Technische Universitat Munchen Max-Planck-Institut fur Physik (Werner-Heisenb erg-Institut ) Top-Quark and Top-Squark Production at Hadron Colliders at Electroweak NLO Monika Kollar Vollstandiger Abdruck der von der Fakultat fur Physik der Technischen Universitat MUnchen zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigten Dissertation. Vorsitzender : Univ.-Prof. Dr. L. Oberauer Prufer der Dissertation : 1. Univ.-Prof. Dr. W. F. L. Hollik 2. Univ.-Prof. Dr. A. J. Buras Die Dissertation wurde am 28.03.2007 bei der Technischen Universitat Munchen eingereicht und durch die Fakultat fur Physik am 31.05.2007 angenommen. To Dano Abstract In this work, the impact of O(a) contributions on the cross sections for the top- quark pair production within the SM and for the top-squark pair production within the MSSM is investigated. For these processes, the EW-QCD interference leads to additional contributions at level which are not present at Born-level. In addi­ tion, parton densities at NLO QED give rise to non-zero photon density in the proton. It is shown that the size of photon-induced production rates is comparable to other EW NLO contributions. The cross sections differential in V! and pT are studied and discussed in kinematic ranges accessible at the LHC and at the Tevatron. The NLO EW contributions become significant at high p T and high VI and should be included in the numerical analysis. iii Contents 1 Introduction 1 2 Standard Model 5 2.1 Basics of the Standard Model .............................................................................. 5 2.2 Open questions and the role of quantum corrections .................................... 8 3 Supersymmetry 11 3.1 Motivation for supersymmetry .............................................................................. 11 3.2 Properties of supersymmetric theories ................................................................ 12 3.2.1 Supersymmetry breaking ....................................................................... 13 3.2.2 R-parity ........................................................................................................... 14 3.2.3 Low-energy supersymmetry .................................................................... 15 3.3 The Minimal Supersymmetric Standard Model .............................................. 17 3.4 Particle content of the MSSM.............................................................................. 20 3.4.1 Quarks and Leptons .................................................................................. 20 3.4.2 Squarks and Sleptons .................................................................................. 21 3.4.3 Higgs and Gauge bosons ........................................................................... 22 3.4.4 Higgsinos and Gauginos ........................................................................... 24 4 Regularization and Renormalization 27 4.1 Regularization .............................................................................................................. 27 4.2 Renormalization ........................................................................................................... 28 4.2.1 Renormalization schemes ........................................................................... 29 5 Hadronic cross sections 33 5.1 Parton model .............................................................................................................. 33 5.2 Factorization .............................................................................................................. 35 5.2.1 Factorization schemes .................................................................................. 37 5.2.2 Splitting functions ..................................................................................... 38 v vi CONTENTS 5.3 Parton distributions with QED contributions .................................................. 39 6 Top pair production at NLO QED 41 6.1 Top pair production ................................................................................................ 41 6.1.1 tt cross section at the partonic level..................................................... 44 6.2 Structure of the NLO QED contributions ......................................................... 45 6.2.1 Virtual corrections ..................................................................................... 45 6.2.2 Real corrections ............................................................................................ 50 6.3 Photon-induced tt production .............................................................................. 53 6.4 Soft and collinear photon/gluon emission ......................................................... 55 6.4.1 Phase space slicing ..................................................................................... 55 6.4.2 Dipole subtraction method ....................................................................... 58 6.5 Hadronic cross sections for pp/pp ^ ttX......................................................... 59 6.5.1 Integrated hadronic cross sections ......................................................... 60 6.5.2 Differential hadronic cross sections ..................................................... 60 6.5.3 Mass factorization ..................................................................................... 62 6.6 Numerical results....................................................................................................... 63 7 SUSY-EW corrections to stop pair production 77 7.1 Top-squark pair production .................................................................................. 77 7.1.1 Partonic cross sections at lowest order .............................................. 79 7.2 General aspects of NLO SUSY-EW corrections .............................................. 80 7.2.1 Quark and squark self-energies at one-loop level............................. 81 7.2.2 On-shell renormalization conditions ..................................................... 84 7.3 Classification of NLO SUSY-EW corrections .................................................. 85 7.3.1 Virtual corrections ..................................................................................... 85 7.3.2 Real corrections ............................................................................................ 90 7.4 Photon-induced top-squark production ............................................................ 92 7.5 Numerical results ....................................................................................................... 92 7.6 Analysis of parameter dependence ........................................................................... 101 8 Conclusions 107 Zusammenfassung 111 A Choice of parameters 113 A.1 Standard Model Parameters...................................................................................... 113 A.2 SPS 1a parameter set of the MSSM................................................................... 114 CONTENTS vii B Basic principles of supersymmetry 117 B.1 Conventions ..................................................................................................................... 117 B.2 Spinors ................................................................................................................................118 B.2.1 Weyl spinors .................................................................................................. 118 B.2.2 Dirac and Majorana spinors .......................................................................119 B.3 Superfields .................................................................................................................... 120 B.3.1 Grassmann variables ..................................................................................... 120 B.3.2 Chiral and vector superfields .......................................................................121 B. 4 Supersymmetric Lagrangian ..................................................................................... 122 C Parton densities 125 C. 1 LO splitting functions ................................................................................................125 C.2 QED-modified DGLAP evolution equations .........................................................126 D Loop integrals 127 E Analytical expressions for the NLO QED corrections 131 Bibliography 135 Acknowledgements 153 viii CONTENTS Chapter 1 Introduction Over the twentieth century, unceasing theoretical and experimental efforts in particle physics were concentrated on building a model that would describe the basic elements of nature in a consistent way. It was found that the protons and neutrons in the nuclei are not fundamental objects, but they are composed of quarks, which together with the leptons are considered to be the elementary particles. The fundamental forces of strong, weak and electromagnetic interactions are widely believed to be described by quantum field theories based on local gauge symmetries. The elementary particles can then interact through exchange of gauge field quanta (gluons, weak bosons and photons). All of this knowledge is embedded into the currently established model of elementary particle physics, the Standard Model (SM) [1-4]. Only the fourth fundamental force, gravity, is not yet included in the quantum theory picture. After many years of testing, which proved that the Standard Model is an impres ­ sively consistent theory for the energy ranges