SO(10)-Grand Unification and Fermion Masses
b"In the state of the art the Standard Model is the best gauge\\ntheory describing interactions among elementary particles. It\\ncomprises all of the fundamental interactions in nature except\\ngravitation. Its predictions have been experimentally tested to a\\nhigh level of accuracy. However, it is not considered to be the\\nfundamental theory of gauge interactions. It contains a lot of\\narbitrary parameters. It can not predict the fermion masses and\\nfails to explain the smallness of neutrino masses which have been\\nobserved by recent experiments. It contains no gauge bosons that\\ncan mediate nucleon decays via baryon and lepton number violating\\nprocess, which are needed to explain the baryon asymmetry in our\\nuniverse. Furthermore, CP violation has to be introduced into\\nthe CKM and MNS matrices by hand.\\n\\nThe shortcomings of the Standard Model can be solved in the\\nframework of grand unified gauge theories (GUTs) which have\\ngreater degrees of freedom. GUT's which have truly one coupling\\nconstant are based on gauge groups that contain the Standard Model\\nas a subgroup. There are a limited number of such gauge groups.\\nSO(10) is a fully symmetric gauge group that has two outstanding\\nfeatures: It unifies all the known gauge interactions under a\\nsingle coupling strength and classifies all the known fermions of\\na family under a single spinor.\\n\\nIn this work, we will study SO(10) grand unification in its full\\nextent by using different explicit matrix representations which\\nexhibit the structure of SO(10) in a very transparent way. Our\\napproach consists mainly of two stages: We will derive the\\nexplicit expressions of the mass-eigenvalues and mass-eigenstates\\nof the physical gauge bosons from a mass squared-matrix that\\ncontains all the information about the mixing parameters among the\\ngauge fields and the phases which are sources for CP violation.\\nIn the light of this analysis, we will derive the explicit\\nexpressions for the interaction Lagrangians of the charged\\ncurrents, the neutral currents and the charged and colored\\ncurrents in SO(10). We will present explicit expressions of the\\nvector and axial-vector couplings of the two neutral currents in\\nSO(10). We will show how the baryon, lepton and baryon minus\\nlepton number violating processes and their explicit CP\\nviolating phases are accommodated in the SO(10) theory.\\n\\n\\nThe Higgs potential that we use to implement in the Higgs\\nmechanism will be constructed in a most general fashion through a\\ncareful study of the Higgs fields of SO(10), where we give\\nspecial emphasis on illustrating the explicit matrix\\nrepresentation of these Higgs fields. The potential part of the\\nHiggs Lagrangian will give us the properties of the minimum of the\\nvacuum, and the kinetic part will give us the mass-squared matrix\\nof the gauge bosons via spontaneous symmetry breakdown. The same\\nHiggs multiplets will be coupled to fermions through a democratic\\nYukawa matrix. Thereby, we will derive explicit expressions for\\nthe fermion masses of the third family including Majorana and\\nDirac masses for neutrinos. We will introduce a flavor-eigenbasis\\nfor neutrinos and find the mass-eigenstates and mass-eigenvalues\\nof the neutrinos. Explicit expressions for CP violation in the\\nneutrino sector will be obtained.\\n\\n\\nIn the second stage of our work, we will evaluate all the above\\nmentioned quantities. We will compare our results with those of\\nthe Standard Model like the W and Z masses and the vector and\\naxial-vector coupling of the NC current and the fermion masses\\nof the third family. In addition, we will present the values of\\nthe physical quantities that are not present in the Standard Model\\nlike the masses of new gauge bosons, the vector and axial-vector\\ncouplings of a new NC current, the masses of a light left-handed\\nand a heavier right-neutrino, the values of various mixing\\nparameters and CP phases etc.\\n\\nThe input values required for these evaluations will be acquired\\nmainly from two sources: First, we will determine the vacuum\\nexpectation values and the coupling strengths of gauge\\ninteractions given by the SO(10) theory in so far as possible\\nthrough studying the mass scales in SO(10) in the framework of\\ncoupling unification. Complementarily, we will determine the\\nvacuum expectation values and their phases by adjusting them to\\nthe masses of the known gauge bosons and fermions below the Fermi\\nscale which are accurately measured and known. We will be able to\\npredict more than 67 parameters with an input of 7 vacuum\\nexpectation values, 5 angles, 1 gauge coupling and 1 Yukawa\\ncoupling."