Phenomenological aspects of noncommutative geometry approach to the standard model.

Abstract

The aim of this thesis is to explore the implications that spectral action principle has on the scalar sector of the models derived from the noncommutative geometry approach. After a brief introduction for noncommutative geometry and some short discussions on why it is a promising tool to describe high energy physics in chapter one, the first fruit of this approach is presented in chapter two. This is effectively a singlet extended standard model with some specific features rooted in the settings of the noncommutative geometry approach. Among these features are the specific scalar potential and the relation between scalar couplings, Yukawa couplings, and the unified gauge coupling. The latter is usually looked at as the initial condition for running of the couplings down from unification scale. Some of the implications of these features such as their consistency with the particle masses and their influence on the running of gauge couplings are discussed in chapter two. It is shown that there is a range of initial values at the unification scale which is able to produce Higgs and top quark masses at low energies. The stability of the vacuum and the deviation of gauge couplings from experimental values are discussed and compared at the two-loop level with a real scalar singlet and the pure standard model. In chapter three, the spectral Pati-Salam model is described concisely. We then study the implications of the tight restrictions of the noncommutative geometry settings along with constraints of the spectral action on the scalar potential. As a result, it will be clear that the scalar potential in the spectral Pati-Salam model does not provide a suitable vacuum to break to the standard model. However, this potential is proton decay free up to tree level even though diquark and leptoquark vertices exist. In the appendix, we introduce some computational tools including a package under Mathematica to find two-loop order renormalization group equations.