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

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

2001-03-14

arxiv.org/abs/hep-ph/0103165v3

Phys.Lett. B506 (2001) 68-76; Erratum-ibid. B508 (2001) 216

Physics

High Energy Physics

High Energy Physics - Phenomenology

14 pages, Latex: With the corrections of an Erratum included in the text of paper

Scientific paper

10.1016/S0370-2693(01)00392-6

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.

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