SO(10)-Grand Unification and Fermion Masses [thesis]

Alp Deniz Özer
In the state of the art the Standard Model is the best gauge theory describing interactions among elementary particles. It comprises all of the fundamental interactions in nature except gravitation. Its predictions have been experimentally tested to a high level of accuracy. However, it is not considered to be the fundamental theory of gauge interactions. It contains a lot of arbitrary parameters. It can not predict the fermion masses and fails to explain the smallness of neutrino masses which
more » ... trino masses which have been observed by recent experiments. It contains no gauge bosons that can mediate nucleon decays via baryon and lepton number violating process, which are needed to explain the baryon asymmetry in our universe. Furthermore, CP violation has to be introduced into the CKM and MNS matrices by hand. The shortcomings of the Standard Model can be solved in the framework of grand unified gauge theories (GUTs) which have greater degrees of freedom. GUT's which have truly one coupling constant are based on gauge groups that contain the Standard Model as a subgroup. There are a limited number of such gauge groups. SO(10) is a fully symmetric gauge group that has two outstanding features: It unifies all the known gauge interactions under a single coupling strength and classifies all the known fermions of a family under a single spinor. In this work, we will study SO(10) grand unification in its full extent by using different explicit matrix representations which exhibit the structure of SO(10) in a very transparent way. Our approach consists mainly of two stages: We will derive the explicit expressions of the mass-eigenvalues and mass-eigenstates of the physical gauge bosons from a mass squared-matrix that contains all the information about the mixing parameters among the gauge fields and the phases which are sources for CP violation. In the light of this analysis, we will derive the explicit expressions for the interaction Lagrangians of the charged currents, the neutral currents and the charged and colored currents in SO(10). W [...]
doi:10.5282/edoc.4695 fatcat:r3v5ajwl4rcotf425g6bkqc44i