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

Pran Nath, Northeastern University
Raza M. Syed, Northeastern University

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Originally posted at http://arxiv.org/abs/hep-ph/0103165v3. Preprint of an article published in Physics Letters B, v.506 no.1-2, 2001.

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_α and 16 − 16 − 12ˉ6_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 12ˉ6 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.