Beyond the Standard Model Identification of Leptoquark Events in Simulated electron-proton Collisions Joshua LaBounty* In collaboration with Dr. Abhay Deshpande and Dr. Nils Feege May 2017 Abstract In the Standard Model (SM) of particle physics, each conservation law is associated with a symmetry, as stated by Emmy Noether's eponymous theorem. Experiments to date have not shown any violations of the observed conservation of lepton flavor (the number of each generation of lepton) for the charged, massive leptons (electron, muon, and tau). However, within the SM there exists no known symmetry which would lead to this observed conservation. In fact, Lepton Flavor Violation (LFV) events have been shown to occur in solar neutrinos (neutrino oscillations, which are possible due to their low masses). Discounting Lepton Flavor Conservation, the SM cross sections of LFV events for the charged leptons are predicted to lie outside the reach of any current or planned experiment. However, many models of Beyond the Standard Model (BSM) physics predict the existence of leptoquarks which would mediate flavor violations and increase the cross sections for LFV to within the realm of planned experiments. Thus, the study of leptoquarks provides an avenue with which to probe BSM physics. Studies done at HERA have put constraints on the mass and coupling strength of such leptoquarks. Here we study the e− ! τ − conversion process using the LQGENEP event generator. We seek to distinguish the characteristic 3-π decay of the τ − from SM Deep Inelastic Scattering (DIS) decay products using Geant4 simulations of the current Electron Ion Collider (EIC) detector design (based around sPHENIX) in the center of mass energy range of 32 − 181 GeV. To do this, we employ standard anti- kt jet finding algorithms to locate jets in concert with machine learning modules to classify them. In doing so, we analyze the effectiveness of the proposed EIC detector for probing beyond the limits set by previous experiments. *[email protected] 1 Contents 1 Introduction 5 1.1 The Standard Model . .5 1.1.1 Deep Inelastic Scattering (DIS) . .6 1.2 Leptoquarks: Looking Beyond the Standard Model . .7 1.3 The Case for the EIC . .9 1.4 The Case for Leptoquark Studies at EIC . 11 2 Generator Level Studies 12 2.1 LQGENEP . 12 2.2 Leptoquark vs. DIS: A Characteristic Signature . 13 3 Detector Level Studies 15 3.1 Geant4 Simulations . 15 3.2 Jet Reconstruction . 18 3.3 Jet Identification . 21 3.3.1 Initial Cuts . 21 3.3.2 Application of Machine Learning . 23 3.3.3 Energy Dependence . 26 4 Results and Discussions 28 5 Future Studies 28 A Monte Carlo Event Generation 30 B Codebase 31 C Additional Figures 33 2 List of Figures 1 The Standard Model of particle physics [20]. .5 2 Two DIS events, one in which the proton breaks up and one in which it remains whole . .6 3 Feynman diagrams depicting the e ! τ scattering process, which is mediated by a leptoquark. Time flows from left to right. α, β = 1, 2, 3 representing the three generations of quarks. .8 4 Profile of the EIC-sPHENIX detector in η (Equation 1) and φ.........9 5 η vs. φ for τ − from a 20x250 GeV collision. 12 6 η vs. transverse momentum for τ − from a 20x250 GeV collision. 12 7 Transverse momentum vs. total momentum for τ − from a 20x250 GeV collision. 12 8 η vs. φ for τ − for various collision energies (1; 000; 000 events). 13 9 ∆η vs. ∆φ for τ − jets (20x250 GeV collision). 14 10 ∆η vs. ∆φ for DIS jets (20x250 GeV collision). 14 11 Annotated diagram of the EIC detector and its major subsystems [18]. 15 12 Jets in the barrel calorimeters for a single event. Each point on this plot represents a tower which was identified as part of a jet. The calorimeters are arranged by an assigned ID number; where 1 is the CEMC, 2 is the Inner HCAL, and 3 is the Outer HCal. 19 13 ∆η vs. ∆φ for τ − jets (20x250 GeV collision). 20 14 ∆η vs. ∆φ for DIS jets (20x250 GeV collision). 20 15 Comparison of DIS and τ jets from a single event (20x250 GeV). 21 16 Plot showing a linear cut between global η and mjet. In this figure, Class A refers to DIS jets and Class B refers to τ jets. 23 17 Accuracy of different machine learning algorithms with the smaller, jet-only data set. 24 18 Accuracy of different machine learning algorithms with the larger, jet+global data set. 24 19 Monte Carlo calculation of the value of π [21]. As we increase the number of points, the accuracy of our calculation increases. 31 20 Scatter plots of all of the parameters in the smaller .csv file, for a 20x250 GeV collision. 33 21 Plot showing the correlation of the different variables used in this analysis. The x and y axes are the same values. A darker box indicates a more correlated set of values. 34 List of Tables 1 Confusion Matrix for a linear division of 20x250 τ vs. DIS jets. This confusion matrix was created using the division in Figure 16. 23 3 2 Confusion Matrix for an AdaBoost Classifier trained on ∼ 800 20x250 τ vs. DIS jets with jet only variables. Total accuracy: 86:7%. 25 3 Confusion Matrix for an AdaBoost Classifier trained on ∼ 800 20x250 τ vs. DIS jets with jet and global variables. Total accuracy: 90:5%. 25 4 Confusion Matrix for a Logistic Regression Classifier trained on ∼ 800 20x250 τ vs. DIS jets with jet and global variables and τ:DIS weighting of 1:1. Total accuracy: 84:4%. ................................. 26 5 Confusion Matrix for a Logistic Regression Classifier trained on ∼ 800 20x250 τ vs. DIS jets with jet and global variables and τ:DIS weighting of 10:1. Total accuracy: 75:6%. ................................. 26 6 Confusion matrices for the AdaBoost algorithm for a variety of different elec- tron and proton beam energies. 27 4 1 Introduction 1.1 The Standard Model Figure 1: The Standard Model of particle physics [20]. The Standard Model (SM) of particle physics is one of the greatest achievements of 20th century physics. It describes all of the known particles of matter and anti-matter and the means through which they interact. The particles of the standard model fall into two categories: fermions and bosons. Fermions have a spin of 1=2 and include both quarks and leptons. Quarks carry color charge, which means that they can interact with the strong nuclear force. They also participate in electromagnetic and weak interactions. Leptons, on the other hand, interact only through the weak and (if electrically charged) electromagnetic forces. There are three generations (columns) of both quarks and leptons, but the reason for this parallel is as yet unknown. Bosons have a spin of 0 (Higgs) or 1 (gauge bosons). These spin-1 particles are mediators of the fundamental forces. These particles make up the fundamental building blocks of the visible universe as we know it. A complete description of the Standard Model, and its underlying physics, can be found in many introductory physics textbooks such as [16]. 5 1.1.1 Deep Inelastic Scattering (DIS) (a) Proton breaks up [1] (b) Proton remains whole [17] Figure 2: Two DIS events, one in which the proton breaks up and one in which it remains whole . Deep Inelastic Scattering (DIS) is a standard model process by which a lepton interacts with one of the quarks inside a nucleon. For the purposes of this paper, we will limit ourselves to the case of an electron interacting with the constituent quarks of a proton. In collider experiments, DIS is useful for using the electron as a probe to explore the internal structure of the proton (see Section 1.3). At low energies (< 1 GeV), interactions between electrons and protons can be considered roughly elastic, and the electron interacts with the proton as if it were a point particle. However, as the energy of the interaction is increased, and the de Broglie wavelength of the electron becomes small compared to the size of the proton, we begin to observe the substructure within the proton. At these high energies, the electron will exchange a virtual photon with one of the quarks inside the proton and cause it to recoil. The energy of the electron is altered (hence inelastic) and it is scattered. The scattering of the electron depends on which of the quarks participated in the reaction, and therefore measurements of the scattering angle can provide insight into the substructure of the proton. Experiments of this nature provided the first direct evidence for the existence of the 3 quark structure of the proton and neutron [23]. Today, the energies of these experiments are sufficient to probe structure which exists beyond the three valance quarks, such as the sea 6 quarks and gluons. The energies of the interaction are also sufficient to cause the proton to break into multiple pieces of hadronic debris (Figure 2a). Some DIS experiments (exclusive and semi-inclusive DIS) endeavor to measure these particles as well, while others (inclusive DIS) measure only the final state lepton. A more mathematical description of these processes can be found in [1, Pg. 18-20, 32] In this study, we expect the majority of the background events to be DIS events as described in Figure 2a. In these events, the quark is ejected from the proton and forms a hadronic jet (see Section 2.2). 1.2 Leptoquarks: Looking Beyond the Standard Model Within the standard model, there are a number of observed conservation laws.