the interplay between natural and accidental supersymmetry

240 Pages·2014·2.15 MB·English

by  Christopher P. Brust

THE INTERPLAY BETWEEN NATURAL AND
ACCIDENTAL SUPERSYMMETRY
by
Christopher P. Brust
A dissertation submitted to The Johns Hopkins University in conformity with the
requirements for the degree of Doctor of Philosophy.
Baltimore, Maryland
February, 2014
c Christopher P. Brust 2014
⃝
All rights reserved
Abstract
In this thesis, we will explore the subject of the little hierarchy problem which
plagues solutions to the big hierarchy problem of the Standard Model of particle
physics.
In the first half of this thesis, we study the theoretical framework for a supersym-
metric resolution of the little hierarchy problem, known as natural supersymmetry,
and argue that regions of the parameter space of this model have been missed by
search strategies employed at the large hadron collider, but could be searched for
with new search strategies.
In the second half of this thesis, we explore the possibility of embedding natural
supersymmetry in models of warped extra dimensions in order to UV-complete them
by utilizing a mechanism known as accidental supersymmetry. We study the mech-
anism of accidental supersymmetry in the Randall-Sundrum framework by focusing
on a toy model, and argue that accidental supersymmetry is capable solving the little
hierarchy problem in that toy model. Finally, as models in the Randall-Sundrum
framework themselves require UV completions, we demonstrate that it is possible to
ii
ABSTRACT
realize the mechanism of accidental supersymmetry within the UV-complete frame-
work of type IIB superstring theory.
iii
Acknowledgments
I would first like to thank my advisor, Raman Sundrum, for his continual support,
useful advice, collaboration and friendship over the duration of my time at Johns
Hopkins. He has truly been the best kind of advisor a graduate student could hope
to have.
I would also like to thank David E. Kaplan, who has served as a co-advisor and
collaborator to me over the years. His support and insight have been invaluable to
me.
I am very grateful for the support from all of my friends, both within and outside
of the PHA community, without whose friendship I surely would be lost.
I am wonderfully grateful for the continual love and support of my family over the
years, and for all of the sacrifices they have made on my behalf.
Finally, I am extremely grateful to my finace´e, April, who has loved me, encour-
aged me to pursue my dreams and supported me in every way possible.
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Dedication
This thesis is dedicated to April, for everything she has done for me.
v
Contents
Abstract ii
Acknowledgments iv
List of Tables xi
List of Figures xiii
1 Introduction and Background 1
1.1 The Standard Model and Motivations for its Extension . . . . . . . . 4
1.1.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.2 The Hierarchy Problem . . . . . . . . . . . . . . . . . . . . . . 8
1.1.3 Other Concerns with the SM . . . . . . . . . . . . . . . . . . . 11
1.2 Extensions of the SM . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.2.1 The Minimal Supersymmetric Standard Model . . . . . . . . . 14
1.2.2 Warped Extra Dimensions . . . . . . . . . . . . . . . . . . . . 20
1.2.3 The Little Hierarchy Problem . . . . . . . . . . . . . . . . . . 23
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CONTENTS
2 Natural SUSY: The Story Below 10 TeV 26
2.1 Introduction and General Concerns . . . . . . . . . . . . . . . . . . . 28
(cid:46)
2.2 Natural SUSY 10 TeV with Light Higgsinos . . . . . . . . . . . . . 31
2.2.1 Effective Lagrangian, Neglecting Third-Generation Mixing . . 33
2.2.2 Higgs Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.2.3 Naturalness in Natural SUSY . . . . . . . . . . . . . . . . . . 37
(cid:46)
2.3 Natural SUSY 1 TeV with Light Higgsinos . . . . . . . . . . . . . . 43
2.3.1 Effective Lagrangian, Neglecting Third-Generation Mixing . . 46
2.3.2 Dark Matter Considerations . . . . . . . . . . . . . . . . . . . 47
(cid:46)
2.4 Natural SUSY 10 TeV with Heavy Higgsinos . . . . . . . . . . . . 48
2.4.1 Effective Lagrangian, Neglecting Third-Generation Mixing . . 49
2.4.2 Higgsino Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
(cid:46)
2.5 Natural SUSY 1 TeV with Heavy Higgsinos . . . . . . . . . . . . . 50
2.5.1 Effective Lagrangian, Neglecting Third-Generation Mixing . . 51
2.5.2 Effective Lagrangian with Neutralino LSP . . . . . . . . . . . 51
2.6 Flavor-Changing Neutral Currents and CP Violation . . . . . . . . . 52
2.7 R-Parity versus R-Parity Violation . . . . . . . . . . . . . . . . . . . 57
2.7.1 Proton Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.7.2 Unification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.7.3 Dark Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.7.4 RPV and FCNCs . . . . . . . . . . . . . . . . . . . . . . . . . 61
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CONTENTS
2.7.5 RPV with Lepton Number Conservation . . . . . . . . . . . . 62
2.7.6 R-Parity Violation with Baryon Number Conservation . . . . 63
2.8 Dirac Gauginos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.8.1 Naturalness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.8.2 R-Parity Violation . . . . . . . . . . . . . . . . . . . . . . . . 67
2.8.3 Electric Dipole Moments . . . . . . . . . . . . . . . . . . . . . 69
3 Natural SUSY at the LHC 71
3.1 Collider Phenomenology of R-Parity Conserving Natural SUSY . . . 72
3.1.1 Neutralino and Squarks . . . . . . . . . . . . . . . . . . . . . 74
3.1.2 Overview of Some Other Possibilities . . . . . . . . . . . . . . 79
3.1.2.1 Gluinos . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.1.2.2 Collider-Stable Squarks . . . . . . . . . . . . . . . . 81
3.1.2.3 Neutralino and Chargino LSPs . . . . . . . . . . . . 82
3.2 R-Parity Violating Phenomenology . . . . . . . . . . . . . . . . . . . 83
3.3 Reduction to the RPV Simplified Model . . . . . . . . . . . . . . . . 88
3.3.1 Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.3.2 Couplings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.3.3 Higgsinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.4 Signals and Strategy of Search . . . . . . . . . . . . . . . . . . . . . . 93
3.5 Details of Event Simulations, Backgrounds and Reach . . . . . . . . . 100
3.6 Brief Comments on Neutral Current Decays . . . . . . . . . . . . . . 107
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CONTENTS
3.7 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4 Accidental SUSY and RS: The Story Above 10 TeV 118
4.1 Intro to Accidental SUSY . . . . . . . . . . . . . . . . . . . . . . . . 120
4.2 A Toy Model of Accidental SUSY . . . . . . . . . . . . . . . . . . . . 122
4.3 Further Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5 Accidental SUSY and String Theory: The Story Above The Story
Above 10 TeV 134
5.1 Accidental SUSY Ingredients . . . . . . . . . . . . . . . . . . . . . . . 135
5.2 The Conifold and its Deformation . . . . . . . . . . . . . . . . . . . . 138
F
5.3 The Complex Cone Over . . . . . . . . . . . . . . . . . . . . . . . 142
0
5.3.1 The Supergravity Side . . . . . . . . . . . . . . . . . . . . . . 143
5.3.2 The Gauge Side . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5.3.3 The AdS/CFT Matching . . . . . . . . . . . . . . . . . . . . . 160
5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
6 Looking Forward 165
A Notations and Conventions 168
B Relevant Mathematical Results 170
B.1 Groups, Algebras and Representations . . . . . . . . . . . . . . . . . 170
B.2 Differential Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
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CONTENTS
B.3 Grassmann Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
C Relevant Physics Results 176
C.1 Introduction to SUSY . . . . . . . . . . . . . . . . . . . . . . . . . . 176
C.2 Anti-de Sitter Space . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
C.3 Conformal Field Theory . . . . . . . . . . . . . . . . . . . . . . . . . 189
C.4 The AdS/CFT correspondence . . . . . . . . . . . . . . . . . . . . . . 190
C.5 IIB Supergravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
C.6 The Conifold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
Bibliography 205
Vita 226
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