Electroweak contributions to SUSY particle production at the LHC [Elektronische Ressource] / Edoardo Mirabella

Eduardo Mirabella

Sujets

• Physik

Informations

• Publié par: technische_universitat_munchen
• Publié le: 01 janvier 2009
• Nombre de lectures: 10
• Langue: English
• Poids de l'ouvrage: 3 Mo

Extrait

Technische Universit¨at Mu¨nchen
Max-Planck-Institut fu¨r Physik
(Werner-Heisenberg-Institut)
Electroweak contributions
to SUSY particle production
processes at the LHC
Edoardo Mirabella
Vollst¨andiger Abdruck der von der Fakult¨at fu¨r Physik
der Technischen Universit¨at Mu¨nchen
zur Erlangung des akademischen Grades eines
Doktors der Naturwissenschaften (Dr. rer. nat.)
genehmigten Dissertation.
Vorsitzender: Univ.-Prof. Dr. L. Oberauer
Pru¨fer der Dissertation: 1. Hon.-Prof. Dr. W. F. L. Hollik
2. Univ.-Prof. Dr. A. J. Buras
Die Dissertation wurde am 25. Juni 2009
bei der Technischen Universit¨at Mu¨nchen eingereicht und
durch die Fakult¨at fu¨r Physik am 22. Juli 2009 angenommen.Contents
1 Introduction 1
2 The Standard Model and the MSSM 7
2.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Lagrangian of the SM . . . . . . . . . . . . . . . . . . 7
2.1.2 Problems of the SM. . . . . . . . . . . . . . . . . . . . 9
2.2 Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.1 Superalgebra and Supergroup . . . . . . . . . . . . . . 12
2.2.2 Superspace and Superfields . . . . . . . . . . . . . . . . 13
2.2.3 Supersymmetric gauge theories . . . . . . . . . . . . . 16
2.3 The Minimal Supersymmetric Standard Model . . . . . . . . . 18
2.3.1 MSSM Lagrangian . . . . . . . . . . . . . . . . . . . . 18
2.3.2 MSSM parameters . . . . . . . . . . . . . . . . . . . . 21
2.3.3 MSSM spectrum . . . . . . . . . . . . . . . . . . . . . 23
3 Supersymmetry at colliders 29
3.1 Direct searches at LEP . . . . . . . . . . . . . . . . . . . . . . 29
3.1.1 Charginos and neutralinos . . . . . . . . . . . . . . . . 31
3.1.2 Sleptons . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.1.3 Squarks . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2 Direct searches at the Tevatron . . . . . . . . . . . . . . . . . 36
3.2.1 Higgs bosons . . . . . . . . . . . . . . . . . . . . . . . 36
3.2.2 Charginos and neutralinos . . . . . . . . . . . . . . . . 39
3.2.3 Squarks and gluinos . . . . . . . . . . . . . . . . . . . 39
3.2.4 Top and bottom squarks . . . . . . . . . . . . . . . . . 41
3.3 Direct searches at HERA . . . . . . . . . . . . . . . . . . . . . 43
3.4 Direct searches at the LHC. . . . . . . . . . . . . . . . . . . . 45
3.4.1 Inclusive searches . . . . . . . . . . . . . . . . . . . . . 45
3.4.2 Higgs bosons . . . . . . . . . . . . . . . . . . . . . . . 52
3.4.3 Charginos and neutralinos . . . . . . . . . . . . . . . . 56
iii CONTENTS
4 Computational techniques and methods 59
4.1 Structure of the tree-level and one-loop contributions . . . . . 59
4.1.1 LO and NLO QCD contributions . . . . . . . . . . . . 60
4.1.2 LO and NLO EW contributions . . . . . . . . . . . . . 62
4.2 UV divergences . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2.1 Regularization . . . . . . . . . . . . . . . . . . . . . . . 66
4.2.2 Renormalization. . . . . . . . . . . . . . . . . . . . . . 69
4.3 Photonic mass singularities . . . . . . . . . . . . . . . . . . . . 77
4.3.1 General features . . . . . . . . . . . . . . . . . . . . . . 78
4.3.2 Phase space slicing . . . . . . . . . . . . . . . . . . . . 80
4.3.3 Dipole subtraction formalism . . . . . . . . . . . . . . 82
4.4 Gluonic mass singularities . . . . . . . . . . . . . . . . . . . . 83
4.4.1 General features . . . . . . . . . . . . . . . . . . . . . . 83
4.4.2 Phase space slicing . . . . . . . . . . . . . . . . . . . . 86
4.4.3 Dipole subtraction formalism . . . . . . . . . . . . . . 87
5 Gluino pair production 89
5.1 Gluino pair production in lowest order . . . . . . . . . . . . . 89
25.2 O(α α) corrections to the hadronic process . . . . . . . . . . . 91s
5.2.1 qq¯annihilation with electroweak loops . . . . . . . . . 92
5.2.2 qq¯annihilation with real photon emission . . . . . . . . 93
5.2.3 qγ and γq¯fusion . . . . . . . . . . . . . . . . . . . . . 93
5.2.4 Factorization of initial collinear singularities . . . . . . 95
5.3 Numerical results, LHC . . . . . . . . . . . . . . . . . . . . . . 95
5.3.1 Dependence on the renormalization scheme . . . . . . . 96
5.3.2 Dependence on the SUSY scenario . . . . . . . . . . . 100
5.3.3 Dependence on the MSSM parameters . . . . . . . . . 102
5.4 Numerical results, Tevatron . . . . . . . . . . . . . . . . . . . 104
5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6 Diagonal squark-anti-squark production 113
6.1 Tree-level contributions to squark pair production. . . . . . . 114
6.1.1 Squark pair production at leading order . . . . . . . . 114
6.1.2 Tree-level electroweak contributions of O(α α) ands
2O(α ) . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
26.2 Virtual and realO(α α) corrections . . . . . . . . . . . . . . . 116s
6.2.1 Gluon fusion with electroweak loops . . . . . . . . . . . 116
6.2.2 Gluon fusion with real photon emission . . . . . . . . . 117
6.2.3 qq¯annihilation with electroweak and QCD loops . . . . 117
6.2.4 qq¯annihilation with real photon emission . . . . . . . . 118
6.2.5 qq¯annihilation with real gluon emission . . . . . . . . 118CONTENTS iii
6.2.6 q(q¯)g fusion . . . . . . . . . . . . . . . . . . . . . . . . 119
6.2.7 Factorization of initial collinear singularities . . . . . . 119
6.3 Numerical analysis . . . . . . . . . . . . . . . . . . . . . . . . 120
6.3.1 Different squark species . . . . . . . . . . . . . . . . . 121
6.3.2 Different SUSY scenarios . . . . . . . . . . . . . . . . . 124
6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7 Squark-gluino production 143
7.1 Tree-level contributions . . . . . . . . . . . . . . . . . . . . . . 143
7.1.1 Leading order contributions . . . . . . . . . . . . . . . 144
7.1.2 Photon induced gluino–squark production . . . . . . . 145
27.2 O(α α) contributions . . . . . . . . . . . . . . . . . . . . . . . 145s
7.2.1 Virtual corrections . . . . . . . . . . . . . . . . . . . . 146
7.2.2 Real photon radiation . . . . . . . . . . . . . . . . . . 147
7.2.3 Real quark radiation . . . . . . . . . . . . . . . . . . . 147
7.2.4 Factorization of initial state singularities . . . . . . . . 148
7.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . 149
7.3.1 Different squark species . . . . . . . . . . . . . . . . . 149
7.3.2 Dependence on the SUSY scenario . . . . . . . . . . . 153
7.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
8 Conclusions 173
A Definitions and conventions 177
B Spinorial representations of the Poincar´e Group 179
B.1 Weyl spinors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
B.2 Dirac and Majorana spinors . . . . . . . . . . . . . . . . . . . 181
C Grassmann variables 183
D Phase space integrations 185
D.1 Two-particle phase space . . . . . . . . . . . . . . . . . . . . . 185
D.2 Three-particle phase space . . . . . . . . . . . . . . . . . . . . 187
E More details on the dipole formalism 189
E.1 Photonic divergences . . . . . . . . . . . . . . . . . . . . . . . 189
E.2 Gluonic divergences . . . . . . . . . . . . . . . . . . . . . . . . 194
F Feynman diagrams entering PP →g˜g˜X 197
∗˜ ˜G Feynman diagrams entering PP →Q Q X 199a aiv CONTENTS
˜H Feynman diagrams entering PP →g˜Q X 207aChapter 1
Introduction
The attempt to explain the complexity of the world in terms ofa small num-
ber of fundamental building blocks has been an usual procedure of mankind
during the centuries. According to Aristotle, the first philosopher using such
reductionist approach was Thales. Thales taught can be stated as: “Wa-
ter constituted the principle of all things” (Diogenes Laertius). Many steps
forward in the understanding of the world were done during the centuries.
Currently it is believed that matter is constituted by a relatively small num-
ber of point-like particles. According to this picture, particles interact, and
these interactions allow the formation of complex structures. These interac-
tion are described by a (spontaneously broken) Yang-Mills Quantum Field
Theory,theStandardModel(SM) [1,2].Almost alltheparticlesentering the
SM have been observed. The only particle missing is the scalar Higgs boson.
The predictions obtained within the SM agree well with the experimental
data. In this sense this model is one of the best-tested theories of physics.
In spite of its success, the SM is not the ultimate theory. Indeed, this
model does not describe gravity and does not provide a candidate for the
observed amount of cold dark matter in the universe. These deficiencies sug-
gest the existence of a a more fundamental theory including the SM. Some
“aesthetic” problems, such as the non-existence of a Grand Unification scale
and the hierarchy problem, reinforce this idea and can beused as a guideline
in the hunting for the new theory.
Among the others, the extensions of the Standard Model fulfilling super-
symmetry (SUSY) [3] are an appealing option, since they can both solve the
hierarchy problem and provide the unification o