MONTE CARLO SIMULATION OF PARTICLE PRODUCTION AND DECAY AT HIGH-ENERGY COLLIDERS A DISSERTATION SUBMITTED TO THE DEPARTMENT OF PHYSICS AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Michael Edmund Davenport August 2010 © 2010 by Michael Edmund Davenport. All Rights Reserved. Re-distributed by Stanford University under license with the author. This work is licensed under a Creative Commons Attribution- Noncommercial 3.0 United States License. http://creativecommons.org/licenses/by-nc/3.0/us/ This dissertation is online at: http://purl.stanford.edu/bm776hk7345 ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Michael Peskin, Primary Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. JoAnne L. Hewett I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Shamit Kachru Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost Graduate Education This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives. iii Acknowledgments I am deeply indebted to a great number of people for helping me to complete my graduate studies and this thesis. In particular I would like to thank my adviser Michael Peskin for his constant help and support and for his patience through these past several years. I would also like to thank the many friends both in the Physics community and throughout Stanford who have helped my persevere and stay sane. They are far to numerous to list both in number or in value of their support. Finally, I could never fully put in words how grateful I am for my parents for their continued love, support, and encouragement iv Contents Acknowledgments iv 1 Introduction 1 2 Overview 6 3 Physics Review 9 3.1 Hard Processes . 12 3.2 Individual decays . 15 3.3 Helicity Amplitudes . 20 3.4 Color Structures . 22 3.5 Multiple decay channels . 27 3.6 Beam Physics . 30 3.7 Calculation Conventions . 33 3.7.1 Angular Conventions . 33 3.7.2 Polarization Conventions . 36 4 Monte Carlo Methods 42 4.1 Monte Carlo Integration . 43 4.2 Monte Carlo Event Generation . 48 4.3 Adaptive Monte Carlo . 50 5 Object-Oriented Programming and Class Hierarchy 56 5.1 Philosophy of Object-Oriented Programming . 56 v 5.1.1 C++ programming conventions . 58 5.2 Class Hierarchy . 60 5.3 Monte Carlo Classes . 61 5.4 Process Classes . 65 5.5 Decay Classes . 68 5.6 Luminosity Classes . 71 5.7 Pandora Class and Output . 72 6 Implementation of New Physics 75 6.1 Common Tools . 75 6.2 Invariants Classes . 79 6.3 Using the kinematic classes . 81 6.3.1 Processes . 81 6.3.2 Decays . 88 6.4 Using an existing completed class . 91 6.5 Using the processtype and decaytype classes . 92 6.5.1 Decays . 93 6.5.2 Processes . 96 6.6 Using the complexdecay class . 99 6.7 A more complex example . 102 6.8 Generating Events . 107 7 Catalog of Implemented New Physics 113 7.1 Standard Model . 113 7.1.1 Standard Model Processes . 114 7.1.2 SM Decays . 117 7.2 SUSY . 119 7.2.1 SUSYspectrum . 123 7.2.2 SUSY processes . 131 7.2.3 SUSY decays . 137 vi 8 Examples 139 8.1 e−e+ → µ−µ+ ............................... 139 8.2 pp → 2 jets . 143 8.3 e−e+ → Ce−Ce+ .............................. 153 A Invariants Classes 167 A.1 Invariants for 2 → 2 processes . 167 A.2 Invariants for 1 → 2 decays . 170 Bibliography 172 vii List of Tables 3.1 PDFs included in pandora . 31 6.1 The xychannel naming convention for initial channel constants . 77 6.2 Common initial channel functions . 78 6.3 LEvent member functions. The integers m and n refer to the index number in the LEvent........................... 112 7.1 The produceOnly() function in eetopairs . 115 7.2 MSSM particles . 120 7.3 SUSYspectrum input parameters . 125 7.4 MSSM particle mass eigenstates. There is mixing in the scalar Higgs sector as well, but we use the mass eigenstates and mixings as inputs. 126 7.5 VFF couplings . 126 7.6 VSS couplings . 127 7.7 SFF couplings. fu refers to up type quarks or neutrinos. fd refers to down type quarks an leptons. 128 7.8 SSS couplings . 128 7.9 SVV couplings . 128 − + + − 8.1 SPS4 properties relevant to e e → Ce1 Ce1 ............... 155 viii List of Figures 3.1 Sketch of full event based on an image from the SHERPA collabora- tion [10]. The hard event on the left is simulated by pandora. On the right it is represented by the white circle in the center, while the rest of the effects including parton showering, hadronization and multiple interactions are pictured. 10 3.2 All four of these diagrams could contribute to the same final state. Diagrams (a) and (b) involve 2 → 2 processes followed by several resonant decays and are included in the pandora calculation. Diagram (c) and (d) could be described as 2 → 5 processes with one resonant decay, and are not considered in basic pandora calculations. In general, they contribute much less than the enhanced resonant decay diagrams (a) and (b). 13 3.3 (a) The expression for the set of all one-particle-irreducible (1PI) in- sertions. (p) The exact propagator which is the geometric series of all 1PI insertions. 16 − + − + 3.4 Some of the diagrams for e e → e e νeνe (there are 49 more). 19 3.5 A basic color structure diagram . 23 3.6 Color structure for an color octet decaying to two octets . 24 3.7 There are three possible color structure diagrams for 88 → 33, diagrams (b), (c), and (d). However, only (b) appears in the gg → qq diagram (a). .................................... 24 ix 3.8 Two overlapping Breit-Wigner resonances. If there is a kinematic con- straint m2 < m1 then a large piece of the m2 resonance may be kine- matically inaccessible at certain points in phase space, strongly affect- ing the width integral . 29 3.9 A general process . 30 3.10 The 2 → 2 event plane (needs work) . 34 3.11 Kinematics for a 2→3 event. The three final particles fall in the 3ˆ0 − 1ˆ0 plane, and the orientation of that plane with respect to the beam axis are defined by three Euler rotation angles φ, θ, and ψ.......... 35 3.12 Weyl spinor Feynman rules . 39 4.1 A peaked 2-dimensional integrand that would not be efficiently sampled by a sampling distribution p(x1, x2) = g1(x1)g2(x2) since it it flat in both variables. A more efficient sampling would use the distribution p(x1, x2) = g1(x1 − x2)g2(x1 + x2) since it is peaked in the x1 − x2 direction. 45 4.2 The peaked Breit-Wigner integrand over masses (a), can be made a reasonably flat integrand over a unit interval (b) by changing variables using the inverse of the Breit Wigner cumulative distribution function. 47 4.3 A peaked function in x2, cut off by the condition x2 < x1........ 53 5.1 Hierarchy image of a pandora object involving the process eetoCC.. 62 5.2 Hierarchy image of a eetoWW object. The location of the function corresponds to the level it is initialized at, and the color to the level it is defined at. So amplitudes() is initialized by the process class as a virutal function and is finally defined by eetoWW........... 65 5.3 Hierarchy image of a eetoWW object. 65 5.4 Hierarchy image of a HiggstoZgdecay object. The location of the func- tion corresponds to the level it is initialized at, and the color to the level it is defined at. So properamplitudes() is initialized by the decay class as a virutal function and is finally defined by HiggstoZgdecay. 68 x − − 6.1 Diagrams for e γ → W νe ........................ 86 6.2 Diagrams contributing to the eetoCC class. 98 7.1 MSSM Coupling diagrams. For scalars, all momenta p are outgoing. ∗ For vectors, should be used for final state vectors. For fermions, Fi should be replaced by the appropriate u or v spinor. 127 − + 7.2 Diagrams contributing to e e → NeiNej................. 133 − + + − 7.3 Diagrams for e e → Cei Cej ....................... 134 7.4 Diagrams contributing to e−e+ → fefe0.................. 135 8.1 Diagrams contributing to the eetomumu class. 140 8.2 The Z peak in e−e+ → µ−µ+ for each polarization state at a ILC type − + collider. The unpolarized peak is overlapped by the eReL peak. 144 8.3 Diagrams contributing to qq0 → q00q000................... 145 8.4 Color indices for the qq0g vertex. 146 8.5 Diagrams contributing to gg → gg.................... 149 − + + − 8.6 Diagrams contributing to e e → C1 C1 ................ 154 8.7 Plots of cos θ from the beam axis for the process e−e+ → C+C− Ce+ e1 e1 − + at benchmark point SPS4. The plots correspond to (a) eL eR at a 500 − + − + GeV ILC (b) eReL at a 500 GeV ILC (c) eL eR at a 1 TeV ILC and (d) − + eReL at a 1 TeV ILC.