Predictive Dirac neutrino spectrum with strong CP solution in SU(5)L × SU(5)R unification

Abstract

We develop a grand unified theory of matter and forces based on the gauge symmetry SU(5)L × SU(5)R with parity interchanging the two factor groups. Our main motivation for such a construction is to realize a minimal GUT embedding of left-right symmetric models that provide a parity solution to the strong CP problem without the axion. We show how the gauge couplings unify with an intermediate gauge symmetry SU(3)cL × SU(2)2L × U(1)L × SU(5)R, and establish its consistency with proton decay constraints. The model correctly reproduces the observed fermion masses and mixings and leads to naturally light Dirac neutrinos with their Yukawa couplings suppressed by a factor MI/MG, the ratio of the intermediate scale to the GUT scale. We call this mechanism type II-Dirac seesaw. Furthermore, the model predicts δCP = ±(130.4±1.2)° and $${m}_{{\nu }_{1}}$$ = (4.8 – 8.4) meV for the Dirac CP phase and the lightest neutrino mass. We demonstrate how the model solves the strong CP problem via parity symmetry.