New Physics Models in the Diphoton Final State at CMS

Citation

Wang, Ann Miao (2015) New Physics Models in the Diphoton Final State at CMS. Senior thesis (Major), California Institute of Technology. doi:10.7907/Z9CC0XMN . https://resolver.caltech.edu/CaltechTHESIS:01152016-102117113

Abstract

Since the discovery of the Higgs boson at the LHC, its use as a probe to search for beyond the standard model physics, such as supersymmetry, has become important, as seen in a recent search by the CMS experiment using razor variables in the diphoton final state. Motivated by this search, this thesis examines the LHC discovery potential of a SUSY scenario involving bottom squark pair production with a Higgs boson in the final state. We design and implement a software-based trigger using the razor variables for the CMS experiment to record events with a bottom quark-antiquark pair from a Higgs boson. We characterize the full range of signatures at the LHC from this Higgs-aware SUSY scenario and demonstrate the sensitivity of the CMS data to this model.

Item Type:	Thesis (Senior thesis (Major))
Subject Keywords:	Higgs, LHC, CMS, supersymmetry, SUSY, sbottom, squark, diphoton, photons, phenomenology, trigger
Degree Grantor:	California Institute of Technology
Division:	Physics, Mathematics and Astronomy
Major Option:	Physics
Awards:	Barry M. Goldwater Scholarship, 2014
Thesis Availability:	Public (worldwide access)
Research Advisor(s):	Spiropulu, Maria (advisor) Duarte, Javier (co-advisor) Pena Herrera, Cristian (co-advisor)
Thesis Committee:	Stone, Edward C. (chair) Golwala, Sunil Politzer, Hugh David Frautschi, Steven C. Libbrecht, Kenneth George Refael, Gil
Defense Date:	21 May 2015
Record Number:	CaltechTHESIS:01152016-102117113
Persistent URL:	https://resolver.caltech.edu/CaltechTHESIS:01152016-102117113
DOI:	10.7907/Z9CC0XMN
Default Usage Policy:	No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:	9535
Collection:	CaltechTHESIS
Deposited By:	Javier Duarte
Deposited On:	15 Jan 2016 21:44
Last Modified:	18 Dec 2020 19:27

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New Physics Models in the Diphoton Final State at CMS Thesis by Ann Miao Wang In Partial Fulfillment of the Requirements for the Degree of Bachelor of Science California Institute of Technology Pasadena, California 2015 (Submitted May 15, 2015) ii c 2015 Ann Miao Wang All Rights Reserved iii Acknowledgments First, I want to express my gratitude to Professor Maria Spiropulu for being the most inspirational leader, mentor, and scientist I could have ever hoped to work for. My deep interest in experimental high energy physics is a result of her passion and tireless enthusiasm for the subject. I would also like to express my deep appreciation for Professor Harvey Newman for being a wonderful teacher and listener. His diligence and love for physics have painted him as a true role model in my life. I am extremely grateful to Javier Duarte for always answering my questions and meeting with me for a countless number of hours over the past three years. His kindness and patience have made an indescribable impact on my research experience. I would also like to Cristian Peña, Dustin Anderson, Alex Mott, and Maurizio Pierini, as well as the entire Caltech CMS group, for their invaluable guidance throughout this thesis. These past four years at Caltech have truly been life-changing in completely surprising ways. One was my unexpected passion for studying physics, which I could not have anticipated. I owe that to the professors and students at this remarkable institution, especially Professor Steven Frautschi for instilling his enthusiasm in me through Ph 1 recitations. Without his extraordinary teaching, I would never have switched my major to physics. Finally, I would like to express my gratitude to my parents and my sister for their love and contagious curiosity. iv Contents Acknowledgments iii 1 Introduction 1 2 The Razor Variables 2 3 CMS Trigger Studies 4 3.1 The CMS Detector and the Trigger System . . . . . . . . . . . . . . . . . . . . . . . 4 3.2 Razor High Level Triggers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2.1 Calorimeter Objects versus PF Objects Investigation . . . . . . . . . . . . . . 5 3.2.2 Trigger Flow Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2.3 Rates of Trigger Menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.3 H→ b b̄ HLT Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.4 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.5 b-tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.6 Trigger Flow Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.7 Rates of H→ b b̄ Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.7.1 Addition of new HCAL local reconstruction method and ECAL Multifit . . . 11 3.7.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4 Investigation of Higgs-Aware Decay Models 12 4.1 The Higgs decay as a tool for new physics searches . . . . . . . . . . . . . . . . . . . 12 4.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4.3 Bottom squark production model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.4 Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.5 Box definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.6 Branching Ratio to χ̃02 Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4.7 Mass Splitting Study with Fixed χ̃01 Mass . . . . . . . . . . . . . . . . . . . . . . . . 20 4.8 Mass Splitting Study with Fixed b̃ Mass . . . . . . . . . . . . . . . . . . . . . . . . . 25 v 4.9 b̃ Mass Study with Fixed M∆ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.10 Investigating the CLT2015-AW1 Model 30 . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.11 Counting Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5 Conclusion 39 A 40 A.1 Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 A.2 Bottom squark production mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Bibliography 42 vi List of Figures 2.1 A cartoon of a disquark production scenario. . . . . . . . . . . . . . . . . . . . . . . . 2 3.1 Comparisons of the razor variables formed with PF objects versus calorimeter objects. 6 3.2 Comparisons of the E/T distributions formed with PF objects versus calorimeter objects. 6 3.3 Comparisons of the E/T and R2 distributions formed with PF objects versus calorimeter objects, vetoing all events that have muons with pT > 30 GeV. . . . . . . . . . . . . . 3.4 Schematic of the H→ b b̄ trigger flow path. The numbers in parentheses correspond to the more detailed list described in the text. . . . . . . . . . . . . . . . . . . . . . . . . 4.1 The contour lines for M∆ = 450 GeV, where M∆ = 14 A schematic for how events are placed into the three boxes. The red rectangles are the two requirements, and the blue rectangles represent the boxes. . . . . . . . . . . . . . 4.3 9 m2b̃ −m2χ̃ , with ± 50 GeV as indicated mb̃ by the dashed lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 6 15 Z-axis scale units are such that the total number of events is normalized to 1. mb̃ = 600 GeV, mχ̃01 = 300 GeV model. (a) R2 versus MR for the 50% (to χ̃02 ) working model. (b) R2 versus MR for the 100% (to χ̃02 ) working model. (c) R2 versus MR for the 90% (to χ̃02 ) working model. (d) R2 versus MR for the 10% (to χ̃02 ) working model. . . . . 4.4 17 Z-axis scale units are such that the total number of events is normalized to 1. mb̃ = 600 GeV, mχ̃01 = 300 GeV model. (a) R2 versus E/T , for the 50% (to χ̃02 ) working model. (b) R2 versus E/T , for the 100% (to χ̃02 ) working model. (c) R2 versus E/T , for the 90% (to χ̃02 ) working model. (d) R2 versus E/T , for the 10% (to χ̃02 ) working model. 18 4.5 Z-axis scale units are such that the total number of events is normalized to 1. mb̃ = 600 GeV, mχ̃01 = 300 GeV model. (a) MR versus E/T for the 50% (to χ̃02 ) working model. (b) MR versus E/T , for the 100% (to χ̃02 ) working model. (c) MR versus E/T , for the 90% (to χ̃02 ) working model. (d) MR versus E/T , for the 10% (to χ̃02 ) working model. . 4.6 19 Characterization of the mb̃ = 550 GeV, mχ̃01 = 300 GeV model with 90% to χ̃02 . Z-scale units are such that the total number of events is normalized to 1. (a) R2 versus MR . (b) R2 versus E/T . (c) MR versus E/T . (d) Number of PF jets, clustered with the anti-kT algorithm with ∆R = 0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 vii 4.7 Characterization of the mb̃ = 450 GeV, mχ̃01 = 300 GeV model with 100% to χ̃02 . Zscale units are such that the total number of events is normalized to 1. (a) R2 versus MR . (b) R2 versus E/T . (c) MR versus E/T . (d) Number of PF jets, clustered with the anti-kT algorithm with ∆R = 0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8 Characterization of the mb̃ = 530 GeV, mχ̃01 = 300 GeV model with 100% to χ̃02 . 22 Z- scale units are such that the total number of events is normalized to 1. (a) R2 versus MR . (b) R2 versus E/T . (c) MR versus E/T . (d) Number of PF jets, clustered with the anti-kT algorithm with ∆R = 0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9 1D distributions. (b) R2 1D distributions. 4.10 23 Razor variable distributions for the various mass splitting with fixed χ̃01 mass. (a) MR . . . . . . . . . . . . . . . . . . . . . . . . Kinematic distributions for the various mass splitting with fixed χ̃01 mass. 24 (a) E/T 1D distributions. (b) Leading jet pT 1D distributions (excluding H → b b̄ jets). . . . . . 24 4.11 The decay spectrum for the mb̃ = 450 GeV model. . . . . . . . . . . . . . . . . . . . . 25 4.12 Characterization of the mb̃ = 600 GeV, mχ̃01 = 200 GeV model with 100% to χ̃02 . Zscale units are such that the total number of events is normalized to 1. (a) R2 versus MR . (b) R2 versus E/T . (c) MR versus E/T . (d) Number of PF jets, clustered with the anti-kT algorithm with ∆R = 0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.13 26 Characterization of the mb̃ = 600 GeV, mχ̃01 = 100 GeV model with 100% to χ̃02 . Zscale units are such that the total number of events is normalized to 1. (a) R2 versus MR . (b) R2 versus E/T . (c) MR versus E/T . (d) Number of PF jets, clustered with the anti-kT algorithm with ∆R = 0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.14 Razor variable distributions for the various mass splitting with fixed b̃ mass. (a) MR 1D distributions. (b) R2 1D distributions. 4.15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Bottom squark kinematic distributions for the various mass splitting with fixed b̃ mass. (a) Leading b̃ pT 1D distributions. (b) ∆Φ between the two bottom squarks particles. 4.18 28 χ̃01 kinematic distributions for the various mass splitting with fixed b̃ mass. (a) Leading χ̃01 pT 1D distributions. (b) ∆Φ between the two χ̃01 particles. 4.17 28 Kinematic distributions for the various mass splitting with fixed b̃ mass. (a) E/T 1D distributions. (b) Leading jet pT 1D distributions (excluding H → b b̄ jets). 4.16 27 Characterization of the mb̃ = 470 GeV, mχ̃01 = 100 GeV model with 100% to χ̃02 . 29 Z- scale units are such that the total number of events is normalized to 1. (a) R2 versus MR . (b) R2 versus E/T . (c) MR versus E/T . (d) Number of PF jets, clustered with the anti-kT algorithm with ∆R = 0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 viii 4.19 Characterization of the mb̃ = 500 GeV, mχ̃01 = 160 GeV model with 100% to χ̃02 . Zscale units are such that the total number of events is normalized to 1. (a) R2 versus MR . (b) R2 versus E/T . (c) MR versus E/T . (d) Number of PF jets, clustered with the anti-kT algorithm with ∆R = 0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.20 The decay spectrum for the mb̃ = 470 GeV model. . . . . . . . . . . . . . . . . . . . . 32 4.21 Razor variable distributions for the various b̃ models with fixed M∆ . (a) MR 1D distributions. (b) R2 1D distributions. 4.22 . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Kinematic distributions for the various b̃ models with fixed M∆ . (a) Leading jet pT 1D distributions (excluding H → b b̄ jets). (b) Subeading jet pT 1D distributions (excluding H → b b̄ jets). (c) Leading χ̃01 pT 1D distributions. (d) Subeading χ̃01 pT 1D distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.23 33 Kinematic distributions for the various b̃ models with fixed M∆ . (a) Leading b̃ pT 1D distributions. (b) Subleading b̃ pT 1D distributions. (c) ∆Φ between the two bottom 4.24 squarks particles. (d) ∆Φ between the two χ̃01 particles. . . . . . . . . . . . . . . . . . √ Event populations of the CLT2015-AW1 Model at s = 8 TeV in each of the boxes, 34 with the total amount of events passing the selection scaled to 100. (a) High pT box 4.25 (b) Hbb box (c) Overflow box. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . √ Event populations of the SM Higgs production background at s = 8 TeV in each of 35 the boxes, with the total amount of events passing the selection scaled to 100. (a) High pT box (b) Hbb box (c) Overflow box. . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1 Chapter 1 Introduction With the discovery of the Higgs boson as the final particle necessary to complete the standard model (SM) picture [1, 2], the field of particle physics is looking towards the search for new physics outside of the SM. One problem with the SM is that it does not include a viable particle candidate for dark matter [3]. At the Large Hadron Collider (LHC) in Geneva, Switzerland, scientists are looking for beyond-the-standard-model (BSM) events resulting from proton-proton collisions. One possible BSM physics scenario is weak-scale supersymmetry (SUSY) which provides a particle candidate for dark matter and solves the heirarchy problem [4]. A major difficulty in any search for new physics is to characterize what the signatures of the BSM physics would look like at the detector level. In the search for these events, there are many components of a physical experiment that must be studied and tuned. This thesis addresses two of the most important components: (1) trigger studies and (2) model kinematics. The overarching theme of this thesis is the use of the newly discovered Higgs particle as a probe for searching for BSM physics. The first half of the thesis focuses on studies related to the Compact Muon Solenoid (CMS) detector, while the second half of the thesis is more broadly applicable to other experiments. Chapter 2 gives a short overview of the razor variables, which have been used to distinguish SUSY from SM background, producing strong limits on SUSY models [5]. The thesis will then employ these razor variables in the design of the custom hardware and software algorithms for deciding whether to record a collision event, and will investigate the distribution of these variables for certain SUSY simplified models. Chapter 3 focuses on trigger design for BSM searches. It first tackles the study of the softwarelevel trigger (known as the High Level Trigger) paths using the razor variables. Then, it includes a proposal of a new trigger path targeting BSM events that include a Higgs boson decaying to a b b̄ pair in the final state. Chapter 4 is motivated by a previous search for supersymmetry with a Higgs decaying to two photons [6]. It discusses the kinematics of Higgs-aware BSM models, with particular focus on bottom squark production. This thesis attempts to fully characterize the range of signatures that bottom squark production would produce. 2 Chapter 2 The Razor Variables The razor variables, MR and R2 , are variables that are useful in searches for supersymmetry (SUSY). They have been successfully employed in previous searches with the CMS Collaboration to produce strong limits on SUSY parameter space [7]. These variables are employed to help distinguish SUSY signal events from the Standard Model (SM) background. Figure 2.1: A cartoon of a disquark production scenario. If we consider the scenario where two squarks (supersymmetric partners of quarks) each decay to a quark and a stable, weakly interacting lightest supersymmetric particle (LSP), the missing energy carried away by the LSP makes it difficult to reconstruct the kinematic attributes of all the particles in the decay. Thus, it is a challenge to identify this as a SUSY decay. For an all-hadronic analysis, we form the two razor variables MR , R2 as follows: first, we cluster the hadronic jets into two hemispheres using an algorithm in which we minimize the sum in quadrature of the invariant masses of the two hemispheres. These jets often have some baseline thresholds for certain kinematic events, such as transverse momentum (pT ) or pseudorapidity (η). Then, we define MR as q MR = j2 2 (|pj1 | + |pj2 |)2 − (pj1 z + pz ) , where pji is the momentum of the ith hemisphere. R is defined as R = MTR /MR , 3 where s MTR = j2 ~/ E/T (pj1 pTj1 + p~Tj2 ) T + pT ) − ET · (~ , 2 and E/T is the missing transverse energy of the event. MR is contains information about the characteristic SUSY mass scales. It is an estimator, in the case of the squark, for M∆ , which we define to be M∆ = m2q̃ − m2χ̃ . mq̃ mq̃ is the mass of the squark, and mχ̃ is the mass of the LSP. Experimentally, MR peaks higher for SUSY events. R2 contains information about the missing energy in the event and helps reduce QCD backgrounds [7]. Because of these advantages, the razor variables have been implemented successfully for new physics searches. In the following chapters, we will use these razor variables extensively. 4 Chapter 3 CMS Trigger Studies 3.1 The CMS Detector and the Trigger System The CMS detector is a general purpose detector at the LHC with various sub-detector components. It includes a lead-tungstate-crystal electromagnetic calorimeter (ECAL), a hadronic calorimeter (HCAL), a silicon tracker, and a muon drift tube system, cathode strip chambers, and resistive plate chambers [8]. The next run of the LHC, scheduled to begin in 2015, requires both software and hardware improvements due to higher energies (13 and 14 TeV) of the proton-proton collisions as well as increased underlying event activity (known as pileup) [9]. The events detected by CMS are too large in number to record all of the data, so a trigger system is required to decide which collision events to record. This trigger system is composed of two levels; the system results in data reduction from the LHC collision rate of 15 MHz down to a rate of 400 Hz for Run 1 (and 1 kHz for Run 2). The two levels are the hardware-based Level-1 (L1) system and the software-based High Level Trigger (HLT). In order to minimize CPU time, particle and event kinematics are only partially reconstructed since triggering is conducted in real-time [10, 11]. The L1 system has three main components: global, muon, and calorimeter. The L1 calorimeter system is based on a set of trigger towers, which are made up of 4×4 regions. These regions are each 20◦ in φ (azimuthal angle), and are also sectioned by η (pseudorapidity). Jets, which are the result of quark and gluon production in the detector, are calorimeter objects at the L1 level. One or more L1 filters can feed into an HLT filter. For the HLT system, muons are reconstructed using isolation algorithms and track fitting, which involves matching inner tracker tracks with outer muon spectrometer tracks. There are two possible collections of jets and E/T at the HLT: calorimeter collections and Particle Flow (PF) collections. Calorimeter objets are crude objects reconstructed from energy deposits in the calorimeters, while PF objects are more sophisticated and rely on the PF algorithm [12]. The PF algorithm takes information from the multiple sub-detectors to produce PF candidates, resulting in tracking and better ECAL measurements to be incorporated into the 5 particle information. These particles are then clustered using the anti-kT jet clustering algorithm to reconstruct the jets [13, 14]. The selected kinematic thresholds for both the L1 and HLT must be thoroughly tested to (1) ensure sufficient data reduction and to (2) maintain the efficiency of keeping events which are interesting for our physics analyses. We will focus on the HLT in the following section. 3.2 Razor High Level Triggers A set of trigger options involving razor variables were implemented for the LHC Run I. Due to higher energies, increased pileup, and shorter bunch spacing, these triggers need to be modified for Run II. In addition, PF objects are now available at the HLT, so the option of using PF objects instead of calorimeter objects must be discussed. Although PF objects have been shown to have a much improved accuracy [15], they are more costly in CPU time at the HLT. As a result, one tactic of using PF objects but still minimizing CPU time is to reduce the number of events that the PF algorithm acts on by imposing loose thresholds on calorimeter-level objects. One important detail before implementing this tactic is to study the correlation of PF objects to calorimeter objects. 3.2.1 Calorimeter Objects versus PF Objects Investigation Because calorimeter objects and PF objects are constructed differently, we conducted a study of PF versus calorimeter variables. We conducted this study with a sample of tt̄+jets, common background to many SUSY signals. This particular sample forces tt̄ to decay leptonically, and details are in Table A.3. The main variables we were concerned with were the razor variables since the HLT triggers include cutoffs based on these variables. Thus, we studied the razor variables constructed with PF objects versus calorimeter objects. Examining Figure 3.1, the R2 correspondence is much worse than the MR correspondence. In addition to using the jet object information, the R2 variables are constructed using the E/T information. We then investigated the correspondence between PF and calo E/T , shown in Figure 3.2. When the HLT E/T is calculated using energy deposit information from the hadronic and electromagnetic calorimeters [10], the information from the muon chambers is excluded. As a result, we suspected that the muon energies were not correctly incorporated into the calorimeter-level E/T . To investigate this, we replotted the distributions with the additional requirement that muons with pT > 30 GeV be vetoed. A remarkable improvement of the correspondence between PF and calorimeter E/T and R2 distributions was exhibited in Figure 3.3. 2000 80 0.8 140 0.7 120 0.6 100 Number of Events 100 PF R2 2500 Number of Events PF MR 6 0.5 1500 80 60 1000 0.4 60 0.3 40 40 0.2 500 20 0 0 0 20 0.1 500 1000 1500 2000 2500 0 0 0.1 0.2 0.3 0.4 0.5 0.6 Calo MR 0.7 0.8 Calo R (a) 0 2 (b) 500 80 450 400 70 350 60 300 50 250 40 200 30 150 20 100 10 50 0 0 Number of Events PF MET Figure 3.1: Comparisons of the razor variables formed with PF objects versus calorimeter objects. 50 100 150 200 250 300 350 400 450 500 0 Calo MET 50 400 350 40 300 250 30 200 20 150 90 0.7 80 0.6 70 0.5 60 0.4 50 40 0.3 30 0.2 100 10 50 0 0 0.8 50 100 150 200 250 300 350 400 450 500 0 20 0.1 0 0 10 0.1 0.2 0.3 0.4 Calo MET (a) Number of Events 60 450 PF R2 500 Number of Events PF MET Figure 3.2: Comparisons of the E/T distributions formed with PF objects versus calorimeter objects. 0.5 0.6 0.7 0.8 Calo R 0 2 (b) Figure 3.3: Comparisons of the E/T and R2 distributions formed with PF objects versus calorimeter objects, vetoing all events that have muons with pT > 30 GeV. Following these studies, recommendations were made for muon information to be incorporated into the calorimeter level razor variables. Muon information was then added to the hemisphere decisions by other members of the Caltech CMS group (Javier Duarte). 7 3.2.2 Trigger Flow Path For a trigger involving the razor variables, the trigger path is as follows: 1. Input from the Level 1 CMS Hardware Trigger. For these triggers, a combination of all hadronic triggers available were used. 2. Algorithms to create calorimeter objects, which use information from the calorimeter [13]. 3. Thresholds implemented on the calorimeter jet kinematic properties. 4. Thresholds implemented on the razor variables constructed from calorimeter objects. 5. Algorithms to create Particle Flow (PF) objects, which use an increased amount of available information from CMS [13]. 6. Thresholds implemented on the PF jet kinematic properties. 7. Thresholds implemented on the razor variables. 3.2.3 Rates of Trigger Menu Various triggers were investigated to optimize the thresholds at the PF level and the calorimeter level. To calculate these rates, the triggers were evaluated within the CMS HLT software framework [16] over a weighted average of a set of QCD Monte Carlo samples (see Table A.1) with various jet pT bins from 30 to 100 GeV, with 40 pile-up (pp collisions per bunch) and bunch-crossings happening every 25 ns. These samples essentially consisted of jets and pileup events. The triggers are in part named according to CMS convention. A short code follows: 1. Rsq0pX indicates R2 > 0.X. 2. MRX indicates MR > X. 3. RsqMRX indicates (R2 − 0.25) ∗ (MR − 300) > X. These offsets of 0.25, 300 approximate the R2 ∗ MR iso-probability contours observed in the CMS 8 TeV dataset [17]. 4. NoRazorCaloCut indicates all calorimeter-level filters on the razor variables are removed. Trigger Name HLT RsqMR300 Rsq0p09 MR200 HLT RsqMR300 Rsq0p09 MR200 Muon Rate (Hz) 12.471 ± 1.244 12.472 ± 1.244 Table 3.1: Table of the razor triggers discussed, where the rate is calculated for an instantaneous luminosity of 1.4e34 cm−2 s−1 . These all have a calorimeter-level filter of hltRsqMR200Rsq0p01MR100Calo. The second trigger has the muon sequence enabled. 8 Trigger Name HLT RsqMR300 Rsq0p09 MR200 Muon NoRazorCaloCut HLT RsqMR300 Rsq0p09 MR200 Muon CaloRsq0p0196 HLT RsqMR300 Rsq0p09 MR200 Muon CaloRsq0p0289 Rate (Hz) 12.967 ± 1.249 11.188 ± 1.145 10.761 ± 1.132 Table 3.2: Table of the razor triggers discussed, where the rate is calculated for an instantaneous luminosity of 1.4e34 cm−2 s−1 . These have a calorimeter-level filter of hltRsqMR240RsqXMR100Calo, where X = 0.0196 for the second trigger and X = 0.0289 for the third trigger. All triggers have the muon sequence enabled. Trigger Name HLT RsqMR300 Rsq0p09 MR200 Muon CaloRsq0p04 HLT RsqMR300 Rsq0p09 MR200 Muon CaloRsq0p0576 Rate (Hz) 9.513 ± 1.025 8.911 ± 1.012 Table 3.3: Table of the razor triggers discussed, where the rate is calculated for an instantaneous luminosity of 1.4e34 cm−2 s−1 . These have a calorimeter-level filter of hltRsqMR260RsqXMR100Calo, where X = 0.04 for the first trigger and X = 0.0576 for the second trigger. All triggers have the muon sequence enabled. We first investigated the addition of the muon sequence mentioned in the previous section. We see that the rate increases marginally in Table 3.1. Therefore, adding the muon sequence to the calorimeter razor variables does not noticeably increase the rate, but would have a beneficial effect on accuracy for backgrounds and signals with a lot of muons, i.e. tt̄+jets. We then investigate the effect of the calorimeter-level razor variable thresholds on rate. Ideally, an increase in calorimeter-level razor variable thresholds would have a minimal effect on the rate when the thresholds are lower than the following PF thresholds. The PF thresholds implemented without any calorimeter-level thresholds on the razor variables are given in line 1 of Table 3.2. As we increase the calorimeter-level razor thresholds, we see the rate slowly decrease to ≈ 10 Hz, which is around the rate that we desire. Note that for Table 3.3, we also raise the R2 × MR threshold in order to match the increase in R2 . This illustrates the fact that there is still a small mismatch between calorimeter objects and PF objects. 3.3 H→ b b̄ HLT Trigger 3.4 Motivation Investigation of an H→ b b̄ trigger has been conducted for possible addition to the Run II trigger menu. This is motivated by the use of Higgs detection as a tool for finding new physics, which will be further elaborated on in Chapter 3. Since H→ b b̄ is the dominant decay mode (branching ratio 57.8%) for a 125 GeV Higgs [18], this trigger is ideal for capturing the maximum amount of events. However, the high SM cross section for bottom production at the LHC poses a problem for the rate of events passing this trigger [19]. As a result, many kinematic thresholds have to be combined in order to minimize the rate to a reasonable level. 9 3.5 b-tagging Bottom quarks, or b quarks, are found in many supersymmetric processes [20]. CMS has several algorithms for b quark identification, or b-tagging. For our study, we will use the Combined Secondary Vertex (CSV) algorithm. This algorithm assigns a value to each jet which indicates the probability of misidentification. There are three working points for this algorithm: loose, medium, and tight, which correspond to ≈10%, ≈1%, and ≈0.1% probabilities for an average jet pT of 60 GeV [21]. These algorithms rely on tracks as well as secondary vertices, which can indicate the lifetime of quark before decay. This exploits the fact that the b quark has a relatively long lifetime, ≈1 picosecond [22]. CSV loose, medium, and tight points also result in varying b-tag efficiencies. The loose point corresponds to ≈ 80-90% efficiency, medium to ≈ 60-70% efficiency, and tight to ≈ 50% efficiency [21]. 3.6 Trigger Flow Path Figure 3.4: Schematic of the H→ b b̄ trigger flow path. The numbers in parentheses correspond to the more detailed list described in the text. The trigger flow path is as follows (Figure 3.4): 1. Input from the Level 1 CMS Hardware Trigger. For these triggers, a combination of all hadronic triggers available were used. 2. Algorithms to create calorimeter objects, which use information from the calorimeter [13]. 3. Thresholds implemented on the calorimeter jet kinematic properties. 10 4. Thresholds implemented on encompassing variables, such as the razor variables or HT , which is a sum of transverse hadronic energies. 5. At least one b-tagged jet with a specified CSV threshold (see Section 3.5). 6. Algorithms to create Particle Flow (PF) objects, which use an increased amount of available information from CMS [13]. 7. Thresholds implemented on the PF jet kinematic properties. 8. Thresholds implemented on the razor variables. 9. At least two b-tagged jets with specified CSV threshold (see Section 3.5). 10. Higgs mass window filter applied to any two b-tagged jets that pass the specified CSV requirements in the previous step. 3.7 Rates of H→ b b̄ Trigger The naming convention carries from Section 3.2.3. A few more abbreviations are as follows: 1. BTagXCSV0YCSV0Z indicates that there are X b-tags required, with a Combined Secondary Vertex (CSV) cutoff of 0.Y and 0.Z for two PF jets. For calorimeter jets, there is a CSV cutoff of 0.Y - 0.1 required for one jet. See Section 3.5 for further information on b-tagging. 2. DiJetX indicates that we require two PF jets with pT > X GeV, and for calorimeter jets we require the leading jet to have pT > X - 10 GeV and the subleading jet to have pT > X - 20 GeV. 3. TriJetX indicates that we require three PF jets with pT > X GeV. 4. MqqMinXMaxY indicates that we require that there be two PF b-jets (with the b-tagging CSV requirements from (1)) that have a invariant mass between X and Y GeV. 5. HTX indicates HT > X GeV. Trigger Name HLT BTag2CSV05CSV02 DiJet80 Rsq0p01 MR200 MqqMin70Max190 HLT BTag2CSV05CSV02 DiJet80 HT200 Rsq0p01 MR300 MqqMin70Max190 HLT BTag2CSV05CSV02 DiJet80 CaloMR200 Rsq0p01 MR300 MqqMin70Max190 HLT BTag2CSV05CSV02 DiJet80 TriJet40 CaloMR200 Rsq0p0196 MR300 MqqMin70Max190 HLT BTag2CSV07CSV04 DiJet80 CaloMR200 Rsq0p01 MR300 MqqMin70Max190 HLT BTag2CSV07CSV04 DiJet80 TriJet40 CaloMR200 Rsq0p0196 MR300 MqqMin70Max190 Rate (Hz) 121.770 ± 7.015 93.946 ± 5.791 93.384 ± 5.774 61.056 ± 5.333 37.483 ± 3.807 25.827 ± 3.685 Table 3.4: Table of the H → b b̄ triggers discussed, where the rate is calculated for an instantaneous luminosity of 1.4e34 cm−2 s−1 . 11 3.7.1 Addition of new HCAL local reconstruction method and ECAL Multifit An update of the calorimeter local reconstruction methods to handle out-of-time pile-up, which is pile-up from adjacent bunch-crossing, was released [23]. This improved energy reconstruction in the hadronic calorimeter endcap and barrel, relies on fitting measured pulses with parameterizations derived from test pulses, then subtracting the out-of-time pileup contribution from the energy measurement. This technique results in better resolution and measurement [24]. A similar update was released for the electromagnetic calorimeter to reduce out-of-time pileup by simulating and fitting the pulse shape from an average of pulses from samples shifted from each other in bunch-crossings [25]. We applied this technique to two of our proposed triggers and measured their rates. Trigger Name HLT BTag2CSV05CSV02 DiJet80 TriJet40 CaloMR200 Rsq0p0196 MR300 MqqMin70Max190 HLT BTag2CSV07CSV04 DiJet80 TriJet40 CaloMR200 Rsq0p0196 MR300 MqqMin70Max190 Rate (Hz) 59.174 ± 5.156 24.112 ± 3.550 Table 3.5: Table of the H → b b̄ triggers discussed, where the rate is calculated for an instantaneous luminosity of 1.4e34 cm−2 s−1 . 3.7.2 Discussion The rates are shown in Table 3.4. We see that the tightening of the CSV thresholds sharply reduces the rate. The addition of the razor variable or HT cut is also effective at reducing the rate and is low enough to keep high signal events. We refrain from a high R2 threshold in an effort to select for different events from the regular razor triggers. We also keep a relatively large Higgs mass window since the main goal of this trigger is to keep events that include a Higgs. The new ECAL and HCAL methods do not reduce the rates significantly (Table 3.5), but should still be implemented due to the improvements in measurement. 12 Chapter 4 Investigation of Higgs-Aware Decay Models 4.1 The Higgs decay as a tool for new physics searches Armed with the discovery of the Higgs Boson, we are able to employ the Higgs as a tool for future physics studies. We can study its mass and other properties, which have implications for the possible existence of beyond-the-standard-model (BSM) phenomena including SUSY and dark matter. We can also use the Higgs boson as a probe for searching for new physics. For example, the Higgs invisible decay channel has been ideal for BSM studies since the branching fraction of the purely SM decay, h → ZZ ∗ → 4ν is small [26]. There have already been studies exploiting this channel [27]. Similarly, we can employ the Higgs to look for SUSY by targeting decays that specifically produce a Higgs, such as those that include a next-to-lightest neutralino decaying to a Higgs and a lightest neutralino, χ02 → hχ01 [28]. The decay of the Higgs to two photons has been observed as a clean, sharp signal [29] and is an ideal decay channel to target. A previous search for supersymmetry with this decay channel motivates this thesis work [6], but we will examine different SUSY models from the search. 4.2 Motivation Many standard SUSY searches rely on missing transverse energy (E/T ) in order to separate signal from Standard Model background. E/T is calculated from energy deposits in the subdetectors [30]. As a result, strong limits have been placed for SUSY models with large E/T [31]. These standard searches look for models with signal events at R2 values of greater than 0.2 - 0.3 [28]. Instead, we would like to investigate models with lower E/T and lower R2 , which may have eluded LHC bounds but are good candidates for Run II. Furthermore, the use of the Higgs decay channels gives us an alternative method for reducing 13 background from our analysis. We can then study models with less E/T and look in areas of the SUSY phase space that have not been extensively studied. We will focus on bottom squark production decaying to Higgses, rather than top squark production. In general, since top quarks decay to a W boson and a bottom quark, top squark models have more complicated topology with higher E/T due to the W bosons decaying to neutrinos. Our goal is to study a viable model for a LHC Run II analysis. In order to achieve this, this thesis will explore the different kinematic parameters in bottom squark production and decay. In particular, we desire models which have low E/T , low R2 , and MR values clustered from 400 to 500 GeV. Higher MR values have a higher probability of already being excluded, and at too low of MR we lose events from the trigger thresholds. We can consider a model where we have a bino-like next-to-lightest supersymmetric particle (NLSP) which would decay predominantly to a Higgs boson and a weakly coupled LSP [32]. The next-to-lightest neutralino can be considered the NLSP, and the lightest neutralino is the LSP. For the dominant mode of bottom squark production, the final state particles will be two bottom quarks and two Higgs bosons. CMS SUSY searches are interpreted in the context of simplified models [20]. A simplified model consists of only relevant particles, specifying the particle production and subsequent decay. It is defined by the model parameters that would influence how an event would look in the detector. For example, the T2qq model described in [20] is a simplified model that focuses on pair-produced squarks decaying to two quarks and two LSPs, where the free parameters are masses of the squark and the LSP. We will use this interpretation for our studies. 4.3 Bottom squark production model We investigated a bottom squark production model, where the bottom squark has two possible decays channels: b̃ → bχ̃02 → bH χ̃01 , and b̃ → bχ̃01 . The bottom squark particle can be produced through several mechanisms, see Section A.2. The dominant production modes result in pair production. We wanted to obtain MR peak values from 400-500 GeV for these events, and we needed to comply with current exclusion limits [33]. Note that these exclusion limits assume a decay of b̃ → bχ̃01 . If we examine Fig. 4.1, we see that the contour lines for M∆ = 450 ± 50 GeV become approximately linear at above χ̃01 ≈ 200-250 GeV. Referring to the limits in [33], we see that mb̃ = 600 GeV and mχ̃01 = 300 GeV is a good starting point. For all of the follow studies, the mχ̃02 is set at mχ̃01 + 130 GeV to minimize the E/T carried away by the lightest neutralino. After choosing appropriate mass points, several working points of the branching ratios for the two decay channels of the b̃ were chosen for examination: 10%, 50%, 90%, and 100% decay to bH χ̃02 . 14 MΔ 1200 1000 m˜b 800 600 400 200 0 100 200 300 400 500 600 mχ˜ Figure 4.1: The contour lines for M∆ = 450 GeV, where M∆ = by the dashed lines. m2b̃ −m2χ̃ , with ± 50 GeV as indicated mb̃ Events were produced at 8 TeV center-of-mass energy using PYTHIA 8.1 [34, 35] interfaced with SUSY Les Houches Accord (SLHA) files [36] and the BSMatLHC package [37]. They were filtered using a selection process described in Section 4.4. The Higgs boson was forced to decay to two photons. 4.4 Selection After events were produced, several requirements were implemented to filter out the events. This selection was loosely modeled after the aforementioned Higgs to diphoton supersymmetry search [6] to reduce potential background, with modifications specific to a generator-level study. 1. The event must have a pair of photons that has a diphoton mass of > 100 GeV. One of these photons should have pT > 40 GeV, and the other should have pT > 25 GeV. 2. Then, if two pairs of photons that satisfy (1) are found, then one of them is randomly set aside to later be counted as an alternate channel for Higgs decay besides two photons. This is done to retain the maximum amount of events generated by PYTHIA. 3. The pair of photons that is not set aside must have pT > 20 GeV and |η| < 1.44. 15 4. The event must have at least one jet with pT > 30 GeV and |η| < 3.0, and have a ∆R > 0.5 with respect to the either of the pair of photons selected. These jets are produced using the PF algorithm, clustered with an anti-kT algorithm using ∆R = 0.5 [15, 14, 38]. 5. We only keep jets with pT > 30 GeV and |η| < 3.0. 4.5 Box definitions Figure 4.2: A schematic for how events are placed into the three boxes. The red rectangles are the two requirements, and the blue rectangles represent the boxes. After selection, the events were further categorized into boxes for further discrimination of potential signal from background. These boxes are all restricted to MR ∈ [150, 3000] GeV and R2 ∈ [0, 1]. The boxes are again motivated by the Higgs to diphoton supersymmetry search and are as follows: 1. High pT Box requires pT of the di-photon system to be > 110 GeV. 2. Hbb Box requires 110 ≤ mbb ≤ 140 GeV, with mbb being the invariant mass of any two b-tagged jets. 3. Overflow Box The events are grouped into the boxes in a hierarchal system. So, if an event passes the requirements for box 1, then it is grouped into box 1. If it fails and passes the requirements for box 2, then it goes in box 2. Else, it goes into the Overflow Box (see Figure 4.2). These boxes are constructed to characterize a potential SUSY signal from background events. The High pT box selects for boosted Higgs bosons (with high momentum), while the Hbb box allows us to select for diHiggs production. For the Hbb box, we assume that the second Higgs produced would decay to two b quarks because of the high branching ratio [18]. Because the branching ratio of H → γγ is low at a fraction of 0.00228 [39], events were produced with an artificial branching ratio of 100%. As previously stated, in the analysis one of the H → γγ 16 photon pairs is randomly set aside to be counted as an alternate channel. We apply a 57.8% chance that this pair should be counted as a H → b b̄ decay channel to simulate the branching ratio [18]. Then, with every b-jet in the event, we emulate the b-tagging efficiency by randomly tagging 60% of generator level b-jets. This approximately corresponds to the efficiency of a CSV medium b-tag requirement (see Section 3.5). The reason this artificial handling of bottom quarks is necessary so we do not overestimate the number of events that would fall in the Hbb box. These box definitions are important for future inclusive analyses and will be used in the later statistical study in Section 4.11. 4.6 Branching Ratio to χ̃02 Study mb̃ 600 GeV 600 GeV 600 GeV 600 GeV mχ̃02 430 GeV 430 GeV 430 GeV 430 GeV mχ̃01 300 GeV 300 GeV 300 GeV 300 GeV BR (to χ̃02 ) 10% 50% 90% 100% Table 4.1: Table of the models investigated in the branching ratio study, with their associated values of M∆ and Msplit . In the following section we will examine the effect of the branching ratios listed in Table 4.1 on the kinematics of the mb̃ = 600 GeV, mχ̃01 = 300 GeV model. If we examine Fig. 4.3, we see that we obtain the MR shape in the desired range as predicted by M∆ , as well as R2 peak values in the desired range. As the branching ratio to χ̃02 decreases, we see that the peak region is less defined. Fig. 4.3d shows that the R2 versus MR distribution with the loosest clustering in the events corresponds to the smallest branching ratio. This can be understood through the chance that the event we capture is asymmetric. With an 100% branching ratio to χ̃02 , we see a marked decrease in events at high R2 . Because of how R2 is defined with E/T dependence, larger E/T in general should result in a larger E/T if the MR is fixed. The 2D distribution shrinks to lower R2 , although the MR distribution, as expected, shifts very little. However, regardless of the branching ratio, the plots still maintain a significant portion of events above R2 ≈ 0.1. With Fig. 4.4, we see a similar phenomenon as the branching ratio to χ̃02 increases. The plot shows the strong dependence of R2 on the E/T distribution. Although the distribution becomes more defined, the rough slope of the R2 vs E/T 2D distribution remains the same. The MR versus E/T 2D plots reveal the robustness of the MR variable with varying branching ratios. Comparing Fig. 4.4a and b shows that increasing the branching ratio clusters the events closer. Examining Fig. 4.4a and d as well, we see that the E/T becomes pushed higher. However, we 1 0.9 CMS Simulation, s = 8 TeV 0.0018 1 0.9 CMS Simulation, s = 8 TeV 0.8 0.0016 0.8 0.7 0.0014 0.7 0.6 0.0012 0.6 0.5 0.001 0.4 0.0008 0.4 0.3 0.0006 0.3 0.2 0.0004 0.2 0.1 0.0002 0.1 0 0 0 0 0 200 400 600 800 1000 1200 1400 R2 R2 17 0.0015 0.5 0.001 0.0005 200 400 600 800 1000 1200 1400 MR [GeV] (a) (b) 0.8 1 0.9 CMS Simulation, s = 8 TeV 0.0025 0.8 0.002 0.7 0.5 0.4 0.001 0.3 0.2 0.0005 0.1 200 400 600 800 1000 1200 1400 0 0.0018 0.0016 0.0012 0.6 R2 0.0015 0 0.0014 0.7 0.6 R2 0.002 MR [GeV] 1 0.9 CMS Simulation, s = 8 TeV 0 0 0.0025 0.5 0.001 0.4 0.0008 0.3 0.0006 0.2 0.0004 0.1 0.0002 0 0 200 400 600 800 1000 1200 1400 MR [GeV] MR [GeV] (c) (d) 0 Figure 4.3: Z-axis scale units are such that the total number of events is normalized to 1. mb̃ = 600 GeV, mχ̃01 = 300 GeV model. (a) R2 versus MR for the 50% (to χ̃02 ) working model. (b) R2 versus MR for the 100% (to χ̃02 ) working model. (c) R2 versus MR for the 90% (to χ̃02 ) working model. (d) R2 versus MR for the 10% (to χ̃02 ) working model. also lose the nicely clustered peak since the decay of the b̃ pair is now mostly asymmetric. However, the MR spread seems to change minimally. The conclusion from this study of the branching ratios with this one mass working point is that an increase in branching ratio to χ̃02 is beneficial for an R2 distribution that evades the current LHC bounds. Varying the branching ratio has little effect on the MR . Furthermore, standard bottom squark searches assume that the bottom squark decays directly to χ̃01 [33], so increasing the branching ratio to χ̃02 would loosen limits. 18 1 0.9 CMS Simulation, s = 8 TeV 1 0.9 CMS Simulation, s = 8 TeV 0.0025 0.8 0.002 0.7 0.5 0.4 0.0025 0.6 0.0015 R2 R2 0.003 0.7 0.6 0.001 0.3 0.5 0.002 0.4 0.0015 0.3 0.2 0.001 0.2 0.0005 0.1 0 0 0.0005 0.1 50 100 150 200 250 300 0 0 0 50 MET [GeV] 100 250 300 1 0.0035 CMS Simulation, s = 8 TeV 0.9 CMS Simulation, s = 8 TeV 0.8 0.003 0.8 0.7 0.0025 0.7 0.6 0.002 0.5 R2 0.6 R2 200 0.5 0.4 0.0015 0.4 0.3 0.001 0.3 0.2 0.2 0.0005 0.1 50 100 150 200 MET [GeV] (c) 0 (b) 1 0 0 150 MET [GeV] (a) 0.9 0.0035 0.8 250 300 0 0.1 0 0 50 100 150 200 250 300 0.0022 0.002 0.0018 0.0016 0.0014 0.0012 0.001 0.0008 0.0006 0.0004 0.0002 0 MET [GeV] (d) Figure 4.4: Z-axis scale units are such that the total number of events is normalized to 1. mb̃ = 600 GeV, mχ̃01 = 300 GeV model. (a) R2 versus E/T , for the 50% (to χ̃02 ) working model. (b) R2 versus E/T , for the 100% (to χ̃02 ) working model. (c) R2 versus E/T , for the 90% (to χ̃02 ) working model. (d) R2 versus E/T , for the 10% (to χ̃02 ) working model. 19 1400 CMS Simulation, s = 8 TeV 0.0012 1200 0.001 MR [GeV] 1000 0.0008 800 CMS Simulation, s = 8 TeV 0.001 800 0.0008 0.0006 400 0.0004 400 200 0.0002 200 50 100 150 200 250 300 0.0012 1000 600 0 0 0.0014 1200 MR [GeV] 1400 0 600 0 0 0.0006 0.0004 0.0002 50 MET [GeV] 100 150 200 250 300 MET [GeV] (a) (b) 1400 1400 0.0014 CMS Simulation, s = 8 TeV 1200 0.0016 CMS Simulation, s = 8 TeV 1200 0.0014 1000 0.0012 MR [GeV] 0.001 800 0.0008 MR [GeV] 0.0012 1000 0.0006 400 0.0004 400 200 0.0002 200 50 100 150 200 MET [GeV] (c) 250 300 0 0.001 800 600 0 0 0 0.0008 600 0.0006 0 0 0.0004 0.0002 50 100 150 200 250 300 0 MET [GeV] (d) Figure 4.5: Z-axis scale units are such that the total number of events is normalized to 1. mb̃ = 600 GeV, mχ̃01 = 300 GeV model. (a) MR versus E/T for the 50% (to χ̃02 ) working model. (b) MR versus E/T , for the 100% (to χ̃02 ) working model. (c) MR versus E/T , for the 90% (to χ̃02 ) working model. (d) MR versus E/T , for the 10% (to χ̃02 ) working model. 20 4.7 Mass Splitting Study with Fixed χ̃01 Mass The next parameter that would affect the kinematics is the mass splitting of the system, i.e. the difference in mass between the bottom squark and lightest neutralino. We can classify this in two ways: using M∆ , or simply Msplit = mb̃ − mχ̃01 . The following subsections investigate the kinematics of models with the characteristics listed in Table 4.2. Notice the caveat that these effects would not necessarily be decoupled from the effects of changing the bottom squark mass. mb̃ 550 GeV 450 GeV 530 GeV mχ̃02 430 GeV 430 GeV 430 GeV mχ̃01 300 GeV 300 GeV 300 GeV M∆ 386.36 GeV 250 GeV 360.19 GeV Msplit 250 GeV 150 GeV 230 GeV BR (to χ̃02 ) 90% 100% 100% Table 4.2: Table of the models investigated in the mass splitting study, with their associated values of M∆ and Msplit . The 1D E/T distributions have a strong dependence on mass splitting since with a smaller mass splitting there is likely less energy available for the decay particles (Fig. 4.10a. With Figures 4.6, 4.7, 4.8, we can also see a strong dependence of MR on M∆ . This is in line with the principle that MR is an estimator of M∆ . If we compare Figure 4.6b to Figure 4.4c, the R2 versus E/T 2D distributions are roughly the same, indicating that the decrease in mass splitting from the mb̃ = 600 GeV model to the mb̃ = 550 GeV has a relatively small effect on these variables. However, when we look at Figure 4.7b, we notice a large difference not only in a tighter clustering at small E/T , R2 , but also a change in the slope for the mb̃ = 450 GeV model. From Figure 4.7c, we also notice that the MR clusters at a center of less than 200 GeV, which is lower than we would expect. There is an unexpected shift of the peaks of the MR distributions if we compare the various models in Figure 4.9a, where the peak for mb̃ = 450 GeV is ≈ 100 GeV lower than the corresponding peaks for the other models. 21 1 0.9 CMS Simulation, s = 8 TeV 0.003 0.8 0.0025 0.7 0.002 0.5 0.0015 0.4 0.3 200 400 600 800 1000 1200 1400 0.8 0.0035 0.7 0.003 0.6 0.0025 0.5 0.002 0.0015 0.3 0.001 0.2 0.0005 0.1 0.004 0.4 0.001 0.2 0 0 R2 R2 0.6 1 0.9 CMS Simulation, s = 8 TeV 0.0005 0.1 0 0 0 50 100 MR [GeV] 150 200 250 300 7 9 0 MET [GeV] (a) (b) 1400 0.3 0.0018 CMS Simulation, s = 8 TeV CMS Simulation, s = 8 TeV 0.0016 1200 0.25 0.0014 0.2 0.0012 800 0.001 600 0.0008 0.0006 400 0.0004 200 0 0 a.u MR [GeV] 1000 0.15 0.1 0.05 0.0002 50 100 150 200 MET [GeV] (c) 250 300 0 0 0 1 2 3 4 5 6 8 Number of Jets (d) Figure 4.6: Characterization of the mb̃ = 550 GeV, mχ̃01 = 300 GeV model with 90% to χ̃02 . Z-scale units are such that the total number of events is normalized to 1. (a) R2 versus MR . (b) R2 versus E/T . (c) MR versus E/T . (d) Number of PF jets, clustered with the anti-kT algorithm with ∆R = 0.5. 1 0.9 CMS Simulation, s = 8 TeV 0.0045 1 0.9 CMS Simulation, s = 8 TeV 0.007 0.8 0.004 0.8 0.006 0.7 0.0035 0.7 0.6 0.003 0.6 0.5 0.0025 0.5 0.004 0.4 0.002 0.4 0.003 0.3 0.0015 0.3 0.2 0.001 0.2 0.1 0.0005 0.1 0 0 0 0 0 200 400 600 800 1000 1200 1400 R2 R2 22 0.005 0.002 0.001 50 100 MR [GeV] 150 250 300 7 9 0 MET [GeV] (a) (b) 1400 0.004 0.35 1200 0.0035 0.3 1000 0.003 0.25 CMS Simulation, s = 8 TeV CMS Simulation, s = 8 TeV 0.0025 800 0.002 600 a.u MR [GeV] 200 0.2 0.15 0.0015 400 0.001 200 0 0 0.0005 50 100 150 200 MET [GeV] (c) 250 300 0 0.1 0.05 0 0 1 2 3 4 5 6 8 Number of Jets (d) Figure 4.7: Characterization of the mb̃ = 450 GeV, mχ̃01 = 300 GeV model with 100% to χ̃02 . Z-scale units are such that the total number of events is normalized to 1. (a) R2 versus MR . (b) R2 versus E/T . (c) MR versus E/T . (d) Number of PF jets, clustered with the anti-kT algorithm with ∆R = 0.5. 23 1 0.9 CMS Simulation, s = 8 TeV 0.0035 1 0.9 CMS Simulation, s = 8 TeV 0.8 0.003 0.8 0.7 0.0025 0.7 0.0015 0.4 0.3 0.001 0.3 0.2 0.003 0.5 0.4 0.002 0.2 0.0005 0.1 0 0 0.004 0.6 0.002 0.5 R2 R2 0.6 200 400 600 800 1000 1200 1400 0.001 0.1 0 0 0 50 100 MR [GeV] 150 MR [GeV] 1000 800 600 400 200 150 200 MET [GeV] (c) 250 300 0.0022 0.002 0.0018 0.0016 0.0014 0.0012 0.001 0.0008 0.0006 0.0004 0.0002 0 300 7 9 0 0.3 CMS Simulation, s = 8 TeV 0.25 0.2 a.u CMS Simulation, s = 8 TeV 1200 100 250 (b) 1400 50 200 MET [GeV] (a) 0 0 0.005 0.15 0.1 0.05 0 0 1 2 3 4 5 6 8 Number of Jets (d) Figure 4.8: Characterization of the mb̃ = 530 GeV, mχ̃01 = 300 GeV model with 100% to χ̃02 . Z-scale units are such that the total number of events is normalized to 1. (a) R2 versus MR . (b) R2 versus E/T . (c) MR versus E/T . (d) Number of PF jets, clustered with the anti-kT algorithm with ∆R = 0.5. In an effort to decipher these effects, we can think of how MR is defined. Since MR is constructed from jets and particles that must have a minimum pT , soft particles will be excluded. In Figure 4.11, we see that the available energy to impart to the bottom quark is only 20 GeV; thus, these b-jets are likely very soft. As a result, they are not clustered in the hemispheres that go into the calculation of MR , and M∆ is not being constructed accurately. Since R = MTR /MR , this also affects the distribution of R2 . A smaller MR than expected thus increases the slope of the R2 versus E/T plot. This explanation is further supported by the plot of the distribution of PF jets that enter the hemispheres (see Figure 4.7d), which has a mode of only two jets. We expect on average four jets for a model with BR = 100% to χ̃02 , with two from the direct decay of the bottom squark particle and two from the Higgs decay. This is validated in Figure 4.6d. Furthermore, the leading jet pT for 24 0.08 CMS Simulation, s = 8 TeV m~b = 450 mχ∼ = 300 0.07 m~b = 550 mχ∼ = 300 0.06 m~b = 530 mχ∼ = 300 10-1 m~b = 550 mχ∼ = 300 m~b = 530 mχ∼ = 300 10-2 a.u 0.05 a.u m~b = 450 mχ∼ = 300 CMS Simulation, s = 8 TeV 0.04 10-3 0.03 0.02 10-4 0.01 0 0 200 400 600 800 10001200140016001800 0 0.2 0.4 0.6 0.8 MR [GeV] R (a) (b) 1 1.2 1.4 2 Figure 4.9: Razor variable distributions for the various mass splitting with fixed χ̃01 mass. (a) MR 1D distributions. (b) R2 1D distributions. CMS Simulation, s = 8 TeV m~b = 450 m∼χ = 300 0.1 CMS Simulation, s = 8 TeV m~b = 550 mχ∼ = 300 0.1 m~b = 550 mχ∼ = 300 m~b = 530 m∼χ = 300 a.u a.u 0.06 0.04 0.04 0.02 0.02 0 0 100 200 300 400 500 600 700 800 m~b = 530 m∼χ = 300 0.08 0.08 0.06 m~b = 450 m∼χ = 300 0 0 100 200 300 400 500 600 700 800 9001000 MET [GeV] Leading Jet pT [GeV] (a) (b) Figure 4.10: Kinematic distributions for the various mass splitting with fixed χ̃01 mass. (a) E/T 1D distributions. (b) Leading jet pT 1D distributions (excluding H → b b̄ jets). the mb̃ = 450 GeV model is shown to be very soft in Figure 4.10b. Following the mb̃ = 450 GeV model, the mb̃ = 530 GeV model was investigated. Here, we see that although the mass splitting is smaller, the slope of the R2 versus E/T plot does not increase dramatically (Figure 4.8b). Thus, we can conclude that there is a threshold of mass splitting in between 530 GeV and 450 GeV, mostly likely around ≈460 GeV, in which the b-jets are too soft to be included in the calculation of MR . The number of jets in Figure 4.8d is also as expected, and MR returns to being a good probe for M∆ (Figure 4.8c). In conclusion, decreasing the mass splitting changes the MR as expected, but has little effect on the R2 up to a certain threshold. After the b-jets are too soft to be included in the calculation of MR , we see a strong drop in MR values and an undesirably high R2 . 25 Figure 4.11: The decay spectrum for the mb̃ = 450 GeV model. 4.8 Mass Splitting Study with Fixed b̃ Mass mb̃ 600 GeV 600 GeV 600 GeV mχ̃02 230 GeV 330 GeV 430 GeV mχ̃01 100 GeV 200 GeV 300 GeV M∆ 583.33 GeV 533.33 GeV 450 GeV Msplit 500 GeV 400 GeV 300 GeV BR (to χ̃02 ) 100% 100% 100% Table 4.3: Table of the models investigated in the mass splitting study with fixed b̃ mass, and their associated values of M∆ and Msplit . Varying the mass splitting by changing the χ̃01 mass has a different effect than varying the b̃ mass. We see that larger mass splitting corresponds to larger MR values, as expected, but causes R2 to fall faster (Fig. 4.14). The 2D R2 versus MR distribution is also clustered more tightly around the peak values (Fig. 4.13a, 4.12a). This is due to an increasing MR accompanied by a relatively constant E/T distribution in Figure 4.15a. Although the larger mass splitting correlates with a larger leading jet pT (Fig. 4.15b), which we expect is the b quark directly decaying from the bottom squark, the χ̃01 pT decreases with larger mass splitting. Furthermore, we can see a dependence of the azimuthal angle, ∆Φ, between the two χ̃01 particles. The 2D MR versus E/T distribution becomes more spread out with larger mass splitting (Fig. 4.13c, 4.12c). We note that the original squarks are almost always produced back-to-back in ∆Φ, regardless of the mass splitting (Fig. 4.17b). Also note that as the leading jet pT increases, the χ̃01 particles will most likely deviate more from the path of the original bottom squark due to the recoil of the χ̃01 from the Higgs, which are produced from χ̃02 particles recoiling against the b quarks. The larger the mass splitting, the larger the leading jet pT , and the more the χ̃01 particles deviate from the original path of the bottom squark. This is illustrated in the χ̃01 ∆Φ distributions in Figure 4.16b. The smaller mass splitting correlates with the χ̃01 particles being produced more often back-to-back in the azimuthal angle. 26 1 0.9 CMS Simulation, s = 8 TeV 1 0.9 CMS Simulation, s = 8 TeV 0.0025 0.8 0.002 0.5 0.4 R2 R2 0.0015 0.003 0.7 0.6 0.001 0.3 0.6 0.0025 0.5 0.002 0.4 0.0015 0.3 0.2 0.001 0.2 0.0005 0.1 0.0005 0.1 200 400 600 800 1000 1200 1400 0 0 0 50 100 MR [GeV] 150 200 250 300 7 9 0 MET [GeV] (a) (b) 1400 0.0012 CMS Simulation, s = 8 TeV 0.3 1200 CMS Simulation, s = 8 TeV 0.001 0.25 1000 0.0008 0.2 800 0.0006 600 400 200 0 0 50 100 150 200 250 300 a.u MR [GeV] 0.0035 0.8 0.7 0 0 0.004 0.15 0.0004 0.1 0.0002 0.05 0 MET [GeV] (c) 0 0 1 2 3 4 5 6 8 Number of Jets (d) Figure 4.12: Characterization of the mb̃ = 600 GeV, mχ̃01 = 200 GeV model with 100% to χ̃02 . Z-scale units are such that the total number of events is normalized to 1. (a) R2 versus MR . (b) R2 versus E/T . (c) MR versus E/T . (d) Number of PF jets, clustered with the anti-kT algorithm with ∆R = 0.5. Even though a smaller mass splitting has less energy available to the χ̃01 , its effect is overshadowed by the explanation that the χ̃01 particles likely have more pT if they remain on the path of the original bottom squark. Examining Figure 4.16a, we see that a smaller mass splitting results in higher leading χ̃01 pT . However, this higher leading χ̃01 pT is balanced by the effect that the χ̃01 particles are produced more often back-to-back in ∆Φ with a smaller mass splitting. As a result, the E/T distribution stays roughly constant due to the two χ̃01 momentum vectors canceling each other. Overall, this effect can be attributed to the two-step decay chain. This phenomena was not present in Section 4.7. In the previous section, any effects from variable √ sampling the s distribution due to the production of bottom squarks of different masses were not removed. This likely counteracted the effect of the particle decay angles, resulting in a E/T distribution that increased with mass splitting. More importantly, however, all jets produced were 27 1 0.9 CMS Simulation, s = 8 TeV 0.0035 1 0.9 CMS Simulation, s = 8 TeV 0.006 0.8 0.003 0.8 0.005 0.7 0.5 0.002 0.4 0.0015 0.3 0.5 0.003 0.4 0.002 0.3 0.001 0.2 0.2 0.0005 0.1 0 0 0.004 0.6 R2 R2 0.7 0.0025 0.6 200 400 600 800 1000 1200 1400 0.001 0.1 0 0 0 50 100 MR [GeV] 150 300 7 9 0 (b) 1400 0.0012 CMS Simulation, s = 8 TeV 0.3 CMS Simulation, s = 8 TeV 1200 0.001 0.25 1000 0.0008 800 0.0006 600 400 200 50 100 150 200 MET [GeV] (c) 250 300 0.2 a.u MR [GeV] 250 MET [GeV] (a) 0 0 200 0.15 0.0004 0.1 0.0002 0.05 0 0 0 1 2 3 4 5 6 8 Number of Jets (d) Figure 4.13: Characterization of the mb̃ = 600 GeV, mχ̃01 = 100 GeV model with 100% to χ̃02 . Z-scale units are such that the total number of events is normalized to 1. (a) R2 versus MR . (b) R2 versus E/T . (c) MR versus E/T . (d) Number of PF jets, clustered with the anti-kT algorithm with ∆R = 0.5. soft due to the relatively smaller mass splittings, which also minimizes the effect of the particle decay angles. In summary: for the larger mass splitting models, the R2 distribution is desirable but the MR distribution is too high. We see a large effect from the two-step decay chain. 28 CMS Simulation, s = 8 TeV m~b = 600 mχ∼ = 300 0.05 m~b = 600 mχ∼ = 300 CMS Simulation, s = 8 TeV 10-1 m~b = 600 mχ∼ = 200 m~b = 600 mχ∼ = 200 m~b = 600 mχ∼ = 100 m~b = 600 mχ∼ = 100 -2 10 a.u a.u 0.04 0.03 10-3 0.02 10-4 0.01 0 0 10-5 0 200 400 600 800 10001200140016001800 0.2 0.4 0.6 0.8 MR [GeV] R2 (a) (b) 1 1.2 1.4 Figure 4.14: Razor variable distributions for the various mass splitting with fixed b̃ mass. (a) MR 1D distributions. (b) R2 1D distributions. m~b = 600 m∼χ = 300 m~b = 600 m∼χ = 200 0.05 m~b = 600 m∼χ = 100 0.04 0.08 CMS Simulation, s = 8 TeV 0.03 m~b = 600 m∼χ = 300 m~b = 600 m∼χ = 200 0.07 m~b = 600 m∼χ = 100 0.06 a.u a.u CMS Simulation, s = 8 TeV 0.06 0.05 0.04 0.03 0.02 0.02 0.01 0 0 0.01 100 200 300 400 500 600 700 800 0 0 100 200 300 400 500 600 700 800 9001000 MET [GeV] Leading Jet pT [GeV] (a) (b) Figure 4.15: Kinematic distributions for the various mass splitting with fixed b̃ mass. (a) E/T 1D distributions. (b) Leading jet pT 1D distributions (excluding H → b b̄ jets). 29 0.08 CMS Simulation, s = 8 TeV 0.06 m~b = 600 mχ∼ = 300 0.07 m~b = 600 mχ∼ = 200 0.05 m~b = 600 mχ∼ = 100 0.06 m~b = 600 mχ∼ = 100 0.04 0.05 a.u a.u m~b = 600 mχ∼ = 300 CMS Simulation, s = 8 TeV m~b = 600 mχ∼ = 200 0.04 0.03 0.03 0.02 0.02 0.01 0.01 0 0 100 200 300 400 500 600 700 800 9001000 0 -3 -2 -1 0 Leading LSP pT [GeV] LSP ∆Φ (a) (b) 1 2 3 Figure 4.16: χ̃01 kinematic distributions for the various mass splitting with fixed b̃ mass. (a) Leading χ̃01 pT 1D distributions. (b) ∆Φ between the two χ̃01 particles. 0.03 CMS Simulation, s = 8 TeV 0.025 m~b = 600 m∼χ = 300 0.2 m~b = 600 m∼χ = 200 0.18 m~b = 600 m∼χ = 200 m~b = 600 m∼χ = 100 0.16 m~b = 600 m∼χ = 100 m~b = 600 m∼χ = 300 CMS Simulation, s = 8 TeV 0.14 a.u a.u 0.02 0.015 0.12 0.1 0.08 0.01 0.06 0.04 0.005 0.02 0 0 100 200 300 400 500 600 700 800 9001000 ~ Leading b p [GeV] T (a) 0 -3 -2 -1 0 1 2 3 ~ b ∆Φ (b) Figure 4.17: Bottom squark kinematic distributions for the various mass splitting with fixed b̃ mass. (a) Leading b̃ pT 1D distributions. (b) ∆Φ between the two bottom squarks particles. 30 4.9 b̃ Mass Study with Fixed M∆ In the following models, we instead vary the bottom squark mass while keeping M∆ roughly the same. The model characteristics are given in Table 4.4. Name CLT2015-AW1 CLT2015-AW2 CLT2015-AW3 mb̃ 470 GeV 500 GeV 600 GeV mχ̃02 230 GeV 290 GeV 430 GeV mχ̃01 100 GeV 160 GeV 300 GeV M∆ 448.72 GeV 448.8 GeV 450 GeV Msplit 370 GeV 340 GeV 300 GeV BR (to χ̃02 ) 100% 100% 100% Table 4.4: Table of the models investigated in the bottom squark mass study, with their associated values of M∆ and Msplit . We see an deficit of events in the R2 tail in the smaller b̃ mass samples (Figures 4.18a, 4.19a, 4.21), as compared to the mb̃ = 600 GeV model. The R2 versus MR distribution for the b̃ = 470 model exhibits very low, clustered R2 events, as well as a tightly clustered R2 versus E/T distribution (see Figure 4.18b). As a result, this model is promising for our desired constraints. From this point, we will refer to it as the CLT2015-AW1 model for convenience. The other two models, mb̃ = 500 GeV and mb̃ = 600 GeV, will be called CLT2015-AW2 and CLT2015-AW3, respectively. This small R2 tail is likely a mixture of the phenomena from the previous two studies, since we have neither fixed b̃ nor fixed χ̃01 masses. However, the deficit of R2 events seems to be more similar to the fixed b̃ mass study. More energy is available for the b quark (Figure 4.20), which is exhibited in the higher leading jet pT if we compare Figures 4.23a and 4.10b, which increases the role of the angles of decay in the kinematics. We again have a χ̃01 ∆Φ distribution that varies greatly between the different models (Figure 4.23d). The model with the smallest mass splitting, CLT2015-AW3, again has the most back-to-back χ̃01 particles. This confirms the dependence we saw in Section 4.8. 31 1 0.9 CMS Simulation, s = 8 TeV 0.0045 0.004 1 0.9 CMS Simulation, s = 8 TeV 0.8 0.0035 0.8 0.7 R2 R2 0.0025 0.5 0.002 0.4 0.0015 0.3 0.005 0.5 0.004 0.4 0.003 0.3 0.001 0.2 0.1 0.0005 0.1 0 0 0 200 400 600 800 1000 1200 1400 0.006 0.6 0.2 0 0 0.007 0.7 0.003 0.6 0.008 0.002 0.001 50 100 MR [GeV] 150 200 250 300 7 9 0 MET [GeV] (a) (b) 1400 0.0018 CMS Simulation, s = 8 TeV 1200 CMS Simulation, s = 8 TeV 0.25 0.0014 1000 0.0012 800 0.001 0.2 a.u MR [GeV] 0.3 0.0016 600 0.0008 0.15 400 0.0006 0.1 0.0004 200 0 0 0.0002 50 100 150 200 MET [GeV] (c) 250 300 0 0.05 0 0 1 2 3 4 5 6 8 Number of Jets (d) Figure 4.18: Characterization of the mb̃ = 470 GeV, mχ̃01 = 100 GeV model with 100% to χ̃02 . Z-scale units are such that the total number of events is normalized to 1. (a) R2 versus MR . (b) R2 versus E/T . (c) MR versus E/T . (d) Number of PF jets, clustered with the anti-kT algorithm with ∆R = 0.5. 32 1 0.9 CMS Simulation, s = 8 TeV 0.0035 0.003 0.8 0.7 0.5 0.8 0.005 0.5 0.4 0.0015 0.4 0.3 0.001 0.3 0.2 0.003 0.002 0.2 0.0005 0.1 0 0 0.004 0.6 R2 R2 0.002 0.006 0.7 0.0025 0.6 1 0.9 CMS Simulation, s = 8 TeV 200 400 600 800 1000 1200 1400 0.001 0.1 0 0 0 50 100 MR [GeV] 150 250 300 7 9 0 MET [GeV] (a) (b) 1400 0.0016 CMS Simulation, s = 8 TeV 0.3 0.0014 1000 0.0012 0.25 0.001 0.2 800 0.0008 600 a.u 1200 MR [GeV] 200 CMS Simulation, s = 8 TeV 0.15 0.0006 0.1 400 0.0004 200 0 0 0.0002 50 100 150 200 MET [GeV] (c) 250 300 0 0.05 0 0 1 2 3 4 5 6 8 Number of Jets (d) Figure 4.19: Characterization of the mb̃ = 500 GeV, mχ̃01 = 160 GeV model with 100% to χ̃02 . Z-scale units are such that the total number of events is normalized to 1. (a) R2 versus MR . (b) R2 versus E/T . (c) MR versus E/T . (d) Number of PF jets, clustered with the anti-kT algorithm with ∆R = 0.5. Figure 4.20: The decay spectrum for the mb̃ = 470 GeV model. 33 CMS Simulation, s = 8 TeV 0.05 m~b = 470 GeV m~b = 500 GeV m~b = 600 GeV 0.04 10-2 a.u a.u m~b = 470 GeV m~b = 500 GeV m~b = 600 GeV CMS Simulation, s = 8 TeV 10-1 0.03 10-3 0.02 10-4 0.01 0 0 10-5 0 200 400 600 800 10001200140016001800 0.2 0.4 0.6 0.8 MR [GeV] R2 (a) (b) 1 1.2 1.4 Figure 4.21: Razor variable distributions for the various b̃ models with fixed M∆ . (a) MR 1D distributions. (b) R2 1D distributions. 0.08 CMS Simulation, s = 8 TeV 0.07 0.12 CMS Simulation, s = 8 TeV 0.1 m~b = 470 GeV m~b = 500 GeV m~b = 600 GeV 0.08 0.05 a.u a.u 0.06 m~b = 470 GeV m~b = 500 GeV m~b = 600 GeV 0.04 0.03 0.06 0.04 0.02 0.02 0.01 0 0 100 200 300 400 500 600 700 800 9001000 0 0 100 200 300 400 500 600 700 800 9001000 Leading Jet pT [GeV] Subleading Jet pT [GeV] (a) (b) 0.1 CMS Simulation, s = 8 TeV 0.06 0.1 CMS Simulation, s = 8 TeV 0.08 a.u a.u 0.08 m~b = 470 GeV m~b = 500 GeV m~b = 600 GeV m~b = 470 GeV m~b = 500 GeV m~b = 600 GeV 0.06 0.04 0.04 0.02 0.02 0 0 100 200 300 400 500 600 700 800 9001000 0 0 100 200 300 400 500 600 700 800 9001000 Leading LSP pT [GeV] Subleading LSP pT [GeV] (c) (d) Figure 4.22: Kinematic distributions for the various b̃ models with fixed M∆ . (a) Leading jet pT 1D distributions (excluding H → b b̄ jets). (b) Subeading jet pT 1D distributions (excluding H → b b̄ jets). (c) Leading χ̃01 pT 1D distributions. (d) Subeading χ̃01 pT 1D distributions. 34 0.04 m~b = 470 GeV m~b = 500 GeV m~b = 600 GeV CMS Simulation, s = 8 TeV 0.035 0.03 m~b = 470 GeV m~b = 500 GeV m~b = 600 GeV 0.05 CMS Simulation, s = 8 TeV 0.04 a.u a.u 0.025 0.02 0.015 0.03 0.02 0.01 0.01 0.005 0 0 100 200 300 400 500 600 700 800 9001000 0 0 100 200 300 400 500 600 700 800 9001000 ~ Leading b p [GeV] ~ Subleading b p [GeV] T T (a) 0.2 (b) 0.16 0.14 m~b = 470 GeV m~b = 500 GeV m~b = 600 GeV CMS Simulation, s = 8 TeV 0.05 0.04 0.12 a.u a.u 0.06 m~b = 470 GeV m~b = 500 GeV m~b = 600 GeV CMS Simulation, s = 8 TeV 0.18 0.1 0.03 0.08 0.02 0.06 0.04 0.01 0.02 0 -3 -2 -1 0 1 2 3 0 -3 -2 -1 0 ~ b ∆Φ LSP ∆Φ (c) (d) 1 2 3 Figure 4.23: Kinematic distributions for the various b̃ models with fixed M∆ . (a) Leading b̃ pT 1D distributions. (b) Subleading b̃ pT 1D distributions. (c) ∆Φ between the two bottom squarks particles. (d) ∆Φ between the two χ̃01 particles. 35 4.10 Investigating the CLT2015-AW1 Model 1 0.9 CMS Simulation, s = 8 TeV 14 1 0.9 CMS Simulation, s = 8 TeV 4 0.8 12 0.8 3.5 10 0.7 3 0.6 2.5 0.7 8 0.5 R2 R2 0.6 0.5 0.4 6 0.4 0.3 4 0.3 0.2 2 0.1 0 0 103 2 1.5 0.2 1 0.1 0.5 0 103 MR [GeV] MR [GeV] (a) (b) 1 0.9 CMS Simulation, s = 8 TeV 0.8 0.6 R2 12 10 0.7 8 0.5 6 0.4 0.3 4 0.2 2 0.1 0 0 103 0 MR [GeV] (c) √ Figure 4.24: Event populations of the CLT2015-AW1 Model at s = 8 TeV in each of the boxes, with the total amount of events passing the selection scaled to 100. (a) High pT box (b) Hbb box (c) Overflow box. We examine the event distribution in each of the boxes in Figure 4.24. The binning boundaries are again motivated by the Higgs to diphoton supersymmetry search [6]. They are as follows: 1. High pT box: MR : {150, 200, 300, 500, 1600, 3000} GeV. R2 : {0, 0.5, 0.1, 0.15,0 .2,1}. 2. Hbb box: MR : {150, 300, 3000} GeV. R2 : {0, 0.5, 1}. 3. Overflow box: MR : {150, 250, 400, 1400, 3000} GeV. R2 : {0, 0.05, 0.1, 0.15, 1}. We see a high clustering of events in the MR ∈ [500, 1600] GeV and R2 ∈ [0, 0.1] region for the High pT box, and in the MR ∈ [400, 1400] GeV and R2 ∈ [0, 0.05] region for the Overflow box. The decrease in events at high R2 is apparent and ideal for complying with current bounds. 36 4.11 Counting Experiment 1 0.9 CMS Simulation, s = 8 TeV 1 0.9 CMS Simulation, s = 8 TeV 10 0.8 0.7 0.8 0.7 8 0.6 0.5 R2 R2 0.6 6 0.4 0.4 4 0.3 0.2 0.3 0.2 2 0.1 0 0.5 0.1 0 103 0 103 MR [GeV] MR [GeV] (a) (b) 1 0.9 CMS Simulation, s = 8 TeV 0.8 0.7 22 20 18 16 14 12 10 8 6 0.6 R2 0.24 0.22 0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0.5 0.4 0.3 0.2 0.1 0 103 4 2 0 MR [GeV] (c) √ Figure 4.25: Event populations of the SM Higgs production background at s = 8 TeV in each of the boxes, with the total amount of events passing the selection scaled to 100. (a) High pT box (b) Hbb box (c) Overflow box. We can do a counting experiment in order to estimate the cross section of the mb̃ = 470 GeV model needed in order for discovery at 8 TeV. We make the assumption that the main background is Standard Model Higgs background. Again, we generate SM Higgs events with PYTHIA 8.1 [34] [35] and then filter using the same selection process as before in Section 4.4. For consistency, we force the Higgs boson to decay to two photons. At 13 TeV, the theoretical total cross section of all SM Higgs production is 22.10 pb [40]. If we also assume an integrated luminosity of 19.3 f b−1 for the data collected by CMS in 2012 [41]. We then scale the amount of events produced by the branching ratio of Higgs to two photons (2.28 37 ×10−3 ) to get the total number of expected events: σSM Higgs × L × BRγγ = 22.1 pb × 19.3 f b−1 × 0.00228 = 972.5 events From the produced PYTHIA events, if we have P events passing out of N produced events, then q δN 2 2 we can calculate a selection efficiency with an error of δe = e × ( δP P ) + ( N ) , where e is the selection efficiency. Out of 208505 events produced, 25230 passed, giving e ≈ 0.1210 ± .0008066, assuming Poisson errors. We then expect 117.7 ± 0.7844 events to pass the selection. We then examine the Standard Model Higgs background events in the three boxes from Section 4.5. For the Overflow box, we have a selection efficiency from the total production of 0.04816 ± 0.00049. We can also calculate the selection efficiencies for each box (see Table 4.5). Then we get 46.84 ± 0.48 events in the Overflow box, 0.5550 ± 0.0509 events in the Hbb box, and 38.26 ± 0.43 events in the High pT box (some events do not pass the MR , R2 definitions of the boxes). Using a likelihood-based statistical test described in [42], we can assume a fixed number of background events and estimate the cross section of total bottom squark production needed for a discovery at 5σ for the fixed background. We will briefly summarize the method that is described in [42]. We assume a Poisson likelihood function of L(µ) = (µs + b)n −(µs+b) e , n! where µ is described as a “signal strength” parameter, s is the number of expected signal events, b is the number of expected background events, and n is the number of observed events. The test statistic is q0 =   −2 ln L(0) L(µ̂ µ̂ ≥ 0,  0 µ̂ < 0. Using asymptotic simplifying assumptions described in [42], the authors derive a median significance value of Z̃ = p 2 ∗ ((s + b) ln(1 + s/b) − s). We then solve for the value of the signal that gives us Z̃ = 5 given a fixed background. We will focus on one box, the Overflow box, which would need 38.17 ± 0.18 signal events. The error on the number of signal events needed is most likely overestimated (ignoring systematic error) since we simplified the calculation by inputing b+ δb into our Z̃=5 equation as it cannot be solved explicitly. Our selection efficiency for signal events in the Overflow box is 0.2798 ± 0.0021 (derived 38 from MC simulation). If we divide the number of events by the Higgs to two photons branching ratio [39], and then by the signal efficiency × integrated luminosity, we round to two significant figures and arrive at a cross section of 3.1 ± 0.3 pb. Box Name High pT Hbb Overflow SM Higgs Efficiency 0.03934 0.0005707 0.04816 Error 0.00044 0.0000523 0.00049 Signal Efficiency 0.4080 0.06748 0.2798 Error 0.0027 0.00094 0.0021 Table 4.5: Selection efficiencies of the SM Higgs production background and the mb̃ = 470 GeV signal in the various boxes. We can improve upon this cross section if we choose a more restricted box with lower background. If we restrict to a sum of bins in the Overflow box where we see a cluster of signal, i.e. MR ∈ [400, 1400] GeV and R2 ∈ [0.05, 1], we have an efficiency for SM Higgs background of 0.000149 ± 0.000027 with Poisson error. That corresponds to 0.145 ± 0.026 SM Higgs events. Then, using the same likelihood test as before, we require 4.76 ± 0.20 signal events in this defined bin. The signal selection efficiency is estimated as 0.1098 ± 0.0012. Again, dividing by the branching ratio, the integrated luminosity, and the signal efficiency, we get a corresponding cross section of 0.99 ± 0.04 pb. The error on these cross sections are most likely greatly underestimated. In a future calculation we will consider the systematic errors more carefully, which would include the error on photon identification, jet energies, photon resolution, b-tagging efficiencies, etc. This is a generator-level study and gives a first estimate of the cross-section needed for discovery. Assuming that the SM Higgs background predominates, the conclusion of this study is that √ s = 8 TeV CMS dataset requires a production cross section of 0.99 pb for a 5 sigma discovery. The predicted cross section for bottom squark pair production at 8 TeV is 0.128326 ± 14.5144% pb for a bottom squark of mb̃ = 470 GeV. This is a good indicator for the future at 13 and 14 TeV. 39 Chapter 5 Conclusion The goal of this thesis was to examine the potential of using the Higgs boson as a tool in searching for new physics. To accomplish this, we investigated the production of bottom squarks that decay to a Higgs boson, where we varied different working parameters of the model. After tuning these parameters, we pinpointed a desirable model which would not likely have been discovered in Run I, but has a large potential for discovery in Run II. Further work would involve studying the model without an 100% branching ratio to the Higgs and instead consider the situation where a Z boson is sometimes produced. We would also like to reproduce the events with a full simulation of the detector. Then, an understanding of the High Level Trigger was developed through the design of a trigger to select for events with H → b b̄. This complements the bottom squark model study extremely well since events that have one Higgs boson decaying to two photons will likely have the other Higgs decaying to two b quarks. As a result, the discussed model should also pass the designed trigger; it has > 3 jets, razor variable distributions that cluster at higher values than the trigger thresholds of MR > 300 GeV and R2 > 0.0196, and two Higgs bosons. This model, CLT2015-AW1, is a non-standard model which does not rely on large E/T for background reduction. Furthermore, the studies were conducted using a simplified model interpretation, which increases the utility of these studies. CLT2015-AW1 simply describes the production of a particle (p̃1 ) largely produced in pairs, that decays p̃1 →b p̃2 →b H p̃3 , where p̃3 is an invisible particle and p̃2 is an intermediate particle. 40 Appendix A A.1 Samples The following tables list the simulated event samples produced by CMS internal members that were used for the trigger studies. These were produced using MadGraph 5 [43], PYTHIA 6 [34], and CMS Fast Simulation [44]. They were made available for members within CMS. /QCD Pt-30to50 Tune4C 13TeV pythia8/Fall13dr-castor tsg PU40bx25 POSTLS162 V2-v1/GEN-SIM-RAW /QCD Pt-50to80 Tune4C 13TeV pythia8/Fall13dr-castor tsg PU40bx25 POSTLS162 V2-v1/GEN-SIM-RAW /QCD Pt-80to120 Tune4C 13TeV pythia8/Fall13dr-castor tsg PU40bx25 POSTLS162 V2-v1/GEN-SIM-RAW /QCD Pt-120to170 Tune4C 13TeV pythia8/Fall13dr-castor tsg PU40bx25 POSTLS162 V2-v1/GEN-SIM-RAW /QCD Pt-170to300 Tune4C 13TeV pythia8/Fall13dr-castor tsg PU40bx25 POSTLS162 V2-v1/GEN-SIM-RAW /QCD Pt-300to470 Tune4C 13TeV pythia8/Fall13dr-castor tsg PU40bx25 POSTLS162 V2-v1/GEN-SIM-RAW /QCD Pt-470to600 Tune4C 13TeV pythia8/Fall13dr-castor tsg PU40bx25 POSTLS162 V2-v1/GEN-SIM-RAW /QCD Pt-600to800 Tune4C 13TeV pythia8/Fall13dr-castor tsg PU40bx25 POSTLS162 V2-v1/GEN-SIM-RAW /QCD Pt-800to1000 Tune4C 13TeV pythia8/Fall13dr-castor tsg PU40bx25 POSTLS162 V2-v1/GEN-SIM-RAW Table A.1: Data samples used to calculate trigger rates. These can be accessed through the data aggregation system (DAS) system. /store/user/dalfonso/T2qq 400 150 /store/user/dalfonso/T2qq 450 400 /store/user/dalfonso/T2tt 800 100 /TT Tune4C 13TeV-pythia8-tauola/Fall13dr-tsg PU40bx50 POSTLS162 V2-v1/GEN-SIM-RAW Table A.2: Data samples used to calculate L1 trigger efficiencies. The first three samples are unpublished to the DAS but may be accessed by CMS members with details located at [45]. The others can be accessed through the DAS system. /RelValTTbarLepton 13/CMSSW 7 3 0-MCRUN2 73 V7-v1/GEN-SIM-DIGI-RAW-HLTDEBUG Table A.3: Data samples used for the muon study. 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