Phenomenological aspects of mirage mediation [Elektronische Ressource] / vorgelegt von Valéri Löwen

Valéri Löwen

Sujets

• Physik

Informations

• Publié par: rheinische_friedrich-wilhelms-universitat_bonn
• Publié le: 01 janvier 2009
• Nombre de lectures: 14
• Langue: English
• Poids de l'ouvrage: 3 Mo

Extrait

Phenomenological Aspects of
Mirage Mediation
Dissertation
zur
Erlangung des Doktorgrades (Dr. rer. nat.)
der
Mathematisch Naturwissenschaftlichen Fakultät
der
Rheinischen Friedrich Wilhelms Universität
zu Bonn
vorgelegt von
Valéri Löwen
aus
Tschernorezk
Bonn2009ii
Angefertigt mit Genehmigung der Mathematisch Naturwissenschaftlichen Fakultät
der Rheinischen Friedrich–Wilhelms–Universität Bonn.
1. Gutachter: Prof. Dr. Hans Peter Nilles
2. Priv. Doz. Dr. Stefan Förste
Tag der Promotion: 14. Juli2009
Diese Dissertation ist auf dem Hochschulschriftenserver der ULB Bonn
http://hss.ulb.uni-bonn.de/diss_online elektronisch publiziert.
Erscheinungsjahr: 2009iii
Abstract
We consider the possibility that string theory vacua with spontaneously broken
supersymmetry and a small positive cosmological constant arise due to hidden
sector matter interactions, known as F uplifting/F downlifting. We analyze this
procedure in a model independent way in the context of type IIB and heterotic
string theory. Our investigation shows that the uplifting/downlifting sector
has very important consequences for the resulting phenomenology. Not only
does it adjust the vacuum energy, but it can also participate in the process of
moduli stabilization. In addition, we find that this sector is the dominant source
of supersymmetry breaking. It leads to a hybrid mediation scheme and its
signature is a relaxed mirage pattern of the soft supersymmetry breaking terms.
The low energy spectra exhibit distinct phenomenological properties and dier
from conventional schemes considered so far.ivv
Acknowledgments
First and foremost, I would like to thank Prof. Dr. Hans Peter Nilles for taking
me into his research group and giving me the unique opportunity to work at
the cutting edge of theoretical high energy physics. I am also very thankful to
the members of Prof. Dr. Nilles’ research group, past and present, for their
helpfulness and encouragement. Especially I would like to thank Dr. Andrea
Zanzi for countless helpful discussions on physics and beyond. I am also grateful
to Dr. Oleg Lebedev for valuable advices. Furthermore, I would like to thank
Dr. Patrick Vaudrevange and Dr. Saúl Noé Ramos Sánchez for special support
during the past years. I am deeply grateful to Michael Blaszczyk, Dr. Christoph
Lüdeling and Dr. Andrea Zanzi for proof readings. I also want to thank the sta
of the theory department, in particular Dagmar Faßbender, Sandra Heidbrink,
Dr. Andreas Wißkirchen and Patricia Zündorf. I wish to express my sincere
thanks to Prof. Dr. Klaus Desch, Priv. Doz. Dr. Stefan Förste and Prof. Dr.
Pavel Kroupa for finding time to participate in the board of examiners.
Finally, I would like to thank my parents and my grandparents for their endless
love and support.viContents
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 Road to mirage mediation 13
2.1 The model of KKLT . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Generalization of the KKLT model . . . . . . . . . . . . . . . . . . 18
2.3 Soft masses in the KKLT scheme . . . . . . . . . . . . . . . . . . . 22
2.3.1 Soft gaugino masses . . . . . . . . . . . . . . . . . . . . . . 22
2.3.2 Soft scalar squared masses . . . . . . . . . . . . . . . . . . . 26
2.4 Mirage mediation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.5 General properties of mirage mediation . . . . . . . . . . . . . . . 29
3 Uplifting in Type IIB string theory 33
3.1 No go theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2 D Uplifting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3 F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.1 Moduli sector . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.2 Matter . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.3 The uplifting . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.4 The pattern of SUSY breaking in F uplifting . . . . . . . . . . . . . 39
3.4.1 The little hierarchy . . . . . . . . . . . . . . . . . . . . . . . 40
3.4.2 Comparison with KKLT . . . . . . . . . . . . . . . . . . . . 40
3.4.3 An example . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.4.4 Soft breaking terms . . . . . . . . . . . . . . . . . . . . . . . 42
4 Downlifting in heterotic string theory 47
4.1 Modular invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Dilaton and a modulus . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.3 Stabilization of the dilaton . . . . . . . . . . . . . . . . . . . . . . . 51
4.3.1 No go with a single condensate . . . . . . . . . . . . . . . . 51
4.3.2 Racetracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.3.3 Kähler stabilization . . . . . . . . . . . . . . . . . . . . . . . 54
4.4 F downlifting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.4.1 Introducing matter fields . . . . . . . . . . . . . . . . . . . 56
4.4.2 A matter field and a condensate . . . . . . . . . . . . . . . 57viii Contents
4.4.3 Adjusting the vacuum energy . . . . . . . . . . . . . . . . . 59
4.4.4 Matter dominated SUSY breaking . . . . . . . . . . . . . . 59
4.5 The pattern of SUSY breaking in F downlifting . . . . . . . . . . . 61
4.5.1 The little hierarchy . . . . . . . . . . . . . . . . . . . . . . . 62
4.5.2 Another example . . . . . . . . . . . . . . . . . . . . . . . . 63
4.5.3 Soft breaking terms . . . . . . . . . . . . . . . . . . . . . . . 64
4.6 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.6.1 The model of DKP . . . . . . . . . . . . . . . . . . . . . . . 67
4.6.2 A benchmark model . . . . . . . . . . . . . . . . . . . . . . 69
5 Phenomenology of uplifting/downlifting 73
5.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.2 Aspects of the soft terms at M . . . . . . . . . . . . . . . . . . . 75GUT
5.3 Constraints on the soft terms at M . . . . . . . . . . . . . . . . . 78TeV
5.3.1 General remarks . . . . . . . . . . . . . . . . . . . . . . . . 79
5.3.2 Electroweak symmetry breaking . . . . . . . . . . . . . . . 79
5.3.3 Color and charge breaking minima . . . . . . . . . . . . . . 80
5.3.4 Neutralino dark matter . . . . . . . . . . . . . . . . . . . . 80
5.3.5 Accelerator constraints . . . . . . . . . . . . . . . . . . . . . 82
5.3.6 The MSSM hierarchy problem . . . . . . . . . . . . . . . . 82
5.4 Phenomenological aspects of F uplifting . . . . . . . . . . . . . . . 84
5.4.1 Aspects of the soft terms at M . . . . . . . . . . . . . . . 84TeV
05.4.2 Dependence on and . . . . . . . . . . . . . . . . . . . . 87
5.4.3 Low energy spectroscopy . . . . . . . . . . . . . . . . . . . 87
5.5 Phenomenological aspects of F downlifting . . . . . . . . . . . . . 91
05.5.1 Dependence on and . . . . . . . . . . . . . . . . . . . . 92
5.5.2 Aspects of the soft terms at M . . . . . . . . . . . . . . . 92TeV
5.5.3 Low energy spectroscopy . . . . . . . . . . . . . . . . . . . 93
5.6 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6 Conclusions 99
A Soft breaking terms in mixed modulus anomaly mediation 101
A.1 Soft terms at tree level . . . . . . . . . . . . . . . . . . . . . . . . . 102
A.2 Soft terms at loop level . . . . . . . . . . . . . . . . . . . . . . . . . 104
A.3 Soft in F uplifting . . . . . . . . . . . . . . . . . . . . . . . . 108
A.4 Soft terms in F downlifting . . . . . . . . . . . . . . . . . . . . . . 109
B MSSM parameters 111
C Renormalization group 117
Bibliography 119Chapter 1
Introduction
1.1 Motivation
The idea that our world is build up from indivisible constituents was formu
lated, for the first time, by Democritus around 400 B.C. in his famous atomic
hypothesis. With John Dalton, about two thousand years later, the exploration
of the composition of matter began and has grown ever since. Today, we be
lieve that the fundamental constituents of matter are leptons and quarks and
that there are four interactions between all elementary particles:
electromagnetism, weak force, strong force and gravity.
Motivated by the desire to find a unified description of nature based on the
smallest possible set of fundamental laws, the enormous progress in theoretical
physics has led to the formulation of the Standard Model (SM) of particle physics
[1–3]: a renormalizable quantum field theory that describes strong, weak and
electromagnetic interactions in terms of the gauge group SU(3) SU(2) U(1) .C L Y
It successfully unifies weak and electromagnetic interactions within the elec
troweak (EW) theory which, below the EW scale M 100 GeV, gets sponta EW
neously broken to electromagnetism by the Higgs mechanism.
Although the predictions of the SM have been confirmed experimentally at
very high precision, the Higgs boson has not been discovered yet. The EW
precision data from the Large Electron Proton Collider (LEP2) suggests that the
Higgs particle, if exis