SO(10) Group Theory for the Unified Model Building
Takeshi Fukuyama, Amon Ilakovac, Tatsuru Kikuchi, Stjepan Meljanac, Nobuchika Okada
Abstract
The complete tables of Clebsh-Gordan (CG) coefficients for a wide class of SO(10) SUSY grand unified theories (GUTs) are given. Explicit expression of all states and corresponding multiplets under standard model gauge group G321 = SU(3)C x SU(2)L x U(1)Y, necessary for evaluation of the CG coefficients are presented. The SUSY SO(10) GUT model considered here incudes most of the Higgs irreducible representations usually used in the literature: 10, 45, 54, 120, 126 126-bar and 210. Mass matrices of all G321 multiplets are found for the most general superpotential. These results are indispensible for the precision calculations of the gauge coupling unification and proton decay, etc.
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