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Topics in Collider Physics TOPICS IN COLLIDER PHYSICS 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 Francis John Petriello August 2003 SLAC-R-644 Work supported in part by U.S. Department of Energy contract DE-AC03-76SF00515 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 Hewett (Principal 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. Lance Dixon 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 Approved for the University Committee on Graduate Studies. iii Abstract It is an exciting time for high energy physics. Several experiments are currently exploring uncharted terrain; the next generation of colliders will begin operation in the coming decade. These experiments will together help us understand some of the most puzzling issues in particle physics: the mechanism of electroweak symmetry breaking and the generation of flavor physics. It is clear that the primary goal of the- oretical particle physics in the near future is to support and guide this experimental program. These tasks can be accomplished in two ways: by developing experimental signatures for new models which address outstanding problems, and by improving Standard Model predictions for precision observables. We present here several results which advance both of these goals. We begin with a study of non-commutative field theories. It has been suggested that TeV-scale non-commutativity could explain the origin of CP violation in the SM. We identify several distinct signatures of non-commutativity in high energy processes. We also demonstrate the one-loop quantum consistency of a simple spontaneously broken non-commutative U(1) theory; this result is an important preface to any attempt to embed the SM within a non-commutative framework. We then investigate the phenomenology of extra-dimensional theories, which have been suggested recently as solutions to the hierarchy problem of particle physics. We first examine the implications of allowing SM fields to propagate in the full five-dimensional spacetime of the Randall-Sundrum model, which solves the hierar- chy problem via an exponential “warping” of the Planck scale induced by a five- dimensional anti de-Sitter geometry. In an alternative exra-dimensional theory, in which all SM fields are permitted to propagate in flat extra dimensions, we show that properties of the Higgs boson are significantly modified. iv Finally, we discuss the next-to-next-to leading order QCD corrections to the dilep- ton rapidity distribution in the Drell-Yan process, an important discovery channel for new physics at hadron colliders. We introduce a powerful new method for calcu- lating differential distributions in hard scattering processes. We apply our results to the analysis of fixed target experiments, which provide important constraints on the parton distribution functions of the proton. v Acknowledgements I thank my advisor, JoAnne Hewett, for her help and especially her patience during my time at SLAC. I thank Hooman Davoudiasl, Lance Dixon, Michael Peskin, Darius Sadri, and the remaining students, postdocs, and professors at SLAC for sharing their knowledge of particle physics with me. Most importantly, I acknowledge my great indebtedness to Babis Anastasiou, Kirill Melnikov, and Tom Rizzo, for their willingness to answer my endless stream of naive questions, for teaching me the proper way of looking at both high energy physics and physicists, and for their friendship. Without them the past four years would have been a much less enjoyable experience. Finally, I thank my family for putting up with me before, during, and hopefully after the completion of this thesis. vi Chapters 2-5 of this thesis are based upon material that has appeared previously in the following publications: • J. L. Hewett, F. J. Petriello and T. G. Rizzo, “Signals for non-commutative interactions at linear colliders,” Phys. Rev. D 64, 075012 (2001); • F. J. Petriello, “The Higgs mechanism in non-commutative gauge theories,” Nucl. Phys. B 601, 169 (2001); • J. L. Hewett, F. J. Petriello and T. G. Rizzo, “Precision measurements and fermion geography in the Randall-Sundrum model revisited,” JHEP 0209, 030 (2002); • F. J. Petriello, “Kaluza-Klein effects on Higgs physics in universal extra dimen- sions,” JHEP 0205, 003 (2002). These have been reprinted with the permission of the respective publishers. The work in Chapter 6 is based upon the preprint “Dilepton rapidity distribution in the Drell-Yan process at NNLO in QCD,” to appear, written in collaboration with Charalampos Anastasiou, Lance Dixon, and Kirill Melnikov. vii Contents Abstract iv Acknowledgements vi 1 Introduction 1 2 Experimental Signatures for Non-commutative Interactions at Lin- ear Colliders 4 2.1IntroductionandBackground...................... 4 2.2MøllerScattering............................. 12 2.3BhabhaScattering............................ 20 2.4PairAnnihilation............................. 24 2.5 γγ → γγ at Linear Colliders . .................... 33 2.6Summary................................. 40 3 The Higgs Mechanism in Non-commutative Gauge Theories 46 3.1Introduction................................ 46 3.2CommutativeAbelianHiggsModel................... 47 3.3Non-commutativeAbelianHiggsModel................. 52 3.3.1 SetupofNCSymmetryBreakinginU(1)............ 52 3.3.2 CalculationofNCdivergences.................. 57 3.4Summary................................. 60 4 Precision Measurements and Fermion Geography in the Randall- Sundrum Model 62 viii 4.1Introduction................................ 62 4.2TheStandardModelOfftheWall.................... 65 4.3 Fermion Mixing and the ρ Parameter.................. 73 4.4 The Third Generation On the Wall and the EW Precision Observables 78 4.5SearchesattheLHC........................... 85 4.6 Searches at Future TeV-scale Linear Colliders ............. 91 4.7ConstraintsfromFCNCs......................... 93 4.8Summary................................. 98 5 Kaluza-Klein Effects on Higgs Physics in Universal Extra Dimen- sions 100 5.1Introduction................................ 100 5.2Kaluza-KleinReductionofthe5-dimensionalStandardModel.... 102 5.3KKEffectsinOneLoopHiggsProcesses................ 109 5.3.1 gg → h .............................. 109 5.3.2 h → γγ .............................. 113 5.3.3 h → γZ .............................. 117 5.4Summary................................. 121 6 The Drell-Yan Rapidity Distribution at Next-to-next-to Leading Order in QCD 123 6.1Introduction................................ 123 6.2DescriptionoftheCalculation...................... 125 6.3NumericalResults............................. 130 6.4Summary................................. 133 7 Conclusions 134 A Formulae for γγ Collisions 136 Bibliography 138 ix List of Tables 2.1 Summary of the 95% CL search limits on the NC scale ΛNC from the various processes considered above at a 500 GeV e+e− linear collider with an integrated luminosity of 500 fb−1. ............... 45 4.1 Abbreviated list of the top quark KK states. The subscripts L and R denote left-handed and right-handed fields. SU(2)L doublets are denoted by capital T and singlets by lower case t.AnX at a location in the table indicates that the state does not exist due to the orbifold symmetry.................................. 73 4.2 Table of m1 ranges allowed by the EW precision data for several rep- resentative values of ν and mH .AnX denotes that the parameter choicecorrespondingtothatlocationisnotallowed........... 85 4.3 Table of expected Drell-Yan events at the LHC for various parameter choices L = 100 fb−1.Boththeµ+µ− and e+e− channels have been included................................... 88 x List of Figures 2.1FeynmanrulesofNCQED......................... 10 2.2 Feynman graphs contributing to Møller scattering, with the exchanged particle corresponding to a photon and Z=boson............ 13 2.3 Binned cross section (top) and polarized asymmetry (bottom) as a function of z =cosθ for Møller scattering at a 500 GeV linear collider assuming an integrated luminosity of 300 fb−1. The histogram is the √ SM expectation while the data corresponds to ΛNC = s. ...... 16 2.4 φ dependence of the Møller cross section (top) and left-right asymme- √ try (bottom) for the SM (straight lines) and for the case ΛNC = s (shown as data) at a 500 GeV linear collider with a luminosity of 300 fb−1. From top to bottom in the top panel a z cut of 0.9(0.7, 0.5) has beenappliedwiththeorderreversedinthelowerpanel......... 17 2.5 95% CL lower bound on ΛNC at a 500 GeV linear collider as a function of the integrated luminosity from Møller scattering via the fit described inthetext................................. 18 2.6 Scaled dependence of the Møller total cross section, subject to a an- gular cut (from top to bottom) of |z|≤0.9(0.7, 0.5) assuming the SM (dashed curves) or ΛNC =500GeV(solidcurves)............ 19 2.7 Feynman graphs contributing to Bhabha scattering with the exchanged particle corresponding to a photon and Z-boson............. 21 2.8 Same as Fig. 2.3 but now for Bhabha scattering assuming that c01 is non-zero..................................
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