Complete Cubic and Quartic Couplings of 16 and 16 in SO(10) Unification

A recently derived basic theorem on the decomposition of SO(2N) vertices is used to obtain a complete analytic determination of all SO(10) invariant cubic superpotential couplings involving 16± semispinors of SO(10) chirality ± and tensor representations. In addition to the superpotential couplings computed previously using the basic theorem involving the 10, 120 and 126 tensor representations we compute here couplings involving the 1, 45 and 210 dimensional tensor representations, i.e., we compute the 16∓16±1, 16∓16±45 and 16∓16±210 Higgs couplings in the superpotential. A complete determination of dimension five operators in the superpotential arising from the mediation of the 1, 45 and 210 dimensional representations is also given. The vector couplings 16±16±1, 16±16±45 and 16±16±210 are also analyzed. The role of large tensor representations and the possible application of results derived here in model building are discussed. Current and permanent address of P.N.