Present and future constraints on supersymmetry from cosmological and electroweak data [Elektronische Ressource] / Eva Barbara Ziebarth. Betreuer: W. de Boer

Eva Ziebarth

Sujets

• Physik

Informations

• Publié par: karlsruher_institut_fur_technologie
• Publié le: 01 janvier 2011
• Nombre de lectures: 25
• Langue: English
• Poids de l'ouvrage: 11 Mo

Extrait

IEKP-KA/2011-22
PRESENT AND FUTURE CONSTRAINTS
ON SUPERSYMMETRY FROM COSMOLOGICAL
AND ELECTROWEAK DATA
EVA ZIEBARTH
Zur Erlangung des akademischen Grades eines
DOKTORS DER NATURWISSENSCHAFTEN
von der Fakultat¨ fur¨ Physik am
Karlsruher Institut fur¨ Technologie (KIT)
genehmigte
Dissertation
von
Dipl.-Phys. Eva Barbara Ziebarth
aus Speyer
Tag der mundlichen¨ Prufung:¨ Freitag der 10. Juni 2011
Referent: Prof. Dr. W. de Boer, Institut fur¨ Experimentelle Kernphysik
Korreferent: Prof. Dr. Th. Muller¨ , Institut fur¨ Exper KernphysikContents
1 Introduction 1
2 Theoretical Framework 3
2.1 The Standard Model of Particle Physics .................... 4
2.1.1 Fermions ................................. 4
2.1.2 Gauge Bosons .............................. 7
2.1.3 Electroweak Unification and the Higgs Mechanism .......... 9
2.1.4 Limits of the Standard Model ...................... 12
2.2 Supersymmetry 13
2.2.1 Motivation for Supersymmetry ..................... 15
2.2.2 The SUSY formalism........................... 17
2.2.3 The MSSM ................................ 26
2.2.4 The Higgs Sector in the MSSM 34
2.3 Dark Matter .................................... 41
2.3.1 Dark Matter Candidates . . ....................... 41
2.3.2 The Cosmological History of Dark Matter ............... 43
3 The MOPS software package 47
3.1 Some Simple Statistics ............................. 48
3.1.1 Frequentist Probability Interpretation and Probability Density .... 48
3.1.2 Chi Square Functions and the Least Square Method ......... 49
3.2 The Brute Force Scan Method . . . ...................... 50
3.3 Markov Chain Monte Carlo ........................... 50
3.3.1 Markov Chains .............................. 51
3.3.2 The Metropolis-Hastings Algorithm................... 51
3.3.3 The Snooker Algorithm . . ....................... 52
3.4 Implementation of the MOPS package ..................... 52
4 Results 55
4.1 Is it possible to measure the Relic Density at the LHC?............ 56
4.1.1 Annihilation of SUSY Dark Matter ................... 56
4.1.2 Determination of tanβ and m from the WMAP constraint ..... 57A
4.1.3 Estimated Uncertainty in the Relic Density Determination from LHC
Data .................................... 63
4.1.4 Constraining Neutralino Masses by Relic Density........... 70
4.2 Constraints on SUSY parameter space .................... 73
4.2.1 Motivation................................. 73
4.2.2 Relic Density Constraint . . ....................... 74
4.2.3 B → μμ Constraint ........................... 75S
4.2.4 b → sγ Constraint ............................ 80
4.2.5 Δa Constraint .............................. 82μ
+ +4.2.6 B → τ ν Constraint.......................... 89τ
4.2.7 Higgs Massaint . . . 95
III CONTENTS
4.2.8 Treatment of the errors . . . ....................... 97
4.2.9 Combination of all constraints...................... 101
4.2.10 Comparison with other anayses..................... 105
4.2.11 Inclusion of first LHC Data . 109
5 Conclusion 111
A Important Equations and Methods i
A.1 Pauli matrices................................... i
A.2 Grassmanian Variables ............................. i
A.3 The Gamma Function .............................. i
A.4 The Maxiumum Likelihood Method ....................... ii
+ +A.5 Input for Br(B → τ ν ) ............................ iiτ
A.6 Confidence levels for two degrees of freedom ................. iii
B Computing Tools v
B.1 MicrOMEGAs v
B.2 ROOT ....................................... vii
B.3 Minuit viiiList of Figures
2.1 SM fermions ................................... 4
2.2 SM bosons .................................... 7
2.3 Spontaneous Symmetry Breaking . ...................... 10
2.4 SM Gauge Couplings .............................. 13
2.5 SM Corrections to Higgs mass . . . 14
2.6 Supersymmetry.................................. 14
2.7 Gauge Couplings in SUSY ........................... 16
2.8 SUSY Corrections to Higgs mass . . 16
2.9 F-type SUSY breaking 25
2.10 Proton Decay 28
2.11 Gluino Production ................................ 30
2.12 The two sectors of the MSSM.......................... 32
2.13 Solutions of the Boltzmann equation ...................... 44
3.1 Class diagram of the MOPS package 54
4.1 Neutralino Annihilation Channels . . 56
4.2 Annihilation channels in the mass plane .................... 58
4.3 Results of the WMAP fit ............................. 59
4.4 Mass ratios in the WMAP fit ........................... 60
4.5 Dependence of m on tanβ 60A
4.6 Values of tanβ obtained by the WMAP fit ................... 61
4.7 tanβ dependence of the Relic Density ..................... 62
4.8 Pseudoscalar Higgs mass values obtained by the WMAP fit ......... 62
4.9 Branching ratio of annihilation via pseudoscalar Higgs bosons........ 63
4.10 Example for Endpoint Determination ...................... 64
4.11 Neutralino mass ratio .............................. 65
4.12 Relative error of Relic Density.......................... 66
4.13 Gluon Fusion ................................... 67
4.14 Determination of m ............................... 67A
4.15 Contribution from m uncertainty . ....................... 68A
04.16 Cross section of associated A production................... 69
4.17 Relative error on tanβ 69
4.18 Contribution from tanβ 70
4.19 Relative Relic Density uncertainty . ...................... 71
4.20 Relic Density dependence of m ........................ 71χ
4.21 Correlation of tanβ with A ........................... 730
4.22 Dependence of Ω on tanβ and A ....................... 740
4.23 Main SUSY contribution to B → μμ 76S
4.24 Br(B → μμ)................................... 77S
4.25 Results of one-dimensional partial tanβ adjustment ............. 78
2 24.26 χ compared to χ 792B →μμ) ΩhS
24.27 tanβ and A dependence of partial χ ..................... 800
IIIIV LIST OF FIGURES
4.28 Results of two-dimensional B → μμ optimisation .............. 81S
4.29 SUSY contributions to b → sγ .......................... 82
4.30 Br(b → sγ) .................................... 83
4.31 Results of one-dimensional partial tanβ adjustment ............. 84
4.32 Br(b → sγ) 85
24.33 tanβ dependence of partial χ ....................... 86b→sγ
2 24.34 χ contributions of Ωh , Br(b → sγ) and Br(B → μμ)............ 87S
4.35 Results of two-dimensional Br(b → sγ) optimisation ............. 88
4.36 SUSY corrections to g-2 ............................. 89
4.37 Δa ........................................ 90μ
4.38 Results of one-dimensional partial tanβ adjustment 91
24.39 tanβ and A dependence of partial χ ..................... 920
4.40 Results of two-dimensional Δa optimisation ................. 93μ
4.41 R 94Bτν
24.42 tanβ dependence of partial χ ...................... 95+B →τν
4.43 Results of one-dimensional partial tanβ adjustment ............. 96
2 24.44 tanβ and A dependence of partial χ +χ .............. 970 2 +Ωh B →τν
+ +4.45 Results of two-dimensional B → τ ν optimisation 98τ
4.46 of tw m optimisation . . ................ 99h
4.47 Comparison of linearly and quadraticly combined errors ........... 100
4.48 Results of two-dimensional optimisation .................... 102
4.49 Partial exclusion curves ............................. 104
4.50 Growing of R + + with m ......................... 105B →τ ν 1/2τ
4.51 Total exclusion curves .............................. 106
4.52 Comparison of the analyses........................... 107
4.53 Direct Comparison with Ref. [1] . . . ...................... 108
4.54 Comparison with Conny Beskidt . . 108
4.55 95% C.L. SUSY exclusion curve . . 110
4.56 95% exclusion curve including CMS 110
5.1 All Results..................................... 112
B.1 Structure of a TFile................................ viii
B.2 Str of a TTree ............................... ixList of Tables
2.1 Number of SUSY states ............................. 18
2.2 Chiral Superfields in the MSSM . . . ...................... 27
2.3 Vector in the . . . 28
2.4 Production Channels............................... 30
4.1 Combined errors ................................. 97
24.2 Resulting χ for linear and quadratic error combination............ 100
24.3 χ for whole fit 101
24.4 Resulting χ contributions from different constraints ............. 103
24.5 partial χ terms ............................ 103
4.6 Constraints used in different analyses ..................... 106
A.1 Confidence levels for two degrees of freedom ................. iv
VVI LIST OF TABLESCHAPTER 1
Introduction
The Standard Model of particle physics (SM) [2–12] was developed in the 1970s. Tested in
many collider and cosmological experiments it stays accepted until today. In the Glashow-
Weinberg-Salam theory (GWS) [13–15] a unification of the electromagnetic and the weak
force could be obtained. A unification of all SM forces (the, the weak and
the strong force) would complete the SM. However, a unification of this kind cannot be
obtained in the standalone SM. Therefore it needs an extension.
In the 1930s Fritz Zwicky postulated the existence of non-illuminating matter, Dark Matter
(DM), to be responsible for the effect that the outer galaxies of the Coma galaxy cluster or-
biti