a and axis, z Deterministic the using tracks algorithm( from clustering reconstructed Annealing are vertices primary All occur. collisions leg. 17 GeV the 8 to the correspond pass figure to right muon The second factor. the scale requiering leg factor, GeV scale 8 leg the GeV to corresponds figure left HLT 5-8. Figure GeVleg. 8 correspond the figure pass right to The muon factor. second scale the leg requiering GeV factor, 8 scale the leg to GeV corresponds 17 figure the left to The G. F, E, HLT 5-7. Figure oiinwithin position inlvre saseilcs fapiayvre,o oiin hr proton-proton where positions or vertex, primary a of case special a is vertex signal A Mu17 Mu17 muon |η| muon |η| 0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8 2.2 2.4 0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8 2.2 2.4 0 2 0 2 20 1 20 1

± 0.98 ± 0.99 ± 0.99 ± 0.99 ± 0.97 ± 0.98 ± 0.99 ± 0.98

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

± 0.98 ± 0.99 ± 0.99 ± 0.99 ± 0.97 ± 0.98 ± 0.99 ± 0.98

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 TrkIsoVVL TrkIsoVVL itiuin o ahlgo h HLT the of leg each for Distributions HLT the of leg each for Distributions 30 30 combRelIsoPF04dBeta_bin0_&_PF_pass combRelIsoPF04dBeta_bin0_&_PF_pass

± 0.98 ± 0.99 ± 0.99 ± 0.99 ± 0.97 ± 0.98 ± 0.99 ± 0.98

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 40 40

± 0.98 ± 0.99 ± 0.99 ± 0.99 ± 0.97 ± 0.98 ± 0.99 ± 0.98

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 24 50 50 mo h eetrcne,arda oiinwithin position radial a center, detector the of cm

± 0.98 ± 0.99 ± 0.99 ± 0.99 ± 0.97 ± 0.98 ± 0.99 ± 0.98

0.00 0.00 0.00 0.00 0.00 0.00 0.04 0.00 60 60 TkMu8 TkMu8 p T 70 70 faleeetr atce soitdwt ie vertex. given a with associated particles elementary all of 80 80 17 TrkIsoVVL TrkIsoVVL

± 0.98 ± 0.99 ± 0.99 ± 0.99 ± 0.97 ± 0.98 ± 0.99 ± 0.98 90 90

0.00 0.00 0.00 0.00 0.00 0.00 0.04 0.00 .Terqieet o l rmr etxcniae r a are candidates vertex primary all for requirements The ). muon p muon p 100 100 T T 110 110 (GeV/c) (GeV/c) 120 120 *tigra ucinof function as trigger v* *tigra ucinof function as trigger v* 0.984 0.986 0.988 0.99 0.992 0.97 0.975 0.98 0.985 0.99 66 Efficiency of hlt_Mu17_Mu8_OR_TkMu8_leg8::above Efficiency of hlt_Mu17_Mu8_OR_TkMu8_leg8::above Mu17 Mu17 muon |η| muon |η| 0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8 2.2 2.4 0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8 2.2 2.4 0 2 0 2 20 1 20 1

± 1.00 ± 1.00 ± 0.99 ± 0.97 ± 0.99 ± 0.99 ± 0.98 ± 0.95

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

± 1.00 ± 1.00 ± 1.00 ± 0.98 ± 0.99 ± 0.99 ± 0.98 ± 0.96

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 30 30 TrkIsoVVL TrkIsoVVL combRelIsoPF04dBeta_bin0_&_PF_pass_&_tag_DoubleIsoMu17Mu8_IsoMu8leg_pass_&_tag_DoubleIsoMu17TkMu8_IsoMu8leg_pass combRelIsoPF04dBeta_bin0_&_PF_pass_&_tag_DoubleIsoMu17Mu8_IsoMu8leg_pass_&_tag_DoubleIsoMu17TkMu8_IsoMu8leg_pass

± 1.00 ± 1.00 ± 1.00 ± 0.98 ± 0.99 ± 0.99 ± 0.99 ± 0.97

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 40 40

± 1.00 ± 1.00 ± 1.00 ± 0.99 ± 0.99 ± 0.99 ± 0.99 ± 0.97

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 50 50

± 1.00 ± 1.00 ± 1.00 ± 0.99 ± 0.99 ± 0.99 ± 0.99 ± 0.97

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 60 60 Mu8 Mu8 p p 70 70 T T 2 and and mo h beamspot the of cm 80 80 ∑ TrkIsoVVL TrkIsoVVL

± 1.00 ± 1.00 ± 1.00 ± 0.99 ± 0.99 ± 0.99 ± 0.99 ± 0.98 90 90

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 p η η T 2 muon p muon p o u ,C D, C, B, Run for o u .The H. Run for 100 100 where , T T 110 110 (GeV/c) (GeV/c) *OR v* OR v* 120 120 ∑ 0.975 0.98 0.985 0.99 0.995 0.95 0.955 0.96 0.965 0.97 0.975 0.98 0.985 0.99 p T 2 Efficiency of hlt_Mu17Mu8_leg17::above Efficiency of hlt_Mu17Mu8_leg17::above is χ2 / ndf 14.85 / 6 p0 0.05273 ± 0.01262 1.4 p1 104 ± 10.24 CMS Preliminary 2016 p2 0.9762 ± 0.001483 -1 1.2 s = 13 TeV, 2016, L = 35.9 fb Z(νν)H(bb) triggers SingleElectron: elept>30 GeV, 2 jets with p >20, |η|<2.5, ∆Φ(ele,MET)<2.5 t

Efficiency 1

0.8

0.6

PFMET110_PFMHT110_IDTight_v 0.4 PFMET120_PFMHT120_IDTight_v

HLT_PFMET170_* 0.2 OR

0 0 50 100150200250300350400450500 min(MHT,MET) [GeV]

Figure 5-9. Distributions of trigger eﬃciency as function of min (MET,MHT) for the data in the single-electron for 2016 full dataset.

Over the course of 2016 the average PU ranged from 40 to 15, depending on the time during each fill (the longer a fill goes, the lower the PU becomes due to proton depletion). The presence of PU has a negative effect on jet resolution and Higgs reconstruction. Two different approaches to mitigate the negative effects of PU exist within the VHbb analysis:

• PFnoPU: also known as Charged Hadron Subtraction (CHS), PFPU is an algorithm embedded in the PF jet processing chain that attempts to filter all charged hadrons that do not appear to originate from the primary interaction. This approach is very effective but only works in the pseudorapidity region covered by the Tracker. Algorithms for tagging b jets are not impacted, since they apply their own track pre-filtering that is also designed to be PU-resistant.

• Fastjet: an external software package from which CMS software takes virtually all its jet reconstruction services(48). In particular it provides the means to calculate the momentum density per unit area ρ due to PU for each event, which can be used to subtract the contamination of jets and lepton isolation cones based on their respective areas. These methods are therefore referred to as ”Fastjet Subtraction.” Both the PFnoPU and Fastjet Subtraction methods are used in the VHbb analysis.

67 5.4.2 Electrons

Electron pre-selection requires all electron candidates to have pT > 7, |η| < 2.4,

dxy < 0.05, dz < 0.2, and a loose isolation cut of 0.4. The next stage of electron selection is done through the output of a multivariate discriminator that is trained on simulated electrons that pass a set of cuts meant to represent electrons that would pass the most common electron triggers. The following variables are currently used to discriminate between real and fake electrons:

• SuperCluster energy / track momentum at vertex

• DeltaEta between SuperCluster position and track direction at vertex extrapolated to ECAL assuming no radiation

• DeltaPhi between SuperCluster position and track direction at vertex extrapolated to ECAL assuming no radiation

• Ratio of energy in HCAL behind SuperCluster to SuperCluster energy

• Energy in 3x3 crystals / energy in 5x5 crystals

• Energy of closest BasicCluster to track impact point at ECAL / outermost track momentum

• Energy of closest BasicCluster to track impact point at ECAL / innermost track momentum

• DeltaPhi between track impact point at ECAL and closest BasicCluster

• 1/E(SuperCluster) - 1/p(track at vertex)

• Brem fraction = (track momentum at vertex - track momentum at ECAL)/ (track momentum at vertex)

• SigmaEtaEta cluster shape covariance

• SigmaPhiPhi cluster shape covariance All electrons used in this analysis therefore require a set of oﬄine cuts based on ECAL quantities that reproduce the conditions used in the electron MVA training. Those cuts are:

pt>15 & ( (abs(superCluster().eta)<1.4442 & full5x5 sigmaIetaIeta<0.012 &

68 hcalOverEcal<0.09 & (ecalPFClusterIso/pt)<0.4 & (hcalPFClusterIso/pt)<0.25 & (dr03TkSumPt/pt)<0.18 & abs(deltaEtaSuperClusterTrackAtVtx)<0.0095 & abs(deltaPhiSuperClusterTrackAtVtx)<0.065) || (abs(superCluster().eta)>1.5660 & full5x5 sigmaIetaIeta<0.033 & hcalOverEcal<0.09 & (ecalPFClusterIso/pt)<0.45 & (hcalPFClusterIso/pt)<0.28 & (dr03TkSumPt/pt)<0.18) ). The resulting electron MVA output, refered to as the electron MVAID, contains various working points (WP) based on selection efficiency. Two working points are used: 90% efficiency (WP90) and 80% efficiency (WP80). Z(ee)H uses the loose WP90 threshold, while W(eν)H uses the WP80 threshold in order to suppress electron misidentification resulting from final states that contain a higher number of fake electrons.

The pT thresholds for Z(ee)H and W(eν)H are 30 and 20 GeV respectively on the leading

electron. In the Z(ee)H channel the trailing electron is required to have pT > 15 GeV. The lepton isolation is calculated using a delta R cone of 0.3. For W(ℓν)H an isolation smaller than 0.06 is required; for Z(ℓℓ)H an isolation less than 0.15 is required. 5.4.3 Muons

All muons in the VHbb analysis are global muons (combined tracker and muon system

objects) with the following basic pre-selections: pT > 5, |η| < 2.4, dxy < 0.5, dz < 1.0, and an isolation cut of 0.4. Two working points are deﬁned by the CMS muon working group: loose and tight deﬁned below.

• Loose muon:

– Particle-Flow Muon: isPFMuon() – is Global or Tracker Muon: isGlobalMuon() || isTrackerMuon()

69 • Tight muon:

– the candidate is reconstructed as a Global Muon: isGlobalMuon() – Particle-Flow Muon: isPFMuon() – χ2/ndof of the global-muon track ﬁt: globalTrack()->normalizedChi2() < 10. – at least one muon-chamber hit included in the global-muon track ﬁt: globalTrack()->hitPattern().numberOfValidMuonHits() > 0 – muon segments in at least two muon stations; this implies that the muon is also an arbitrated tracker muon: numberOfMatchedStations() > 1 – tracker track transverse impact parameter w.r.t. the primary vertex: fabs(muonBestTrack()->dxy(vertex->position())) < 0.2 – longitudinal distance of the tracker track wrt. the primary vertex: fabs(muonBestTrack()->dz(vertex->position())) < 0.5 – number of pixel hits: innerTrack()->hitPattern().numberOfValidPixelHits() > 0 – cut on number of tracker layers with hits: innerTrack()->hitPattern().trackerLayersWithMeasurement() > 5 W(µν)H uses the tight muon requirements, while Z(ℓℓ)H uses the loose muon

requirements. The pT lower threshold for the leading muon in both W(ℓν)H and Z(ℓℓ)H is 20 GeV, while the trailing muon has lower threshold of 10 GeV. An isolation cone of 0.4 is used with cut-oﬀ points of 0.06 for W(µν)H and 0.25 for Z(µµ)H. 5.4.4 Jets

All jets are reconstructed from particle ﬂow candidates and use the anti-kT algorithm with an R value of 0.4(19; 49), as described in Section 4.4. In order to reject fake jets resulting from detector noise and jets that are contaminated with PU, loose jet criteria is applied to all jets. Loose jet criteria satisfy the following:

• Neutral Hadron Fraction < 0.99

• Neutral EM Fraction < 0.99

70 • Number of Constituents > 1 And for η < 2.4 in addition apply

• Charged Hadron Fraction > 0

• Charged Multiplicity > 0

• Charged EM Fraction < 0.99 Any jet that overlaps with an isolated lepton within a delta R cone of 0.4 is rejected. The minimum pT requirements for all jets in the W(ℓν)H and Z(νν)H channels is 25 GeV and 20 GeV in Z(ℓℓ)H due to cleaner final state. Lastly all jets with |η| < 2.4 are rejected. Identifying b-jets is done through the use of the CMVA algorithm of Section 4.6. Each jet is assigned a CMVA value that can aid in deciding whether to discard or select the jet. Working points are defined for loose (CMVA> 0.5884), medium (CMVA> 0.4432), and tight (CMVA> 0.9432), which correspond to light jet mistag rates of 10%, 1%, and 0.1% respectively. The different background and signal regions require different btag working points depending on b-jet purity and statistic contraints and will be detailed more in Section 5.5.1. 5.4.5 Missing Energy

Identiﬁcation of missing energy (neutrinos) is critical in the W(ℓν)H and Z(νν)H channels, as well as aiding the Z(ℓℓ)H channel in obtaining a pure t¯t control region. The

˜miss missing transverse energy (ET ) in an event is defined as the negative vectorial sum of the transverse momenta of all particle-flow objects in the event. A recommended set of filters designed to remove instrumental noise and problematic events are used. Additional

˜miss improvements to ET is achieved by taking into account the diﬀerence between the raw

(uncorrected) jet pT, which does not contain missing energy contributions, and the corrected jet pT for jets with pT > 15, and |η| < 4.7. In the Z(νν)H channel a minumum threshold on ˜miss the magnitude of ET of 125 GeV is applied. 5.5 Multivariate Strategy

In order to fully utilize the discriminating power of the most relevant variables in signal and background events, a multivariate output is used as the ﬁnal discriminant in a binned

71 shape analysis. The Boosted Decision Tree (BDT) algorithm, implemented in TMVA(50), is choosen in order to utlize the BDTs ability to filter out variables with low target correlation, high sensitivity to outliers, and high robustness against overtraining when compared to other supervised learning methods. A BDT is a collection of shallow learners: decision trees with only a few layers of depth. A single decision tree learns the most discriminating variables when attempting to classify signal versus background events. Each tree creates a set of weights that is fed to the next tree and used to correct the next iteration of signal versus background classification. The final product from this learning procedure is a set of weights that take as input the set of variables used to train the BDT. Every event in data and simulation is fed into the BDT output weights and a score is assigned in the range of -1 to 1, where 1 is more signal like and -1 more background like. Separate BDTs have been trained with simulated events in each channel, where even events are selected for training and odd events for testing the BDT performance. The full list of training variables for each channel are given in Table 5-10. Optimization of the BDT parameters -tree depth, learning rate, number of trees- was performed using a grid search over the BDT parameters and used the ROC curve integral as a figure of merit. The BDT output for the train and test sets in each channel can be seen in Figures 5-10. In each channel it is necessary to construct a signal region which is topologically favorable for signal versus background separation, but also one which is not statistically limited in order to provide the BDT with sufficient training events. Table 5-11 lists the signal region preselections for each channel. The efficiency for the signal region preselection cuts for the Z(ℓℓ)H analysis is shown in Figure 5-11. 5.6 Control Regions

Control regions are constructed for each signiﬁcant background in each channel in order to adjust Monte Carlo estimates when compared to data. The resulting Monte Carlo corrections

72 Table 5-10. Variables used in the BDT training. Variable Channels utilizing M(jj): dijet invariant mass All pT(jj): dijet transverse momentum All pT(V): vector boson transverse momentum All CMVAmax: value of CMVA for the Higgs daughter Z(ℓℓ)H, Z(νν)H with largest CMVA value CMVAmin: value of CMVA for the Higgs daughter All with second largest CMVA value CMVAadd: value of CMVA for the additional jet Z(νν)H with largest CMVA value ∆ϕ(V, H): azimuthal angle between V and dijet All pT(j): transverse momentum Z(ℓℓ)H, Z(νν)H of each Higgs daughter pT(add.): transverse momentum Z(νν)H of leading additional jet ∆η(J1, J2): difference in η Z(ℓℓ)H, Z(νν)H between Higgs daughters ∆R(j, j): distance in η–ϕ Z(ℓℓ)H between Higgs daughters pT(add.): transverse momentum Z(νν)H of leading additional jet ∆η(J1, J2): difference in η Z(ℓℓ)H, Z(νν)H between Higgs daughters ∆R(j, j): distance in η–ϕ Z(ℓℓ)H between Higgs daughters Naj: number of additional jets W(ℓν)H, Z(ℓℓ)H N.B. definition slightly different per channel pT(jj)/pT(V): pT balance between Higgs Z(ℓℓ)H candidate and vector boson MZ: Z boson mass Z(ℓℓ)H SA5: number of soft activity jets All with pT > 5 GeV Mt: reconstructed top mass W(ℓν)H ∆φ(pfMET, lept.): azimuthal W(ℓν)H ˜miss angle between ET and lepton ˜miss ET : missing transverse energy W(ℓν)H, Z(ℓℓ)H mT (W ): W transverse mass W(ℓν)H ∆φ(pfMET, jet.): azimuthal Z(νν)H angle between and the closest jet with pT > 30

73 TMVA overtraining check for classifier: BDT

dx Signal (test sample) Signal (training sample)

/ 1.6 Background (test sample) Background (training sample) 1.4 Kolmogorov-Smirnov test: signal (background) probability = 0.083 (0.009)

(1/N) dN 1.2

0.8

0.6

0.4

0.2

0 U/O-flow (S,B): (0.0, 0.0)% / -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 BDT response

TMVA overtraining check for classifier: BDT_Znn_HighPt

dx Signal (test sample) Signal (training sample)

/ 2.5 Background (test sample) Background (training sample) Kolmogorov-Smirnov test: signal (background) probability = 0.105 (0.017) 2 (1/N) dN

1.5

0.5

0 U/O-flow (S,B): (0.0, 0.0)% / −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 BDT_Znn_HighPt response

Figure 5-10. The plots above show the BDT output for signal and background simulation in each of the three analysis channels. From left to right, top to bottom: W(ℓν)H Z(ℓℓ)H(low and high boost), Z(νν)H.

are refered to as scale factors and act as event weights applied to the relevant simulated processes. The background scale factors are the result of a simultaneous binned maximum likelihood ﬁt with the signal regions and thus the control regions are ensured to be orthogonal to the signal region. The obtained scale factors account for cross section discrepancies and any diﬀerences in the selection of physics objects. This section describes the control regions for Z + udscg(Z+LF), t¯t, and Z + bb(Z+HF) production as reconstructed in the Z(ℓℓ)H channel. Table 5-12 summarizes the selection

74 Table 5-11. Preselection cuts for each channel to deﬁne the signal region. Variable W(ℓν)H Z(ℓℓ)H Z(νν)H pT(V) > 100 [50 − 150], > 150 > 170 mℓℓ – [75 − 105] – ℓ pT (> 25, > 30) > 20 – pT(j1) > 25 > 20 > 60 pT(j2) > 25 > 20 > 35 pT(jj) > 100 – > 120 M(jj) [90 − 150] [90 − 150] [60 − 160] CMVAT CMVAL CMVAT CMVAL CMVAL CMVAL Naj < 2 – – Nal = 0 – = 0 – – > 170 Anti-QCD – – Yes ∆ϕ(V, H) > 2.5 > 2.5 > 2.0 – – < 0.5 < 2.0 – – Tightened Lepton Iso. (0.06, 0.06) – –

1 1 0.753558 ZHbb Signal MC 0.55089

DY BKG MC 0.205727 0.194925

0.124651 − 10 1 0.0944205 0.0896175

0.0261762 0.023876

10−2 0.0062602

− 10 3

0.000522074 0.000507669

pT(ll)>50 pT(ll)>150 75loose φ(V,H)>2.5

Figure 5-11. Eﬃciency and background reduction after each cut used in the signal region deﬁnition for the Z(ℓℓ)H channel, for signal and Z+jets, the dominant background. The plot has been obtained requiring at least two jets and one lepton with pT > 20.

75 criteria used to deﬁne each control region that enters the scale factor ﬁt. Two regions of

varying sensitivity are identified for the vector boson pT that allow for a more powerful BDT training in each region. For Z + bb the dijet mass is vetoed around the signal mass peak of 125 GeV and a tight cut on the btag discriminat (CMVA) is used in order to filter out Z + udscg events. In both the Z + udscg and Z + bb regions a vector boson mass veto around the Z mass is applied on order to reduce t¯t contamination. In the t¯t region an opposite Z mass veto is applied, as well as tight CMVA restrictions in order to reduce Z + udscg contamination. Z(ℓℓ)H control region plots are shown in Figures 5-12, 5-13, 5-14, 5-15, 5-16, 5-17. Table 5-12. Definition of control regions for the Z(ℓℓ)H channel. Variable Z+LF t¯t Z+HF pT(V) [50, 150],> 150 [50, 150],> 150 [50, 150],> 150 CMVAV2max < CMVAV2 Tight > CMVAV2 Tight > CMVAV2 Tight CMVAV2min < CMVAV2 Loose > CMVAV2 Loose > CMVAV2 Loose MET – – < 60 ∆ϕ(V, H) – – > 2.5 mℓℓ 75–105 veto 0–10, 75–120 85–97 M(jj) – – veto 90–150

The scale factors for backgorund normalization are ultimately accounted for and fitted during the signal extraction, however these scale factors are needed earlier for use within the BDT training and for model validation when plotting the most important variables. For the Z(ℓℓ)H channel the Z+jets and t¯t scale factors represent the dijet and dilepton sidebands of the signal region respectively. Muon and electron regions are fitted together. The fitted

variable is CMVAmin (the sub-leading jet CMVA value). Systematic uncertainties on the fitted scale factors are determined by evaluating the effect on the template shapes from various sources of systematics, which will be discussed in the next section. Table 5-13 summarizes the fit results in all three topologies for 13 TeV data for the SR+CRs fit. 5.7 Systematics

The full suite of uncertainties that aﬀect the VHbb analysis, from theoretical modeling to experimental object reconstruction, are refered to as systematics and accounted for in the ﬁnal

76 ×103

140 CMS Preliminary Data tt CMS Preliminary Data tt s = 13TeV, L = 35.9 fb-1 80000 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 VVHF - ZH(bb) 125 VVHF Z(µ-µ+)H(bb) Z(e e+)H(bb) 120 Low p (V) Z + bb VVLF Low p (V) Z + bb VVLF T 70000 T Z + b Single top Z + b Single top 100 Z+udscg MC uncert. (stat.) 60000 Z+udscg MC uncert. (stat.) Entries / 20 GeV Entries / 20 GeV

80 50000 40000 60 30000 40 20000

20 10000

0 0 χ2 χ2 0 /dof50 = 2.66 100 150MC uncert.200 (stat.)250 300 350 400 0 /dof50 = 2.11 100 150MC uncert.200 (stat.)250 300 350 400 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 Regressed m(jj) [GeV] Regressed m(jj) [GeV]

×103 160 CMS Preliminary Data tt 90000 CMS Preliminary Data tt s = 13TeV, L = 35.9 fb-1 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 VVHF - ZH(bb) 125 VVHF 140 Z(µ-µ+)H(bb) 80000 Z(e e+)H(bb) Low p (V) Z + bb VVLF Low p (V) Z + bb VVLF T T 120 Z + b Single top 70000 Z + b Single top Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) Entries / 10 GeV Entries / 10 GeV 100 60000 50000 80 40000 60 30000 40 20000

20 10000

0 0 χ2 χ2 0 /dof50 = 5.72 100 150MC uncert.200 (stat.)250 300 350 400 0 /dof50 = 3.35 100 150MC uncert.200 (stat.)250 300 350 400 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 Regressed p (jj) [GeV] Regressed p (jj) [GeV] T T

×103 ×103 240 140 CMS Preliminary Data tt CMS Preliminary Data tt 220 s = 13TeV, L = 35.9 fb-1 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 VVHF - ZH(bb) 125 VVHF Z(µ-µ+)H(bb) 120 Z(e e+)H(bb) 200 Low p (V) Z + bb VVLF Low p (V) Z + bb VVLF T T 180 Z + b Single top Z + b Single top 100 Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) Entries / 10 GeV 160 Entries / 10 GeV 140 80 120 100 60 80 40 60

40 20 20 0 0 χ2 χ2 0 /dof50 = 31.50100 150MC uncert.200 (stat.)250 300 350 400 0 /dof50 = 16.76100 150MC uncert.200 (stat.)250 300 350 400 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 p (V) [GeV] p (V) [GeV] T T

CMS Preliminary CMS Preliminary Data tt 35000 Data tt 60000 s = 13TeV, L = 35.9 fb-1 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 VVHF - ZH(bb) 125 VVHF Z(µ-µ+)H(bb) Z(e e+)H(bb) Low p (V) Z + bb VVLF 30000 Low p (V) Z + bb VVLF T T 50000 Z + b Single top Z + b Single top Entries / 0.12 Entries / 0.12 Z+udscg MC uncert. (stat.) 25000 Z+udscg MC uncert. (stat.) 40000 20000 30000 15000 20000 10000

10000 5000

0 0 χ2 χ2 −0.8 −/dof0.6 = 9.49−0.4 −MC(stat.)0.2 0 0.2 0.4 0.6 0.8 1 −0.8 −/dof0.6 = 5.36−0.4 −MC(stat.)0.2 0 0.2 0.4 0.6 0.8 1 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 BDT Output BDT Output

Figure 5-12. Distributions of variables in data and simulated samples in the Z + udscg control region for Z(µµ)H(left) and Z(ee)H(right) in the low V pTbin. From top to bottom: dijet invariant mass, dijet pT, pT(Z), and BDT output The plots are normalized using the SFs to facilitate shape comparison. 77 14000 9000 CMS Preliminary Data tt CMS Preliminary Data tt s = 13TeV, L = 35.9 fb-1 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 VVHF - ZH(bb) 125 VVHF 12000 Z(µ-µ+)H(bb) 8000 Z(e e+)H(bb) High p (V) Z + bb VVLF High p (V) Z + bb VVLF T T Z + b Single top 7000 Z + b Single top 10000 Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) Entries / 20 GeV Entries / 20 GeV 6000 8000 5000

6000 4000 3000 4000 2000 2000 1000

0 0 χ2 χ2 0 /dof50 = 1.36 100 150MC uncert.200 (stat.)250 300 350 400 0 /dof50 = 1.31 100 150MC uncert.200 (stat.)250 300 350 400 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 Regressed m(jj) [GeV] Regressed m(jj) [GeV]

6000 9000 CMS Preliminary Data tt CMS Preliminary Data tt s = 13TeV, L = 35.9 fb-1 s = 13TeV, L = 35.9 fb-1 - ZH(bb) 125 VVHF - + ZH(bb) 125 VVHF 8000 Z(µ µ+)H(bb) 5000 Z(e e )H(bb) High p (V) Z + bb VVLF High p (V) Z + bb VVLF T T 7000 Z + b Single top Z + b Single top Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) Entries / 10 GeV Entries / 10 GeV 4000 6000

5000 3000 4000

3000 2000

2000 1000 1000

0 0 χ2 χ2 0 /dof50 = 2.71 100 150MC uncert.200 (stat.)250 300 350 400 0 /dof50 = 2.50 100 150MC uncert.200 (stat.)250 300 350 400 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 Regressed p (jj) [GeV] Regressed p (jj) [GeV] T T

22000 14000 CMS Preliminary Data tt CMS Preliminary Data tt 20000 s = 13TeV, L = 35.9 fb-1 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 VVHF ZH(bb) 125 VVHF µ-µ+ 12000 - + 18000 Z( )H(bb) Z(e e )H(bb) High p (V) Z + bb VVLF High p (V) Z + bb VVLF T T 16000 Z + b Single top 10000 Z + b Single top Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) Entries / 10 GeV 14000 Entries / 10 GeV 12000 8000 10000 6000 8000 6000 4000 4000 2000 2000 0 0 χ2 χ2 0 /dof50 = 2.86 100 150MC uncert.200 (stat.)250 300 350 400 0 /dof50 = 2.11 100 150MC uncert.200 (stat.)250 300 350 400 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 p (V) [GeV] p (V) [GeV] T T

5000 7000 CMS Preliminary Data tt CMS Preliminary Data tt s = 13TeV, L = 35.9 fb-1 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 VVHF - ZH(bb) 125 VVHF Z(µ-µ+)H(bb) Z(e e+)H(bb) 6000 High p (V) Z + bb VVLF 4000 High p (V) Z + bb VVLF T T Z + b Single top Z + b Single top Entries / 0.12 Entries / 0.12 5000 Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) 3000 4000

3000 2000

2000 1000 1000

0 0 χ2 χ2 −0.8 −/dof0.6 = 9.91−0.4 −MC(stat.)0.2 0 0.2 0.4 0.6 0.8 1 −0.8 −/dof0.6 = 10.35−0.4 −MC(stat.)0.2 0 0.2 0.4 0.6 0.8 1 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 BDT Output BDT Output

Figure 5-13. Distributions of variables in data and simulated samples in the Z + udscg control region for Z(µµ)H(left) and Z(ee)H(right) in the high V pTbin. From top to bottom: dijet invariant mass, dijet pT, pT(Z), and BDT output The plots are normalized using the SFs to facilitate shape comparison. 78 CMS Preliminary Data tt CMS Preliminary Data tt s = 13TeV, L = 35.9 fb-1 3500 s = 13TeV, L = 35.9 fb-1 6000 ZH(bb) 125 VVHF - ZH(bb) 125 VVHF Z(µ-µ+)H(bb) Z(e e+)H(bb) Low p (V) Z + bb VVLF Low p (V) Z + bb VVLF T 3000 T 5000 Z + b Single top Z + b Single top Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) Entries / 20 GeV Entries / 20 GeV 2500 4000 2000 3000 1500 2000 1000

1000 500

0 0 χ2 χ2 0 /dof50 = 1.47 100 150MC uncert.200 (stat.)250 300 350 400 0 /dof50 = 1.63 100 150MC uncert.200 (stat.)250 300 350 400 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 Regressed m(jj) [GeV] Regressed m(jj) [GeV]

CMS Preliminary Data tt CMS Preliminary Data tt s = 13TeV, L = 35.9 fb-1 3000 s = 13TeV, L = 35.9 fb-1 5000 ZH(bb) 125 VVHF - ZH(bb) 125 VVHF Z(µ-µ+)H(bb) Z(e e+)H(bb) Low p (V) Z + bb VVLF Low p (V) Z + bb VVLF T T Z + b Single top 2500 Z + b Single top 4000 Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) Entries / 10 GeV Entries / 10 GeV 2000 3000 1500 2000 1000

1000 500

0 0 χ2 χ2 0 /dof50 = 1.66 100 150MC uncert.200 (stat.)250 300 350 400 0 /dof50 = 1.02 100 150MC uncert.200 (stat.)250 300 350 400 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 Regressed p (jj) [GeV] Regressed p (jj) [GeV] T T

6000 10000 CMS Preliminary Data tt CMS Preliminary Data tt s = 13TeV, L = 35.9 fb-1 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 VVHF - ZH(bb) 125 VVHF Z(µ-µ+)H(bb) Z(e e+)H(bb) Low p (V) Z + bb VVLF 5000 Low p (V) Z + bb VVLF 8000 T T Z + b Single top Z + b Single top Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) Entries / 10 GeV Entries / 10 GeV 4000 6000 3000

4000 2000

2000 1000

0 0 χ2 χ2 0 /dof50 = 0.87 100 150MC uncert.200 (stat.)250 300 350 400 0 /dof50 = 2.25 100 150MC uncert.200 (stat.)250 300 350 400 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 p (V) [GeV] p (V) [GeV] T T

9000 CMS Preliminary Data tt CMS Preliminary Data tt s = 13TeV, L = 35.9 fb-1 s = 13TeV, L = 35.9 fb-1 8000 ZH(bb) 125 VVHF 5000 - ZH(bb) 125 VVHF Z(µ-µ+)H(bb) Z(e e+)H(bb) Low p (V) Z + bb VVLF Low p (V) Z + bb VVLF 7000 T T Z + b Single top Z + b Single top Entries / 0.12 Entries / 0.12 4000 6000 Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.)

5000 3000 4000

3000 2000

2000 1000 1000

0 0 χ2 χ2 −0.8 −/dof0.6 = 15.91−0.4 −MC(stat.)0.2 0 0.2 0.4 0.6 0.8 1 −0.8 −/dof0.6 = 2.64−0.4 −MC(stat.)0.2 0 0.2 0.4 0.6 0.8 1 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 BDT Output BDT Output

Figure 5-14. Distributions of variables in data and simulated samples in the t¯t control region for Z(µµ)H(left) and for Z(ee)H(right) in the low V pTbin. From top to bottom: dijet invariant mass, dijet pT, pT(Z), and BDT output The plots are normalized using the SFs to facilitate shape comparison. 79 400 CMS Preliminary Data tt 250 CMS Preliminary Data tt s = 13TeV, L = 35.9 fb-1 s = 13TeV, L = 35.9 fb-1 350 ZH(bb) 125 VVHF - ZH(bb) 125 VVHF Z(µ-µ+)H(bb) Z(e e+)H(bb) High p (V) Z + bb VVLF High p (V) Z + bb VVLF T 200 T 300 Z + b Single top Z + b Single top Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) Entries / 20 GeV 250 Entries / 20 GeV 150 200

150 100

100 50 50

0 0 χ2 χ2 0 /dof50 = 0.88 100 150MC uncert.200 (stat.)250 300 350 400 0 /dof50 = 1.07 100 150MC uncert.200 (stat.)250 300 350 400 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 Regressed m(jj) [GeV] Regressed m(jj) [GeV]

250 CMS Preliminary Data tt 160 CMS Preliminary Data tt s = 13TeV, L = 35.9 fb-1 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 VVHF ZH(bb) 125 VVHF µ-µ+ - + Z( )H(bb) 140 Z(e e )H(bb) High p (V) Z + bb VVLF High p (V) Z + bb VVLF T T 200 Z + b Single top Z + b Single top 120 Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) Entries / 10 GeV Entries / 10 GeV

150 100 80

100 60

40 50 20

0 0 χ2 χ2 0 /dof50 = 0.96 100 150MC uncert.200 (stat.)250 300 350 400 0 /dof50 = 1.20 100 150MC uncert.200 (stat.)250 300 350 400 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 Regressed p (jj) [GeV] Regressed p (jj) [GeV] T T

CMS Preliminary Data tt 600 CMS Preliminary Data tt 900 s = 13TeV, L = 35.9 fb-1 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 VVHF - ZH(bb) 125 VVHF Z(µ-µ+)H(bb) Z(e e+)H(bb) 800 High p (V) Z + bb VVLF High p (V) Z + bb VVLF T 500 T 700 Z + b Single top Z + b Single top Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) Entries / 10 GeV Entries / 10 GeV 600 400 500 300 400

300 200 200 100 100

0 0 χ2 χ2 0 /dof50 = 0.69 100 150MC uncert.200 (stat.)250 300 350 400 0 /dof50 = 0.74 100 150MC uncert.200 (stat.)250 300 350 400 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 p (V) [GeV] p (V) [GeV] T T

800 CMS Preliminary Data tt CMS Preliminary Data tt s = 13TeV, L = 35.9 fb-1 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 VVHF 500 - ZH(bb) 125 VVHF 700 Z(µ-µ+)H(bb) Z(e e+)H(bb) High p (V) Z + bb VVLF High p (V) Z + bb VVLF T T Z + b Single top Z + b Single top Entries / 0.12 600 Entries / 0.12 400 Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) 500 300 400

300 200

200 100 100

0 0 χ2 χ2 −0.8 −/dof0.6 = 2.02−0.4 −MC(stat.)0.2 0 0.2 0.4 0.6 0.8 1 −0.8 −/dof0.6 = 1.28−0.4 −MC(stat.)0.2 0 0.2 0.4 0.6 0.8 1 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 BDT Output BDT Output

Figure 5-15. Distributions of variables in data and simulated samples in the t¯t control region for Z(µµ)H(left) and for Z(ee)H(right) in the high V pTbin. From top to bottom: dijet invariant mass, dijet pT, pT(Z), and BDT output The plots are normalized using the SFs to facilitate shape comparison. 80 1200 2000 CMS Preliminary Data tt CMS Preliminary Data tt s = 13TeV, L = 35.9 fb-1 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 VVHF - ZH(bb) 125 VVHF 1800 Z(µ-µ+)H(bb) Z(e e+)H(bb) Low p (V) Z + bb VVLF 1000 Low p (V) Z + bb VVLF T T 1600 Z + b Single top Z + b Single top Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) Entries / 20 GeV 1400 Entries / 20 GeV 800 1200 1000 600 800 400 600

400 200 200 0 0 χ2 χ2 0 /dof50 = 1.03 100 150MC uncert.200 (stat.)250 300 350 400 0 /dof50 = 1.99 100 150MC uncert.200 (stat.)250 300 350 400 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 Regressed m(jj) [GeV] Regressed m(jj) [GeV]

1600 CMS Preliminary Data tt 900 CMS Preliminary Data tt s = 13TeV, L = 35.9 fb-1 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 VVHF - ZH(bb) 125 VVHF 1400 Z(µ-µ+)H(bb) 800 Z(e e+)H(bb) Low p (V) Z + bb VVLF Low p (V) Z + bb VVLF T T Z + b Single top 700 Z + b Single top 1200 Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) Entries / 10 GeV Entries / 10 GeV 600 1000 500 800 400 600 300 400 200

200 100

0 0 χ2 χ2 0 /dof50 = 1.06 100 150MC uncert.200 (stat.)250 300 350 400 0 /dof50 = 1.21 100 150MC uncert.200 (stat.)250 300 350 400 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 Regressed p (jj) [GeV] Regressed p (jj) [GeV] T T

2200 CMS Preliminary Data tt 1200 CMS Preliminary Data tt s = 13TeV, L = 35.9 fb-1 s = 13TeV, L = 35.9 fb-1 2000 ZH(bb) 125 VVHF - ZH(bb) 125 VVHF Z(µ-µ+)H(bb) Z(e e+)H(bb) 1800 Low p (V) Z + bb VVLF 1000 Low p (V) Z + bb VVLF T T Z + b Single top Z + b Single top 1600 Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) Entries / 10 GeV Entries / 10 GeV 800 1400 1200 600 1000 800 400 600

400 200 200 0 0 χ2 χ2 0 /dof50 = 0.96 100 150MC uncert.200 (stat.)250 300 350 400 0 /dof50 = 2.08 100 150MC uncert.200 (stat.)250 300 350 400 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 p (V) [GeV] p (V) [GeV] T T

2000 1200 CMS Preliminary Data tt CMS Preliminary Data tt s = 13TeV, L = 35.9 fb-1 s = 13TeV, L = 35.9 fb-1 1800 ZH(bb) 125 VVHF ZH(bb) 125 VVHF µ-µ+ - + Z( )H(bb) 1000 Z(e e )H(bb) Low p (V) Z + bb VVLF Low p (V) Z + bb VVLF 1600 T T Z + b Single top Z + b Single top Entries / 0.12 Entries / 0.12 1400 Z+udscg MC uncert. (stat.) 800 Z+udscg MC uncert. (stat.) 1200 1000 600 800 400 600 400 200 200 0 0 χ2 χ2 −0.8 −/dof0.6 = 0.44−0.4 −MC(stat.)0.2 0 0.2 0.4 0.6 0.8 1 −0.8 −/dof0.6 = 0.88−0.4 −MC(stat.)0.2 0 0.2 0.4 0.6 0.8 1 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 BDT Output BDT Output

Figure 5-16. Distributions of variables in data and simulated samples in the Z + bb control region for Z(µµ)H(left) and for Z(ee)H(right) in the low V pT bin. From top to bottom: dijet invariant mass, dijet pT, pT(Z), and BDT output The plots are normalized using the SFs to facilitate shape comparison. 81 300 180 CMS Preliminary Data tt CMS Preliminary Data tt s = 13TeV, L = 35.9 fb-1 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 VVHF - ZH(bb) 125 VVHF Z(µ-µ+)H(bb) 160 Z(e e+)H(bb) 250 High p (V) Z + bb VVLF High p (V) Z + bb VVLF T T Z + b Single top 140 Z + b Single top Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) Entries / 20 GeV 200 Entries / 20 GeV 120

100 150 80

100 60

40 50 20

0 0 χ2 χ2 0 /dof50 = 0.77 100 150MC uncert.200 (stat.)250 300 350 400 0 /dof50 = 0.58 100 150MC uncert.200 (stat.)250 300 350 400 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 Regressed m(jj) [GeV] Regressed m(jj) [GeV]

CMS Preliminary Data tt 100 CMS Preliminary Data tt 140 s = 13TeV, L = 35.9 fb-1 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 VVHF - ZH(bb) 125 VVHF Z(µ-µ+)H(bb) Z(e e+)H(bb) High p (V) Z + bb VVLF High p (V) Z + bb VVLF 120 T 80 T Z + b Single top Z + b Single top Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) Entries / 10 GeV 100 Entries / 10 GeV 60 80

60 40

40 20 20

0 0 χ2 χ2 0 /dof50 = 0.63 100 150MC uncert.200 (stat.)250 300 350 400 0 /dof50 = 1.31 100 150MC uncert.200 (stat.)250 300 350 400 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 Regressed p (jj) [GeV] Regressed p (jj) [GeV] T T

220 CMS Preliminary Data tt CMS Preliminary Data tt s = 13TeV, L = 35.9 fb-1 200 s = 13TeV, L = 35.9 fb-1 300 ZH(bb) 125 VVHF - ZH(bb) 125 VVHF Z(µ-µ+)H(bb) Z(e e+)H(bb) High p (V) Z + bb VVLF 180 High p (V) Z + bb VVLF T T 250 Z + b Single top 160 Z + b Single top Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) Entries / 10 GeV Entries / 10 GeV 140 200 120 150 100 80 100 60 40 50 20 0 0 χ2 χ2 0 /dof50 = 0.65 100 150MC uncert.200 (stat.)250 300 350 400 0 /dof50 = 1.39 100 150MC uncert.200 (stat.)250 300 350 400 1.5 1.5

1 1 Data/MC Data/MC 0.5 0.5 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 p (V) [GeV] p (V) [GeV] T T

450 CMS Preliminary Data tt s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 VVHF 400 Z(µ-µ+)H(bb) High p (V) Z + bb VVLF T 350 Z + b Single top Entries / 0.12 Z+udscg MC uncert. (stat.) 300

250

200

150

100

0 χ2 −0.8 −/dof0.6 = 1.14−0.4 −MC(stat.)0.2 0 0.2 0.4 0.6 0.8 1 1.5

1 Data/MC 0.5 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 BDT Output

Figure 5-17. Distributions of variables in data and simulated samples in the Z + bb control region for Z(µµ)H(left) and for Z(ee)H(right) in the high V pT bin. From top to bottom: dijet invariant mass, dijet pT, pT(Z), and BDT output The plots are normalized using the SFs to facilitate shape comparison. 82 Table 5-13. 13 TeV Data/MC scale factors for each control region in each decay mode for the SR + CRs fit. The errors include the statistical uncertainty from the fit, and a systematic uncertainty accounting for possible data/MC shape differences in the discriminating variables. Electron and muons samples in Z(ℓℓ)H and W(ℓν)H are fit simultaneously to determine average scale factors. The values refer to the simultaneuos control regions plus signal region fit used for the signal extraction, and we checked that we get compatible fitted value for a fit inthe control regions only.

Process W(ℓν)H Z(ℓℓ)H(low ZpT) Z(ℓℓ)H(high ZpT) Z(νν)H W0b 1.14 0.07 – – 1.14 0.07 W1b 1.66 0.14 – – 1.66 0.14 W2b 1.49 0.12 – – 1.49 0.12 Z0b – 1.02 0.06 1.02 0.06 1.02 0.07 Z1b – 0.98 0.06 0.99 0.10 1.28 0.17 Z2b – 1.08 0.07 1.29 0.09 1.60 0.10 0.91 0.03 0.99 0.03 1.02 0.05 0.78 0.05 – – – 1.50 0.25 signal extraction via a binned maximum likehood ﬁt. Two types of systematics are implented in the ﬁt: log normal (lnn) and shape uncertainty. The sources of uncertainty considered in the VHbb analysis are:

• Luminosity: an uncertainty of 2.5% is assessed for 2016 luminosity.

• Lepton Efficiency: muon and electron trigger, reconstruction, and identification efficiencies are determined in data using the standard tag-and-probe technique with Z bosons. The systematic uncertainty is evaluated from the statistical uncertainties in the bin-by-bin efficiencies and scale factors as applied to signal Monte Carlo samples. The total uncertainty is 1.6% per muon, and 1.5% per electron, which we take as a constant 2% per charged lepton. No shape uncertainties are considered.

• Unclustered MET: we follow the suggested procedure from the JetMET POG and ﬁnd a 3% systematic uncertainty on the calibration of unclustered MET (ie, missing energy associated with particles not clustered into jets). No shape uncertainties are considered.

• MET+jets Trigger: the parameters describing the trigger eﬃciency curve have been varied within their statistical uncertainties. An uncertainty of 3% is estimated, and no shape uncertainties are considered.

• Jet Energy Scale: the jet energy scale for each jet is varied within one standard deviation based on pT and η, and the eﬃciency of the analysis selection is recomputed to assess the systematic variation on the normalization of the signal and all background components. An uncertainty of 2% is found for signal, while background can vary up to 3%. For the shape variation, the BDT output is recomputed after shifting the scale up

83 and down, and the observed variation in the BDT is used to set shape variation. Each source of uncertainty assessed by the JETMET group is varied individually.

• Jet Energy Resolution: we smear the energy resolution for each jet using the JetMET prescription as our default, and then assign a systematic uncertainty based on further smearing (up and down). An uncertainty of 3% is estimated for the normalization. For the shape uncertainty, the BDT is recomputed after the smearing and the modiﬁed output is used to deﬁne the shape variation.

• b-jet Tagging: official b-tagging scale factors are applied consistently to jets in signal and background events. An average systematic uncertainty of 6% per b-jet, 12% per c-jet, and 15% per fake tag (light quarks and gluons) are used to account for the normalization uncertainty. For the shape, we vary the reshaping of the CMVA output based on the official uncertainties provided by the BTV POG. This gives two new shapes for the CMVA output (“up” and “down”) that we then input to the BDT. The resulting modified BDT output is then used as the shape variation due to b-tagging uncertainties. Decorrelation in pT and η is impelmented. systematic assessments).

• Cross section: the total signal cross section has been calculated to next-to-next-to-leading order accuracy, and the total uncertainty is 4%(51), including the eﬀect of scale and PDF variations.

• Theoretical pT Spectrum: this analysis is performed in the boosted regime, and thus, potential differences in the pT spectrum of the V and H between data and Monte Carlo generators could introduce systematic effects in the signal acceptance and efficiency estimates. Recently, two calculations have become available that estimate the NLO electroweak(52; 53; 54) and NNLO QCD(55) corrections to VH production in the boosted regime. Both the EWK and NNLO QCD corrections have been applied to the signal MC samples. The estimated effect from NNLO electroweak corrections are 2% for ZH and 2% for WH(52; 53; 54). For the remaining QCD correction an uncertainty of 5% for both ZH and WH is estimated.

• ∆ϕ(V, H): systematic uncertainty on the jet angular resolution is assumed to be negligible, and this is conﬁrmed by the good agreement observed in the control regions.

• Nal: the eﬃciency of the lepton veto is found to be 100% in the simulation, and no additional uncertainty is assigned.

• Background Estimate: a mix of data-driven methods, simulation, and theory uncertainties contribute to the total uncertainty on the background estimates. Correlated (luminosity, b-tagging, JEC/JER, and TnP eﬃciencies) and uncorrelated uncertainties (statistical, control region, and cross section) are combined separately. An uncertainty of 30% is assumed for single top (approximately the uncertainty on the measured cross section) and diboson (assumed to have the same uncertainty as the signal). The other backgrounds are taken directly from data, with the associated uncertainties from the control regions.

84 • Monte Carlo Statistics: the ﬁnite size of the signal and background MC samples are included in the normalization uncertainties. In addition, the shape of the BDT is allowed to vary within the bin-by-bin statistical uncertainties from the MC samples (in a coherent way), while also constraining the total integral within its uncertainty.

• V+jets Monte Carlo model: we consider the difference in the shapes output (BDT and Mjj) of a different Monte Carlo V+jets with respect to the nominal Madgraph MC. In particular Herwigpp high pt V+jets samples were compared with the Madgraph ones. The difference in BDT shape observed between these two generators is then symmetrized and used to define the shape variation.

• PDF uncertainties: the imperfect knowledge of the proton quark content is encoded in a set of NNPDF MC replicas. For each process, the RMS of all the variations is checked in each bin of the BDT distribution and the largest variation is used as normalization nuisance in the datacards.

• QCD scale variations: The QCD normalization and factorization scale variations 1/2 and 2 are considered separately for each process and taken as uncorrelated sources of systematic uncertainties (shape + normalization). A summary plot showing the impact and pulls on the signal strength of the most important systematic uncertainties is shown in Figure 5-18.

85 Unconstrained Gaussian ± Poisson AsymmetricGaussian CMS Internal r = 0 0 +0.0934 SF_Wj2b_Wln 1 1.45−0.099 2 CMS_vhbb_LHE_weights_scale_muR_Wj2b 3 CMS_vhbb_ptwweights_whf 4 CMS_vhbb_LHE_weights_scale_muR_Zj2b 5 CMS_vhbb_bTagWeightLF_pt4_eta1 6 QCDscale_VH_ggZHacceptance_highPt 7 CMS_vhbb_boost_QCD_13TeV 8 QCDscale_VH +0.147 SF_Zj1b_Znn 9 1.3−0.149 10 CMS_vhbb_LHE_weights_scale_muF_Zj2b 11 CMS_vhbb_bTagWeightcErr1_pt4_eta1 12 CMS_vhbb_bTagWeightLF_pt2_eta2 13 CMS_vhbb_ST 14 CMS_vhbb_VV +0.0443 SF_TT_Znn 15 0.789−0.0454 16 CMS_vhbb_scale_j_FlavorQCD_13TeV 17 QCDscale_VH_ggZHacceptance_lowPt 18 CMS_vhbb_bTagWeightLF_pt1_eta1 19 CMS_vhbb_LHE_weights_scale_muF_ZH +0.0917 SF_Wj1b_Wln 20 1.64−0.085 +0.0821 SF_Zj2b_Znn 21 1.61−0.0801 22 CMS_vhbb_bTagWeightLF_pt1_eta2 23 CMS_vhbb_LHE_weights_scale_muR_ZH 24 CMS_vhbb_bTagWeightLF_pt4_eta2 25 pdf_qqbar 26 CMS_vhbb_boost_EWK_13TeV 27 CMS_vhbb_bTagWeightLF_pt2_eta1 28 CMS_vhbb_bTagWeightLF_pt0_eta1 29 CMS_vhbb_scale_j_PileUpPtRef_13TeV 30 pdf_gg −2 −1 0 1 2 −0.05 0 0.05 σ σ θ θ ∆θ ∆ Pull +1 Impact -1 Impact ( - 0)/ r

Figure 5-18. Impact and pulls on the signal strength of the systematic sources with the highest impact on the signal strength.

86 CHAPTER 6 RESULTS The final amount of predicted VHbb signal events, and whether this corresponds to an excess in data when considering the background only hypothesis, is determined with a simultaneous binned-likelihood fit of the background control regions (CR) and the signal regions (SR). The fitted variables are minCMVA for the control regions and BDT output for the signal regions. Z(νν)H and W(ℓν)H use one category, while Z(ℓℓ)H uses two categories:

low and high vector boson pT . In this section all results and ﬁt methodolgy will be given. 6.1 Signal and Control Regions ﬁts

The distributions of the BDT output (SR) and minCMVA (CR) used for the final combined fit of all channels are shown for the Z(ℓℓ)H channel in Figures 6-1–6-2. The post-fit plots consider the adjustments of all nuisance parameters in the final maximum likelihood fit to extract the signal. We consider both shape and rate changes in the post-fit plots. Table 6-1 reports the expected signal and backgounds in the signal region bins.

Table 6-1. The total number of events in each channel, for the 20% most-sensitive region of the BDT output distribution, for the expected backgrounds, for the 125SM Higgs boson VH signal, and for data. The signal-to-background ratio (S/B) is also shown. Z(νν)H W(ℓν)H Z(ℓℓ)H Process Low pT(V) High pT(V) Vbb 216.8 102.5 617.5 113.9 Vb 31.8 19.9 141.1 17.2 V + udscg 10.2 9.8 58.4 4.1 34.7 98.0 157.7 3.2 Single-top-quark 11.8 44.6 2.0 0.2 VV(udscg) 0.4 1.5 6.4 0.6 VZ() 7.7 6.9 22.9 3.8 Total backgrounds 267.0 283.3 1005.9 142.9 VH 34.7 26.0 33.5 22.1 Data 334 320 1030 179 S/B 0.13 0.11 0.033 0.156

6.2 Signal Strength Calculation

The primary technique for extracting the signiﬁcance of the observed and expected signal yields is computed using the standard LHC proﬁle likelihood asymptotic approximation (56),

87 107 7 CMS Preliminary Data tt CMS Preliminary Data tt 10 -1 -1 s = 13TeV, L = 35.9 fb ZH(bb) 125 6 s = 13TeV, L = 35.9 fb ZH(bb) 125 VVHF - VVHF Z(µ-µ+)H(bb) 10 Z(e e+)H(bb) 106 ggZH(bb) 125 ggZH(bb) 125 Low p (V) VVLF Low p (V) VVLF T Z + bb 5 T Z + bb 5 Single top 10 Single top Entries / 0.12 10 Z + b Entries / 0.12 Z + b Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) 104 104 103 103 2 102 10

10 10

1 1

− 10−1 10 1

− − − −MC(stat.+Prefit syst.) MC(stat.+Postfit syst.) − − − −MC(stat.+Prefit syst.) MC(stat.+Postfit syst.) 0.8 0.6 0.4 MC(stat.)0.2 0 0.2 0.4 0.6 0.8 1 0.8 0.6 0.4 MC(stat.)0.2 0 0.2 0.4 0.6 0.8 1 2 2

1 1 Data/MC Data/MC 0 0 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 BDT Output BDT Output

5 CMS Preliminary Data tt 10 CMS Preliminary Data tt 5 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 10 VVHF VVHF µ-µ+ - + Z( )H(bb) ggZH(bb) 125 4 Z(e e )H(bb) ggZH(bb) 125 High p (V) VVLF 10 High p (V) VVLF 4 T Z + bb T Z + bb 10 Single top Single top Entries / 0.12 Z + b Entries / 0.12 Z + b 3 Z+udscg MC uncert. (stat.) 10 Z+udscg MC uncert. (stat.) 103 102 102

10 10

1 1

− 10−1 10 1

1 1 Data/MC Data/MC 0 0 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 BDT Output BDT Output

Figure 6-1. Post-ﬁt distributions of BDT output for combined ﬁt for the Z(ℓℓ)H channel after all selection criteria have been applied.

which we use with the proﬁle likelihood test statistic q˜µ: ˆ L(data|µ, θµ) q˜µ = −2 ln , 0 ≤ µˆ ≤ µ, (6–1) L(data|µˆ, θˆ)

. where we have restricted µ to take only positive values. The likelihood is given by the product of the individual likelihoods for each channel

L(data | µ, θ) = Poisson ( Ni | µ · si (θ) + bi (θ) ) · p(θ˜| θ). (6–2)

Here “data” is either the actual experimental observation or pseudo-data used to construct sampling distributions. The symbols Ni , si and bi represent the observed, expected

88 ×103 1600 22000 CMS Preliminary Data tt CMS Preliminary Data tt 180 CMS Preliminary Data tt s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 VVHF VVHF VVHF - + 1400 - + - + 20000 Z(µ µ )H(bb) ggZH(bb) 125 Z(µ µ )H(bb) ggZH(bb) 125 160 Z(µ µ )H(bb) ggZH(bb) 125 Low p (V) VVLF High p (V) VVLF Low p (V) VVLF T Z + bb T Z + bb T Z + bb 18000 Single top 1200 Single top Single top Entries / 0.10 Entries / 0.10 Z + b Entries / 0.10 Z + b 140 Z + b 16000 Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) 1000 120 14000 100 12000 800 10000 80 600 8000 60 6000 400 40 4000 200 2000 20 0 0 0 χ2 MC(stat.+Prefit syst.) MC(stat.+Postfit syst.) χ2 MC(stat.+Prefit syst.) MC(stat.+Postfit syst.) χ2 MC(stat.+Prefit syst.) MC(stat.+Postfit syst.) −1 − /dof0.8 = 1.58−0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −1 − /dof0.8 = 0.75−0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −1 − /dof0.8 = 0.77−0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.5 MC(stat.) 1.5 MC(stat.) 1.5 MC(stat.)

1 1 1 Data/MC Data/MC Data/MC 0.5 0.5 0.5 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 min CMVAv2 min CMVAv2 min CMVAv2

18000 CMS Preliminary Data tt CMS Preliminary Data tt CMS Preliminary Data tt s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 16000 VVHF 3000 VVHF VVHF - + - + - + Z(µ µ )H(bb) ggZH(bb) 125 Z(µ µ )H(bb) ggZH(bb) 125 500 Z(µ µ )H(bb) ggZH(bb) 125 High p (V) VVLF Low p (V) VVLF High p (V) VVLF 14000 T Z + bb T Z + bb T Z + bb Single top 2500 Single top Single top Entries / 0.10 Entries / 0.10 Z + b Entries / 0.10 Z + b Z + b 12000 Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) 400 Z+udscg MC uncert. (stat.) 2000 10000 300 8000 1500

6000 200 1000 4000 500 100 2000

0 0 0 χ2 MC(stat.+Prefit syst.) MC(stat.+Postfit syst.) χ2 MC(stat.+Prefit syst.) MC(stat.+Postfit syst.) χ2 MC(stat.+Prefit syst.) MC(stat.+Postfit syst.) −1 − /dof0.8 = 0.05−0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −1 − /dof0.8 = 0.42−0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −1 − /dof0.8 = 1.37−0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.5 MC(stat.) 1.5 MC(stat.) 1.5 MC(stat.)

×103 14000 CMS Preliminary Data CMS Preliminary Data CMS Preliminary Data tt 900 tt tt s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 VVHF VVHF 100 VVHF 12000 - + - + - + Z(e e )H(bb) ggZH(bb) 125 800 Z(e e )H(bb) ggZH(bb) 125 Z(e e )H(bb) ggZH(bb) 125 Low p (V) VVLF High p (V) VVLF Low p (V) VVLF T Z + bb T Z + bb T Z + bb Single top Single top Single top Entries / 0.10 Entries / 0.10 10000 Z + b Entries / 0.10 700 Z + b 80 Z + b Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) 600 8000 500 60

6000 400 40 4000 300 200 20 2000 100

0 0 0 χ2 MC(stat.+Prefit syst.) MC(stat.+Postfit syst.) χ2 MC(stat.+Prefit syst.) MC(stat.+Postfit syst.) χ2 MC(stat.+Prefit syst.) MC(stat.+Postfit syst.) −1 − /dof0.8 = 0.93−0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −1 − /dof0.8 = 0.85−0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −1 − /dof0.8 = 0.44−0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.5 MC(stat.) 1.5 MC(stat.) 1.5 MC(stat.)

CMS Preliminary Data tt 1800 CMS Preliminary Data tt 350 CMS Preliminary Data tt s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 s = 13TeV, L = 35.9 fb-1 ZH(bb) 125 VVHF VVHF VVHF 10000 - + - + - + Z(e e )H(bb) ggZH(bb) 125 1600 Z(e e )H(bb) ggZH(bb) 125 Z(e e )H(bb) ggZH(bb) 125 High p (V) VVLF Low p (V) VVLF 300 High p (V) VVLF T Z + bb T Z + bb T Z + bb Single top Single top Single top Entries / 0.10 Entries / 0.10 Z + b Entries / 0.10 1400 Z + b Z + b 8000 Z+udscg MC uncert. (stat.) Z+udscg MC uncert. (stat.) 250 Z+udscg MC uncert. (stat.) 1200

6000 1000 200

800 150 4000 600 100 400 2000 50 200

0 0 0 χ2 MC(stat.+Prefit syst.) MC(stat.+Postfit syst.) χ2 MC(stat.+Prefit syst.) MC(stat.+Postfit syst.) χ2 MC(stat.+Prefit syst.) MC(stat.+Postfit syst.) −1 − /dof0.8 = 0.17−0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −1 − /dof0.8 = 0.71−0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −1 − /dof0.8 = 1.13−0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.5 MC(stat.) 1.5 MC(stat.) 1.5 MC(stat.)

Figure 6-2. Post-ﬁt distributions of the control regions for the Z(ℓℓ)H channel after all selection criteria have been applied.

89 signal, and expected background rates in bin i. The parameter µ is the signal strength modiﬁer, µ=σ/σSM , and θ represents the full suite of nuisance parameters, with θ˜ representing the best estimate of the nuisance prior to the data analysis. Poisson (Ni | µ · si (θ) + bi (θ) )

stands for the Poisson probabilities to observe Ni events given the expected event rate

µ · si (θ) + bi (θ), with the understanding that some analyses are unbinned and use the extended likelihood formalism. The probabilities p(θ˜| θ) encode information on the systematic errors. The maximum likelihood estimates or best-fit-values of µ and θ are denoted µˆ and θˆ, ˆ while θµ denotes the conditional maximum likelihood estimate of all nuisance parameters with µ fixed. In this analysis the range of µ is restricted to the physically meaningful regime, i.e. it is not allowed to be negative. The shape and normalization of all distributions are allowed to vary within the systematic and statistical uncertainties. These uncertainties are treated as independent nuisance parameters in the fit and are allowed to float freely and are adjusted by the fit. 6.3 Blinding

In order to prevent fine tuning of results exctracted from data observations, we employ a safeguard called blinding. Furthermore, all analyses at CMS are required to stay blinded until approved to unblind. Staying blind means we do not look at data in the sensitive region of the BDT and dijet mass spectrums until all optimizations and analysis parameters have been chosen. All optimizations are done with reference to an expected level of data, which is derived from a toy Asimov dataset. Once approved for unblinding, we perform the the full MLE fit on data for the first time and look at the actual fitted signal strength. Whatever results are found, regardless if it matches our expectations or not, are the results presented in this thesis. 6.4 Results VH

For a Higgs Boson mass of 125 GeV, the excess of observed events corresponds to a local signiﬁcance of 3.3 standard deviations when compared to the background-only hypothesis. The best ﬁt value for the signal strength (production cross section for a 125 GeV Higgs boson,

+0.21 +0.34 relative to the SM cross section) µH,SM = σ/σSM, is 1.19−0.20(stat.)−0.32(syst.). With

90 µH,SM = 1.0 the expected signiﬁcance is 2.8 standard deviations. Within error, the observed signal strength is consistent with a Standard Model Higgs Boson of 125 GeV. Table 6-2 contains the expected and observed sensitivities for the three VHbb channels, as well as the combined result. Figure 6-3 displays the best-ﬁt values of the signal strength (µ) for the three channels independently, in addition to the WH and ZH production modes independently. The WH and ZH production modes are each consistent with the Standard Model predictions within uncertainties. Figure 6-4 combines the BDT output values of all channels and bins the events in similar expected signal-to-background ratios. The most sensitive bins (large S/B values) contain an excess of events when taking the ratio of data to simulated background, indicating that signal events are present in order to correct the data/MC ratio.

Table 6-2. The expected and observed signiﬁcances for VH production with H → b¯b are shown for each channel ﬁt individually as well as for the combination of all three channels.

mHiggs = 125 Signiﬁcance Signiﬁcance expected observed 1.5 0.0 1.5 3.2 1.8 3.1 All channels 2.8 3.3

6.5 Next Steps

Although the evidence threshold for Higgs decays to bottom quarks has been reached, the next goal is in sight: discovery (5 standard deviations). During the current year of 2017, another 70 fb−1 of data has been collected. This new quantitiy of data presents unique challenges: suﬃcient levels of montel carlo simulation are needed to scale with data and systematic errors due to background uncertainties will increase. No longer will low levels of data plague this analysis, but rather it will be uncertainties from mismodelling and experimental uncertainties that will have to be the focus of the next generation of VHbb analyses.

91 35.9 fb-1 (13 TeV) CMS Preliminary pp → VH; H → bb Combined µ = 1.2 ± 0.4

ZH(bb) µ = 0.9 ± 0.5

WH(bb) µ = 1.7 ± 0.7

0 lept. µ = 0.0 ± 0.5

1 lept. µ = 1.9 ± 0.6

2 lept. µ = 1.8 ± 0.6

−1 0 1 2 3 Best fit µ

Figure 6-3. The best-fit value of the production cross section for a 125 GeV Higgs boson relative to the SM cross section is shown in black with green error band. Above the dashed line are the WH and ZH signal strengths when each production mode has an independent signal strength parameters in the fit. When each channel is fit with its own signal strength parameter, the results are shown below the dashed line.

In addition to focusing on simulation and systematics, progress can be made by exploiting the larger dataset. Currently, the BDT signal regions have been limited to two at most. This is mainly due to insuﬃcient statistics when creating more categories. Initial tests indicate that three to four singal regions seperated in bins of vector boson momentum would provide a boost in sensitivity compared to the current value of two. The training model can also be upgraded by exploring neural networks to perform the supervised training component. Neural networks can also be used in an unsupervised fashion in order to build new features from our existing ones that could then be fed into the current BDT model.

92 106 CMS Data Preliminary VH(bb) Entries -1 VH(bb) 105 s = 13TeV, L = 35.9 fb Bkg. uncert. Background 104

103

102

1 1.5-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0

1 Data/MC(B) 0.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 log (S/B) 10

Figure 6-4. Combination of all channels into a single event BDT distribution. Events are sorted in bins of similar expected signal-to-background ratio, as given by the value of the output of the value of their corresponding BDT discriminant (trained with a Higgs boson mass hypothesis of 125). The bottom inserts show the ratio of the data to the background-only prediction.

6.6 Conclusions

This thesis has described in detail the measurement of the standard model Higgs Boson production in association with vector bosons and decaying into b-quark pairs. A data sample with an integrated luminosity of 35.9 fb−1 corresponding to the full 2016 running period and recorded by the CMS experiment, has been analyzed in ﬁve modes: Z(µµ)H, Z(ee)H, Z(νν)H, W(µν)H, and W(eν)H.

The ﬁtted signal strength for a Higgs Boson mass of 125 GeV is µ=σ/σSM = 1.19+0.35, with an observed (expected) signiﬁcance of 3.3 (2.8) standard deviations. The threshold for evidence (3 standard deviations) has been reached for a Standard Model Higgs boson coupling to bottom quarks.

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96 BIOGRAPHICAL SKETCH David Curry was born in Pasadena, California, in the year of our Lord 1981. In 2007 David started studying physics at the University of Oregon. A decade later he successfully defended his PhD in physics at the University of Florida.