Complete cubic and quartic couplings of 16 and 16 in SO(10) unification Original Research Article

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.