SO(10) - Grand unification and fermion masses

In this work, we 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 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 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 present explicit expressions of the vector and axial-vector couplings of the two neutral currents in SO(10). We 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 is 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 derive explicit expressions for the fermion masses of the third family including Majorana and Dirac masses for neutrinos. We 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 are obtained. In the second stage of our work, we evaluate all the above mentioned quantities. In addition, we 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 are acquired mainly from two sources: First, we 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 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 are able to predict more than 67 parameters with an input of 7 vacuum expectation values, 5 angles, 1 gauge coupling and 1 Yukawa coupling. (Orig.)