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 $16-16-{\overline{126}}_s$ couplings. The possible role of large tensor representations in the generation of quark lepton textures is discussed. It is shown that the couplings involving $\overline{126}$ 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.

arXiv comment14 pages, Latex: With the corrections of an Erratum included in the text of paper

References in corpus (20)

• Predictive Neutrino Spectrum in Minimal $SO(10)$ Grand Unification
• Nucleon Decay in the Minimal Supersymmetric $SU(5)$ Grand Unification
• Stitching the Yukawa Quilt
• Fermion masses, neutrino oscillations, and proton decay in the light of SuperKamiokande
• Natural Suppression of Higgsino-Mediated Proton Decay in Supersymmetric SO(10)
• Effect of an RRRR dimension 5 operator on the proton decay in the minimal SU(5) SUGRA GUT model
• Unified Theories with U(2) Flavor Symmetry
• Nucleon Decay Matrix Elements from Lattice QCD
• Natural Gauge Hierarchy in SO(10)
• Neutrino Oscillations in an SO(10) SUSY GUT with U(2)xU(1)${}^n$ Family Symmetry
• Nucleon Decay in a Realistic SO(10) SUSY GUT
• See-saw and Supersymmetry or Exact R-parity
• Suggested new modes in supersymmetric proton decay
• From CKM Matrix to MNS Matrix: A Model Based on Supersymmetric $SO(10)\times U(2{)}_F$ Symmetry
• Construction of a Minimal Higgs SO(10) SUSY GUT Model
• Bi-maximal Neutrino Mixings And Proton Decay In SO(10) With Anomalous Flavor $\mathcal{U}(1)$
• Hierarchies and Textures in Supergravity Unification
• Textured Minimal and Extended Supergravity Unification and Implications for Proton Stability
• Effects of Large CP Phases on the Proton Lifetime in Supersymmetric Unification
• E_6 unification model building II. Clebsch-Gordan coefficients of 78$\otimes$78

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