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

Abstract

We develop techniques for the analysis of SO(2 N) 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(2 N) 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– 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 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.