Phenomenological Aspects of the $E_6$SSM

1.2 MB·English

by  Jonathan Peter Hall

UNIVERSITY OF SOUTHAMPTON
FACULTY OF PHYSICAL AND APPLIED SCIENCES
School of Physics and Astronomy
Southampton High Energy Physics Group
2
1
0
2

n
a
Phenomenological Aspects
J

6
2
of the E SSM

] 6
h
p
-
p
by
e
h
[

1
Jonathan Peter Hall
v
8
8
4
5
.
1
0
2
1
:
v
i Presented for the degree of
X
r
a
Doctor of Philosophy
November 2011

UNIVERSITY OF SOUTHAMPTON
ABSTRACT
FACULTY OF PHYSICAL AND APPLIED SCIENCES
SCHOOL OF PHYSICS AND ASTRONOMY
Doctor of Philosophy
PHENOMENOLOGICAL ASPECTS OF THE E(6)S.S.M.
by Jonathan Peter Hall
The work in this thesis explores various phenomenological aspects of the E SSM
6
with a particular focus on the inert neutralino sector of the model and on the dark
matter implications. The E SSM is a string theory inspired supersymmetric
6
extension to the Standard Model with an E grand unification group. The model
6
provides a solution to the hierarchy problem of the Standard Model, provides an
explanation for neutrino mass, and has automatic gauge anomaly cancellation.
The inert neutralino sector of the E SSM and the dark matter that naturally
6
arises from this sector is studied for the first time. Limits on the parameter space
from experimental and cosmological observations relating to the inert neutralino
dark matter are explored and the consequences for Higgs boson phenomenology are
investigated. In plausible scenarios it is found that the couplings of the lightest
inert neutralinos to the SM-like Higgs boson are always rather large. This has
major implications for Higgs boson collider phenomenology and leads to large
spin-independent LSP-nucleon cross-sections. Because of the latter, scenarios in
which E SSM inert neutralinos account for all of the observed dark matter are now
6
severely challenged by recent dark matter direct detection experiment analyses. In
plausible scenarios consistent with observations from both cosmology and LEP the
lightest inert neutralino is required to have a mass around half of the Z boson mass
if it contributes to cold dark matter and this means that tan(β) cannot be too large.
A new variant of the E SSM called the E ZSSSM is also presented in which the
6 6 2
dark matter scenario is very different to the inert neutralino cold dark matter
scenario and in which the presence of supersymmetric massless states in the early
universe modifies the expansion rate of the universe prior to Big Bang
Nucleosynthesis. The new dark matter scenario is consistent with current
observations and the modified expansion rate provides a better explanation of
various data than the SM prediction. The prospects for a warm dark matter
scenario in the E SSM are also briefly discussed.
6
i
ii
Dedicated to my friends and family
and to those whom we have lost.
iii
iv
Contents
List of Figures ix
List of Tables xi
Author’s Declaration xv
Acknowledgements xvii
Abbreviations and Conventions xix
Overview 1
1 The Standard Model 3
1.1 Gauge Symmetry and Matter Content . . . . . . . . . . . . . . . . . . 4
1.2 Gauge Anomaly Cancellation, Generations, and the Invisible Z Boson
Decay Width as Measured at LEP . . . . . . . . . . . . . . . . . . . . 8
1.2.1 Gauge anomalies . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.2 The effective number of neutrinos contributing to the invisible
Z boson decay width . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3 The Higgs Potential and GWS EWSB . . . . . . . . . . . . . . . . . . 12
1.4 Induced Dirac Fermion Masses, the CKM Matrix, and Neutrino Mass 16
1.4.1 Neutrino mass and the type-I see-saw mechanism . . . . . . . . 17
1.5 Baryon and Lepton Number Conservation . . . . . . . . . . . . . . . . 19
1.6 The Hierarchy Problem of the SM . . . . . . . . . . . . . . . . . . . . 20
1.7 Unsolved Problems in Particle Physics . . . . . . . . . . . . . . . . . . 24
2 Supersymmetry and Grand Unification 27
v
2.1 Superpotentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2 The Matter Content of the MSSM . . . . . . . . . . . . . . . . . . . . 30
2.2.1 R-parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2.2 The µ problem of the MSSM . . . . . . . . . . . . . . . . . . . 33
2.3 Soft Supersymmetry Breaking . . . . . . . . . . . . . . . . . . . . . . . 34
2.4 Grand Unification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.4.1 Unification of SSB masses . . . . . . . . . . . . . . . . . . . . . 39
3 The E SSM 41
6
3.1 Gauge Symmetry and Matter Content . . . . . . . . . . . . . . . . . . 42
3.1.1 Discrete symmetries of the superpotential . . . . . . . . . . . . 45
3.1.2 Non-Higgs supermultiplets and RH neutrinos . . . . . . . . . . 47
3.2 U(1) Gauge Boson and Gaugino Mixing, EWSB Scale Gaugino Mass
Relations, and Z-Z Mixing . . . . . . . . . . . . . . . . . . . . . . . . 48
′
3.2.1 Soft Gaugino Masses . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2.2 Z-Z mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
′
3.3 EWSB and the Active Higgs Boson Mass Eigenstates . . . . . . . . . . 51
4 Thermal Relic Dark Matter 55
4.1 The Boltzmann Equation . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2 The Freeze-Out Temperature . . . . . . . . . . . . . . . . . . . . . . . 58
4.3 Supersymmetric Dark Matter . . . . . . . . . . . . . . . . . . . . . . . 61
5 Dark Matter in the E SSM 63
6
5.1 The Trilinear Higgs Yukawa Couplings . . . . . . . . . . . . . . . . . . 64
5.2 The Neutralino and Chargino Mass Matrices . . . . . . . . . . . . . . 66
5.3 Analytical Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.3.1 The neutralino masses and mixing for one inert generation . . 69
5.3.2 Annihilation Channels . . . . . . . . . . . . . . . . . . . . . . . 71
5.4 Numerical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.4.1 The parameter space of the model . . . . . . . . . . . . . . . . 75
5.4.2 The neutralino and chargino spectra . . . . . . . . . . . . . . . 76
5.4.3 The dark matter relic density . . . . . . . . . . . . . . . . . . . 78
vi
5.4.4 Deviations from the considered parametrisation . . . . . . . . . 82
5.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 83
6 Novel Higgs Decays in the E SSM 85
6
6.1 Inert Charginos and Neutralinos . . . . . . . . . . . . . . . . . . . . . 87
6.1.1 The diagonal inert Yukawa coupling approximation . . . . . . . 89
6.1.2 ∆ and pseudo-Dirac lightest inert neutralino states . . . . . . 91
27
6.1.3 The couplings of Higgs bosons to inert neutralinos . . . . . . . 93
6.2 Novel Higgs Decays and Dark Matter . . . . . . . . . . . . . . . . . . . 96
6.3 Benchmarks, Constraints, and Predictions . . . . . . . . . . . . . . . . 98
6.3.1 Benchmark scenarios . . . . . . . . . . . . . . . . . . . . . . . . 102
6.3.2 Neutralino and chargino collider limits . . . . . . . . . . . . . . 107
6.3.3 Dark matter direct detection . . . . . . . . . . . . . . . . . . . 109
6.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 112
7 Dark Matter and Big Bang Nucleosynthesis in the E ZSSSM 115
6 2
7.1 The E ZSSSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6 2
7.1.1 The neutralinos of the E ZSSSM . . . . . . . . . . . . . . . . . 118
6 2
7.2 Dark Matter in the cE ZSSSM . . . . . . . . . . . . . . . . . . . . . . 120
6 2
7.2.1 The dark matter calculation . . . . . . . . . . . . . . . . . . . . 121
7.2.2 The cE ZSSSM dark matter scenario . . . . . . . . . . . . . . 121
6 2
7.3 The Inert Singlinos and their Contribution to the Effective Number of
Neutrinos prior to BBN . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.3.1 The calculation of N . . . . . . . . . . . . . . . . . . . . . . . 127
eff
7.3.2 The inert singlino decoupling temperature . . . . . . . . . . . . 129
7.3.3 N in the E ZSSSM . . . . . . . . . . . . . . . . . . . . . . . 132
eff 6 2
7.4 Benchmark Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.5 Warm Inert Singlino Dark Matter in the E SSM . . . . . . . . . . . . 137
6
7.6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 139
8 Summary and Conclusions 141
A Weyl, Majorana, and Dirac Spinors in 3+1 Dimensions 145
vii
B The Pseudoreality of the Spinor Representation of SU(2) 149
Bibliography 151
viii