Analysis of Couplings with Large Tensor Representations in SO(2N) and Proton Decay

Abstract

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 ${16-16-10_s}$, ${16-16-120_a}$ and ${16-16-\bar{126}_s}$ couplings. The possible role of large tensor representations in the generation of quark lepton textures is discussed. It is shown that the couplings involving $\bar{126}$ 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 $10^3$. These results also have implications for neutrino mass textures.