Couplings of vector-spinor representation for SO(10) model building

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

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Originally posted at http://arxiv.org/abs/hep-ph/0511172v1. Preprint of an article published in Journal of High Energy Physics, no.2, 2006.

Abstract

Higgs multiplet in the vector-spinor representations of SO(10), i.e., the 1̄4̄4̄ + 144 multiplet can break the SO(10) gauge symmetry spontaneously in one step down to the Standard Model gauge group symmetry SU(3)_C×SU(2)_L×U(1)_Y and a recent analysis has used such vector-spinors for building a new class of SO(10) grand unification models (hep-ph/0506312). Here we discuss the techniques for the computation of several classes of vector-spinor couplings using the Basic Theorem on the SO(2N) vertex expansion developed by the authors. The computations include the cubic couplings of the vector-spinors with SO(10) tensors, quartic selfcouplings of the vector-spinors, and couplings of the vector-spinors with spinor representations of SO(10). The last set include couplings of vector-spinors with the 16-plets of quarks and lepton and with the 16 and 1̄6̄ of Higgs. These couplings provide a crucial tool for further development of the SO(10) grand unification using vector-spinor representations. These include study of quark-lepton masses, analysis of dimension five operators including baryon and lepton number violating operators, and study of neutrino masses and mixings. Illustrative examples are given for their computation using a sample of vector-spinor couplings.