engleski

SO(10) group theory for the unified model building

The complete tables of Clebsch-Gordan (CG) coefficients for a wide class of $SO(10)$ SUSY grand unified theories (GUTs) are given. Explicit expressions of states of all corresponding multiplets under standard model gauge group $G_{; ; ; 321}; ; ; = SU(3)_{; ; ; C}; ; ; \times SU(2)_{; ; ; L}; ; ; \times U(1)_{; ; ; Y}; ; ; $, necessary for evaluation of the CG coefficients are presented. The SUSY $SO(10)$ GUT model considered here includes most of the Higgs irreducible representations usually used in the literature: ${; ; ; \bf 10}; ; ; $, ${; ; ; \bf 45}; ; ; $, ${; ; ; \bf 54}; ; ; $, ${; ; ; \bf 120}; ; ; $, ${; ; ; \bf 126}; ; ; $, ${; ; ; \bf \overline{; ; ; 126}; ; ; }; ; ; $ and ${; ; ; \bf 210}; ; ; $. Mass matrices of all $G_{; ; ; 321}; ; ; $ multiplets are found for the most general superpotential. These results are indispensable for the precision calculations of the gauge couplings unification and proton decay, etc.

SUSY; GUT; SO(10) Clebsch Gordan coefficients; SUSY; mass matrices; proton decay

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