SO(10)À LA PATI–SALAM

Abstract

To facilitate explicit analysis of SO (10) GUT's we present rules for rewriting SO (10) tensor and spinor invariants in terms of invariants of its "Pati–Salam" maximal subgroup ( SU (4)× SU (2) L × SU (2) 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)↔ SU (4)× SU (2) L × SU (2) R 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 receives novel contributions from exchange of triplet Higgsinos contained the in "neutrino mass" Higgs submultiplets [Formula: see text]. This further tightens the emerging connection between neutrino mass and proton decay.