SO(10) a la Pati-Salam

Abstract

We present rules for rewriting SO(10) tensor and spinor invariants in terms of invariants of its ``Pati-Salam'' maximal subgroup (SU(4)$\times {\mathrm{SU}(2)}_{\mathrm{L}}\times {\mathrm{SU}(2)}_{\mathrm{R}})$ supplemented by the discrete symmetry called D parity. Explicit decompositions of quadratic and cubic invariants relevant to GUT model building are presented and the role of D parity in organizing the terms explained. Our rules provide a complete and explicit method for obtaining the "Clebsch-Gordon" Coefficients for $SO(10)\leftrightarrow G_{PS}$ in a notation appropriate for field theory models. We illustrate the usefulness our methods by calculating previously unavailable mass matrices and couplings of the $SU(2{)}_L$ doublets and $SU(3{)}_c$ triplets in the minimal Susy SO(10) GUT which are essential to specify the phenomenology of this model. We also present the bare effective potential for Baryon number violation in this model and show that it recives novel contributions from exchange of triplet Higgsinos contained the in ``neutrino mass'' Higgs submultiplets ${\bar{\mathbf{\Sigma }}}_{126}(10,1,3)$. This further tightens the emerging connection between neutrino mass and proton decay.

Added result on effective potential for Baryon violation in the minimal Susy SO(10) GUT. New channel due to exchange of triplet from (10,1,3) ("neutrino mass vev") submultiplets of 126bar Higgs representation. Direct contradiction of central results of hep-ph/0401213

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• Direct Evidence for Neutrino Flavor Transformation from Neutral-Current Interactions in the Sudbury Neutrino Observatory
• The minimal supersymmetric grand unified theory
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• Truly Minimal Unification : Asymptotically Strong Panacea ?
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