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Özer, Alp Deniz (2005): SO(10)-Grand Unification and Fermion Masses. Dissertation, LMU München: Faculty of Physics
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Abstract

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 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). We will present explicit expressions of the vector and axial-vector couplings of the two neutral currents in SO(10). We will show how the baryon, lepton and baryon minus lepton number violating processes and their explicit CP violating phases are accommodated in the SO(10) theory. The Higgs potential that we use to implement in the Higgs mechanism will be constructed in a most general fashion through a careful study of the Higgs fields of SO(10), where we give special emphasis on illustrating the explicit matrix representation of these Higgs fields. The potential part of the Higgs Lagrangian will give us the properties of the minimum of the vacuum, and the kinetic part will give us the mass-squared matrix of the gauge bosons via spontaneous symmetry breakdown. The same Higgs multiplets will be coupled to fermions through a democratic Yukawa matrix. Thereby, we will derive explicit expressions for the fermion masses of the third family including Majorana and Dirac masses for neutrinos. We will introduce a flavor-eigenbasis for neutrinos and find the mass-eigenstates and mass-eigenvalues of the neutrinos. Explicit expressions for CP violation in the neutrino sector will be obtained. In the second stage of our work, we will evaluate all the above mentioned quantities. We will compare our results with those of the Standard Model like the W and Z masses and the vector and axial-vector coupling of the NC current and the fermion masses of the third family. In addition, we will present the values of the physical quantities that are not present in the Standard Model like the masses of new gauge bosons, the vector and axial-vector couplings of a new NC current, the masses of a light left-handed and a heavier right-neutrino, the values of various mixing parameters and CP phases etc. The input values required for these evaluations will be acquired mainly from two sources: First, we will determine the vacuum expectation values and the coupling strengths of gauge interactions given by the SO(10) theory in so far as possible through studying the mass scales in SO(10) in the framework of coupling unification. Complementarily, we will determine the vacuum expectation values and their phases by adjusting them to the masses of the known gauge bosons and fermions below the Fermi scale which are accurately measured and known. We will be able to predict more than 67 parameters with an input of 7 vacuum expectation values, 5 angles, 1 gauge coupling and 1 Yukawa coupling.