Universit`
a degli Studi di Pisa
Corso di Laurea Specialistica in Scienze Fisiche
Anno Accademico 2006-2007 Riassunto tesi di laurea specialistica
Supersymmetry without
a Light Higgs Boson
Candidato Relatore
Stefania Gori Prof. Riccardo Barbieri
In this work we want to study from a theoretical point of view some important features of a Supersymmetric Model, in order to make predictions on the masses of the Higgs sector (Higgs bosons and Higgsinos) and of other particles, such as stops and gluinos.
The most often quoted aspect of supersymmetric models is the presence of a relatively light Higgs boson. In this work we consider the Next to Minimal Supersymmetric Standard Model (NMSSM) in a region of parameter space where the lightest Higgs boson can be as heavy asp200 300q GeV . At the same time, at variance with previous works, we consider a setup of the theory where the µ-problem is potentially solved.
In particular the model is defined by the superpotential: f λ ˆS ˆH1Hˆ2
k 3Sˆ
3 uyˆ¯
uQ ˆˆH2 ˆ¯dydQ ˆˆH1 ˆ¯eyeL ˆˆH1 (1)
and the supersymmetry breaking lagrangian: Lbreaking µ2 s|S| 2 m2 1|H1|2 m22|H2|2 AλSpH1H2q Gk3S3 h.c. ¸ φ m2φ|φ|2 1 2 3 ¸ i1 Mig˜ig˜i (2)
Unlike the case of the standard NMSSM analysis, we shall allow coupling constants λ and k that are perturbative not until the unification scale but only up to an energy of 10T eV . This is the big price to pay to obtain a heavier Higgs boson. In this way we can take at low energy ( 500GeV ) two coupling constants λ and k of order 2 and therefore
neglect the gauge couplings. We will show how these two constants permit to make the lightest Higgs boson relatively heavy (up to about 300 GeV).
We begin with the investigation of the stability of the potential and of the symmetries of the theory (such as Up1qem, CP invariance and the breaking of the SUp2q U p1q symmetry). Then we consider the spectrum of the theory (both the bosonic and the fermionic one), starting from the general features. We find that there is a special point in the parameter space in which an exact symmetry appears (the custodial symmetry). At this point, to be able to look in detail at the spectrum of the theory in an analytic way, we shall restrict ourselves to the region of parameter space where the vacuum expectation value of the singlet S is somewhat bigger than those of the Higgs doublets. We conclude with some numerical examples of the spectrum and with an analysis of the fine tuning conditions.
