• Higgs boson
• Supersymmetry

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 as 200-300GeV . At the same time, at variance with previous works, we consider
a setup of the theory where the ì-problem is potentially solved.
In particular the model is defined by the superpotential:

f=lambda*S*H1*H2+k/3*S^3+u*Y*Q*H2-d*Y1*Q*H1-e*Y2*L*H1

and the supersymmetry breaking lagrangian:

Lsoft=-ì^2*S^2-m1^2*H1^2-m2^2*H2^2+(A*lambda*S*(H1*H2)+G*k/3*S^3+h.c.)+...

Unlike the case of the standard NMSSM analysis, we shall allow coupling constants
lambda and k that are perturbative not until the unification scale but only up to an energy of
10TeV . 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 lambda 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 U(1)em, CP invariance and the breaking of the SU(2)*U(1) 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.