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JOINT INSTITUTE FOR NUCLEAR RESEARCH BOGOLIUBOV LABORATORY OF THEORETICAL PHYSICS
Manuel Gerardo PAUCAR ACOSTA
Long-lived Superpartners in the Minimal Super symmetric Standard Model
Speciality: 01.04.02—Theoretical Physics
Thesis for the candidate degree in physical and mathematical sciences.
Scientific Supervisors:
Doctor of physical and mathematical sciences D.I. Kazakov
Candidate of physical and mathematical sciences A.V Gladyshev
Dubna 2010
Abstract
The discovery of Supersymmetry is one of the main goals in the proposed experiments at the Large hadron collider (LHC). However, search for supersymmetric particles at colliders usually proceeds from the assumption that all of them are relatively heavy (few hundreds of GeV) and shortlived. In this thesis, we performed a study on the probable existence of long-lived charged superpartners in some regions of parameter space in the framework of the MSSM with supergravity-inspired soft SUSY breaking. Three regions of interest are the co-annihilation region with light scalar charged taus, the region with large negative trilinear scalar coupling Ao distinguished by light scalar top quarks and the focus point region with light higgsino-like charginos where the Higgs parameters [x is small (less than Mz)- The phenomenology of long-lived superpartners at the LHC is discussed.
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Contents
1 Introduction 1
2 Supersyrnmetry and the Supersymmetric Extension of the Standard
Model 5
2.1 Supersyrnmetry................................................................ 7
2.2 MSSM.......................................................................... 9
2.2.1 Structure of the MSSM.................................................. 10
2.3 Minimal Supergravity......................................................... 14
2.4 The mSUGRA Sparticle Spectrum ............................................... 19
2.4.1 Squarks and Sleptons................................................... 19
2.4.2 Neutralinos and Charginos.............................................. 21
2.4.3 A Sample of mSUGRA Sparticle Spectrum.................................. 22
3 Favoured Regions of mSUGRA Parameter Space 25
3.1 Theoretical and Experimental Constraints..................................... 26
3.2 (m0-mi/2) Plane of Parameters Space.......................................... 30
3.2.1 Favoured Parameter Regions............................................. 30
3.2.2 The case for Non-zero A0............................................... 35
4 mSUGRA Co-annihilation Region and Long-lived Charged Sleptons 39
4.1 The (x?-tO Co-annihilation Region -motivations for Long-lived Sparticles 41
4.2 Long-lived r Charged Sparticle .............................................. 43
4.3 Production Cross Section of Long-lived r Charged Sparticle at LHC ... 47
4.4 Discussion................................................................... 51
it)
5 Light Scalar top quarks 52
5.1 The Light Stop Scenario -Long-lived, Scalar lop quarks...................... 53
5.2 Phenomenological Consequences of the Light Stop Scenario.................... 58
5.2.1 Stop decay modes and lifetime....................................... 59
5.3 Discussion.................................................................. 63
6 Long-lived Charginos in the Focus Point Region 64
6.1 The Focus Point Region of rnSUGRA Parameter Space........................... 65
6.2 Phenomenological consequences of the light
Chargino................................................................... 73
6.3 Discussion.................................................................. 79
7 Conclusions 81
Bibliography 84
List of Tables 101
List of Figures 102
Acknowledgements 106
Chapter 1
Introduction
An expected discovery of Supersymmetry (SUSY) at the Large Hadron Collider (LHC) is based on the predictions of the Minimal Supcrsym-metric Standard Model (MSSM) with a wide range of possibilities and uncertainties [1, 2, 3]. The usual pattern is that one has heavy shortlived superparticles which are created in strong and weak interactions and then decay (almost immediately) to usual Standard Model particles with additional missing energy taken away by the Lightest Super symmetric Particle (LSP). Almost everywhere in the parameter space of the Constrained MSSM (CMSSM) (or also known as the minimal Supergravity model, mSUGRA) [4, 5, 6], the LSP is the lightest neutralinoL
However, there are some regions in mSUGRA conventions where the LSP is not the lightest neutralino Xi, but is a Stau r, or a Stop t, or the first chargino xT- These regions are obviously considered as forbidden ones. At the border of these regions when masses of superpartners are degenerate with the neutralino mass and hence the decay rate is suppressed, the Staus, Stops, and charginos become long-lived superparticles. As one
1 Other SUSY breaking scenarios lead to different experimental signatures and different LSP [7, 8, 9, 10, 11, 12, 13, 14, 15].
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departs from the border line, super partners are slightly heavier than the neutralino and thus unstable, then they decay very fast This narrow band along the Stau border line (the co-annihilation region), the Higgs limit line and the radiative electroweak symmetry breaking (REWSB) line (the focus-point region) is consistent with the neutralino relic density constraint (the WMAP restriction on the amount of the dark matter).
We will show that in this band Staus, Stops, and charginos (the Next to Lightest Super symmetric particles (NLSP)) might be rather stable with the lifetime long enough to go through the detector, or produce secondary decay vertices inside the detector. Due to relatively small masses the production cross-section of long-lived NLSP at LHC may reach a few per cent of pb for Staus and charginos, and tens or even hundreds pb for Stops. In this thesis we will investigate these possibilities in detail.
The thesis is organized as follows: ► In Chapter 2, we give a brief overview into the principles of Super symmetry. Then the focus is set on the simplest Supersymmetric Extension of the Standard Model or MSSM. Furthermore, the mSUGRA model is introduced being one possible realization of the MSSM and the framework in which this study has been carried out. ► In Chapter 3, we proceed to analyze the mSUGRA parameter space and examine which parameter regions are worthwhile to explore. Here, we are particularly interested in finding the regions where mass degeneracy between the LSP and NLSP can take place.
► In Chapter 4, we discuss the narrow band near the so-called coannihilation region where Sleptons may be long-lived particles. This region is consistent with the WMAP restrictions on the neutralino dark matter and depends on the value of tan fi. We also discuss the possible creation of
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long-lived Staus at the LHC. ► Then in Chapter 5, we consider the regions of the mSUGRA parameter space where the top Squarks become light and even may be the LSP. This happens when the trilinear scalar coupling Aq becomes very big compared to tuq. We show that in this case the requirement that the LSP is neutral imposes noticeable constraint on the parameter space excluding low mo and m\/2 similar to the constraint from the Higgs mass limit. In some cases these constraints overlap. This picture takes place in a wide region of tan [3. In a narrow band close to the border line the Stops are long-lived particles and decay into quarks and neutralino (chargino). The cross-section of their production at LHC via gluon fusion mechanism in this region may reach a few tens or even hundreds of pb. We discuss this possibility in detail. Then, wc analyze the possibility to get light long-lived charginos ► in Chapter 6. Here, we discuss the so-called focus-point region of parameter space where this possibility can be realized. The mass degeneracy of higgsino-like chargino and two higgsino-like neutralinos is the necessary condition for a long lifetime. It requires the fine-tuning of parameters, but being a single additional constraint in the whole parameter space it can be fulfilled in the mSUGRA along the border line where REWSD fails. In a narrow band close to the border line the charginos are long-lived particles. The cross-sections of their production and co-production at the LHC via electroweak interactions may reach a few tenth of pb. This possibility is investigated in detail. Finally, ► in Chapter 7, we present bur conclusions.
The presence of superpartners with a long-lifetime is also predicted in other theoretical scenarios beyond the Standard Model. For example, in SUSY with 77-parity violation [16]. In this model, the scale of 77-breaking
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is very small since it is determined by the neutrino majorana mass. Consequently, the LSP is a long-lived charged Sparticle and decays with a long lifetime into Standard Model particles. In split SUSY models [17, 18, 19], a long-lived gluino was proposed. In these models, however, the SUSY breaking occurs at high scale ms » 1000 TeV; hence, all Sparticles acquire masses at this scale. In this respect, the gluino is a long-lived Sparticle since the Squarks which mediate its decay are very heavy.
It has also been pointed out that previous searches for long-lived top and bottom Squarks were performed at electron-positron and hadi'on colliders with a center of mass energy up to y/s = 209 GeV and = 1-9 TeV for LEP2 and Tevatron [20, 21, 22], respectively. This led to limits on superpartner masses.
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