Analysis of couplings with large tensor representations in SO(2N) and proton decay

We develop techniques for the analysis of SO(2N) invariant couplings which allow a full exhibition of the SU(N) invariant content of the spinor and tensor representations. The technique utilizes a basis consisting of a specific set of reducible SU(N) tensors in terms of which the SO(2N) invariant couplings have a simple expansion. The technique is specially useful for couplings involving large tensor representations. We exhibit the technique by performing a complete determination of the trilinear couplings in the superpotential for the case of SO(10) involving the 16 plet of matter, i.e., we give a full determination of the 16–16–10s, 16–16–120a and 16–16–126̄s couplings. The possible role of large tensor representations in the generation of quark lepton textures is discussed. It is shown that the couplings involving 126̄-dimensional representation generate extra zeros in the Higgs triplet textures which can lead to an enhancement of the proton decay lifetime by a factor of 103. These results also have implications for neutrino mass textures.