Measurements of Event Shapes in Deep Inelastic Scattering at HERA with ZEUS docx

Measurements of Event Shapes in Deep Inelastic Scattering at HERA with ZEUS by Adam A. Everett A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Physics) at the University of Wisconsin – Madison 2006 c  Copyright by Adam A. Everett 2006 All Rights Reserved Measurements of Event Shapes in Deep Inelastic Scattering at HERA with ZEUS Adam A. Everett Under the supervision of Professor Wesley H. Smith At the University of Wisconsin — Madison Mean values and differential distributions of event-shape variables have been studied in neutral current deep inelastic scattering using an integrated luminosity of 82.2 inverse pico-barns collected with the ZEUS detector at HERA. The kinematic range was Q-squared from 80 to 20480 GeV-squared and Bjorken-x from 0.0024 to 0.6, where Q-squared is the virtuality of the exchanged boson. The Q-dependence is com- pared with a model based a combination of next-to-leading-order QCD calculations with next-to-lead-logarithm corrections and the Dokshitzer-Webber non-perturbative power corrections. 4 i Abstract Mean values and differential distributions of event-shape variables have been studied in neutral current deep inelastic scattering using an integrated luminosity of 82.2 pb −1 collected with the ZEUS detector at HERA. The kinematic range was 80 < Q 2 < 20480 GeV 2 and 0.0024 < x < 0.6, where Q 2 is the virtuality of the exchanged boson and x is the Bjørken variable. The Q-dependence is compared with a model based a combination of next-to-leading-order QCD calculations with next-to-lead- logarithm corrections and the Dokshitzer-Webber non-perturbative power corrections. ii Acknowledgements I would like to thank the High Energy Physics de- partment at the University of Wisconsin for the opportunity to perform research with an outstanding group of physicists at an outstanding university. I would especially like to acknowledge and thank Wesley Smith and Don Reeder for their guidance, support, and superb dedication. I would also like to thank the members of the ZEUS Collaboration who made data taking possible, and who gave me great advice on all of the details of an analysis. A very special thanks are due to my colleagues from the University of Glasgow, Ian Skillicorn and Steven Hanlon, who very patiently taught me the ropes of an event shape analysis, and shared so much of their knowledge and experience with me. And, of course, I thank Alexandre Savin and Dorian K¸cira for being my ”advisors away from home.” Thank you to the friends who were always willing to play cards, watch movies, and play when we were in danger of doing too much work. I give special thanks to my parents and family for their support and teasing. And I offer a huge thank you to my wife, Jayda, for putting up with me and following me around the globe. I will never be able to thank you enough for all you have done for me during this adventure. iii Contents Abstract i Acknowledgements ii 1 Introduction 1 1.1 Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.1 Leptons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.2 Quarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.3 Bosons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.4 Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Quantum Chromodynamics . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.1 Perturbative Quantum Chromodynamics . . . . . . . . . . . . . 12 2 Event Shapes in Deep Inelastic Scattering 15 2.1 Deep Inelastic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.1 Kinematic description . . . . . . . . . . . . . . . . . . . . . . . 20 2.1.2 DIS Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.1.3 QCD Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 iv 2.2 Introduction to Event Shapes in Deep Inelastic Scattering . . . . . . . 26 2.2.1 Hadronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.2.2 Power Corrections . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.2.3 Mean Non-Perturbative Calculations . . . . . . . . . . . . . . . 30 2.2.4 Differential Non-Perturbative Calculations . . . . . . . . . . . . 31 2.3 Definition of the Event Shapes . . . . . . . . . . . . . . . . . . . . . . . 31 2.4 The Breit Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3 Experimental Setup 39 3.1 Detection of Particle Interactions . . . . . . . . . . . . . . . . . . . . . 39 3.1.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.1.2 Basic Experimental Design . . . . . . . . . . . . . . . . . . . . . 44 3.2 Deutsches Elektronen Synchrotronen . . . . . . . . . . . . . . . . . . . 48 3.3 Hadron-Elektron Ring Anlage . . . . . . . . . . . . . . . . . . . . . . . 49 3.3.1 HERA Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.3.2 HERA Experiment Halls . . . . . . . . . . . . . . . . . . . . . . 53 3.3.3 HERA Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.4 The ZEUS Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.4.1 The Tracking Detectors . . . . . . . . . . . . . . . . . . . . . . 59 3.4.2 The Uranium Calorimeter and Plastic Scintillator . . . . . . . . 63 3.4.3 Background Rejection . . . . . . . . . . . . . . . . . . . . . . . 67 3.5 Trigger and Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . 69 4 Event Simulation 73 4.1 Monte Carlo Event Generation . . . . . . . . . . . . . . . . . . . . . . 74 v 4.1.1 Monte Carlo Input: Parton Distribution Functions and Parton Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.1.2 Hard Process and Higher Order Effects . . . . . . . . . . . . . . 76 4.1.3 Soft Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.2 Monte Carlo Programs in HEP . . . . . . . . . . . . . . . . . . . . . . 80 4.3 Detector Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.4 Hadronic Final States . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5 NLO Calculations 83 5.1 The Running Coupling Constant . . . . . . . . . . . . . . . . . . . . . 83 5.2 NLO Integration Techniques . . . . . . . . . . . . . . . . . . . . . . . . 84 5.3 NLO Parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.3.1 Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.3.2 Differential Distributions . . . . . . . . . . . . . . . . . . . . . . 87 5.4 DISENT, DISASTER, DISPATCH, and DISRESUM Programs . . . . . 88 5.4.1 Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5.4.2 Differential Distributions . . . . . . . . . . . . . . . . . . . . . . 89 6 Event Reconstruction 95 6.1 Particle Track and Vertex Reconstruction . . . . . . . . . . . . . . . . . 95 6.2 Calorimeter Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 6.2.1 Calorimeter Cell Removal . . . . . . . . . . . . . . . . . . . . . 98 6.2.2 Calorimeter Energy Corrections . . . . . . . . . . . . . . . . . . 98 6.3 Electron Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.4 Hadronic System Reconstruction . . . . . . . . . . . . . . . . . . . . . 102 vi 6.5 Event Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.5.1 The Electron Method . . . . . . . . . . . . . . . . . . . . . . . . 105 6.5.2 The Jacquet-Blondel Method . . . . . . . . . . . . . . . . . . . 107 6.5.3 The Double-Angle Method . . . . . . . . . . . . . . . . . . . . . 107 6.6 Calorimeter Cells and Energy Flow Objects (EFOs) . . . . . . . . . . . 108 6.7 Boosting to the Breit Frame . . . . . . . . . . . . . . . . . . . . . . . . 110 6.8 Reconstruction Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 111 7 Event Selection 113 7.1 Online Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 7.1.1 First Level Trigger (FLT) . . . . . . . . . . . . . . . . . . . . . 115 7.1.2 Second Level Trigger (SLT) . . . . . . . . . . . . . . . . . . . . 116 7.1.3 Third Level Trigger (TLT) . . . . . . . . . . . . . . . . . . . . . 116 7.2 Offline Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 7.2.1 Trigger Bits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 7.2.2 Electron Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 118 7.2.3 Background Rejection . . . . . . . . . . . . . . . . . . . . . . . 119 7.2.4 Kinematic Selection and Phase Space Definition . . . . . . . . . 120 7.2.5 Particle Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 121 8 Analysis Method 125 8.1 Monte Carlo Description of the Data . . . . . . . . . . . . . . . . . . . 126 8.2 Data Corrected to the Hadron Level . . . . . . . . . . . . . . . . . . . 133 8.3 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . 137 [...]... scattering formulae, describing the internal structure of the proton (also discussed in Section 2.1.2) 2.1 Deep Inelastic Scattering Deep Inelastic Scattering is the name given to the scattering process used to probe the insides of hadrons using leptons The interaction proceeds through the exchange of a probe Figures 2.1 and 2.2 are representative diagrams of deep inelastic scattering (DIS) events... Chapter 2 Event Shapes in Deep Inelastic Scattering e(k’) θe e(k) 0 ± γ ,Z ,W (q=k-k’) P(p) X(p+q) Figure 2.1: Diagram representation of a deep inelastic scattering process with a boson exchanged between a lepton and a proton In particle physics, scattering is a class of phenomena by which particles are deflected by collisions with other particles Scattering experiments consist of bombarding a target with. .. themselves, are left intact Inelastic Scattering: the target particle is excited For example if a nucleus is bombarded by neutrons, it may be excited to some nuclear resonance Deep Inelastic Scattering: the target (and sometimes the incident particle) is destroyed and completely new particles may be created Mathematic descriptions of scattering involve parameters which (1) describe the distance of closest approach... incident particle would come to the target if it moved in a straight line) and (2) the angle of deflection The distribution of deflection angles is described by a function known as the differential cross section which is discussed in Section 2.1.2 In more complicated cases of scattering, such as deep inelastic scattering of electrons and protons, so-called form factors have to be multiplied to the scattering. .. a beam of particles and measuring the number of particles emerging in various directions The measured distribution leads to understanding about the interactions that take place between the target and the scattered particle Three categories of particle physics scattering experiments are: Elastic Scattering: only the momentum of the target and incident particles is changed 16 The target and incident... U(1) The U signifies that the transformation is unitary: M † M = I The unitary property implies that there is an inherently conservative nature to the transformation The 1 signifies that the matrix is of dimension 1 The success of QED led eventually to the combination of the U(1) description of QED with an SU(2) description of the weak force to form a SU(2) × U(1) structure for a combined electroweak theory... discoveries of the electron and proton helped to lead to Max Born’s declaration that “Physics as we know it will be over in six months.” Figure 1.1: Conceptual views reflecting our understanding of the atom at different times in history Atoms were once thought to be the smallest constituent of matter, but the ability to probe the atom at higher energies has led to a deeper understanding of its internal... effect means that the strength of the interaction actually increases approximately linearly with distance Coupling Constant The strength of the strong coupling is characterized by the coupling constant αs Mathematically, αs is expressed as: 1 β0 µ2 = ln( 2 R ) αs (µ2 ) 4π ΛQCD R (1.2) µR , the renormalization scale, is the scale at which divergences in the theory are factored into the coupling [4] It... A Treatment of Statistical Uncertainties 227 A.1 Differential Distribution 227 A.2 Means 230 B Data Tables 233 viii ix List of Tables 3.1 The integrated luminosity delivered by HERA I and HERA II and gated by ZEUS for each year of running 55 3.2 Active and inactive dimensions of the CTD 60 3.3 Radiation... generators, which corresponds to the number of colorless combinations of two gluons discussed above Additionally, QCD is non-Abelian which means that the group operations are not commutative and that the generators can be self interacting as described above 1.2 Quantum Chromodynamics Quantum chromodynamics currently stands as the framework for describing the interactions of all strongly interacting . Measurements of Event Shapes in Deep Inelastic Scattering at HERA with ZEUS by Adam A. Everett A dissertation submitted in partial fulfillment of the requirements. Reserved Measurements of Event Shapes in Deep Inelastic Scattering at HERA with ZEUS Adam A. Everett Under the supervision of Professor Wesley H. Smith At the University of