Spontaneous CP violation in the Next-to-Minimal Supersymmetric Standard Model

In this thesis we will investigate CP violation within the Next-to-Minimal Supersymmetric Standard Model (NMSSM). The study of the violation of the CP symmetry is relevant for several reasons. The origin of CP symmetry violation observed experimentally in the kaon system and nowhere else, is still uncertain and under active investigation. Also, and perhaps more intriguing, CP violation is a necessary ingredient of explanations of baryogenesis: supersymmetric theories allow for several sources of CP violation, whether explicit or not, therefore guaranteeing the necessary amount of CP violation. In fact, there are potentially so many CP violating phases, that it is an issue whether supersymmetry is compatible with the tight experimental constraints on the electron and neutron electric dipole moments. In particular we will concentrate on the study of Spontaneous CP Violation (SCPV), where the vacuum is CP non conserving. In the Standard Model, although the Electroweak symmetry is spontaneously broken, SCPV cannot occur, as at least two Higgs doublets are needed. Also, within the simplest extension of the Standard Model, the Minimal Supersymmetric Standard Model, SCPV, although possible in principle, is ruled out experimentally. Here we will show a detailed analysis of possible SCPV under general assumptions within the NMSSM. The implications of this are also addressed both for experiments at high energy colliders and also at low energy for the neutron and electron electric dipole moments when the CP violating phases are large. We have considered these phases as arbitrary parameters, and have studied the consequences as a function of the amount of CP violation present. In chapter 1 and 2 we briefly review the MSSM and the NMSSM. In chapter 3 we review the literature on SCPV, in both models, as a comparison. We also discuss the assumptions and formalism which will be used extensively in the following analysis. In chapter 4 we discuss weak SCPV 1 and its possible experimental consequences. The study of this scenario will effectively constitute the main aim of this work. In chapter 5 we present a thorough numerical analysis of SCPV both weak and not, over a vast area of the parameter space. The chapter also includes a discussion of the Higgs sector when CP is not violated, and when it is violated explicitly. In chapter 6 we address the issue of whether SCPV within the NMSSM is experimentally testable with emphasis on the weak SCPV case. In chapter 7 we then discuss the constraints coming from the neutron and electron electric dipole moments, which are relevant when SCPV is not weak. We then summarise our overall conclusions.