An SO(10) grand unified theory of flavor

We present a supersymmetric SO(10) grand unified theory (GUT) of flavor based on an S4 family symmetry. It makes use of our recent proposal to use SO(10) with type II seesaw mechanism for neutrino masses combined with a simple ansatz that the dominant Yukawa matrix (the 10-Higgs coupling to matter) has rank one. In this paper, we show how the rank one model can arise within some plausible assumptions as an effective field theory from vectorlike 16 dimensional matter fields with masses above the GUT scale. In order to obtain the desired fermion flavor texture we use S4 flavon multiplets which acquire vevs in the ground state of the theory. By supplementing the S4 theory with an additional discrete symmetry, we find that the flavon vacuum field alignments take a discrete set of values provided some of the higher dimensional couplings are small. Choosing a particular set of these vacuum alignments appears to lead to an unified understanding of observed quark-lepton flavor: (i) the lepton mixing matrix that is dominantly tri-bimaximal with small corrections related to quark mixings; (ii) quark lepton mass relations at GUT scale: mb ≃ mτ and mμ ≃ 3ms and (iii) the solar to atmospheric neutrino mass ratio m⨀/matm ≃ θCabibbo in agreement with observations. The model predicts the neutrino mixing parameter, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {U_{e3}} \simeq {{{\theta_{\text{Cabibbo}}}} \mathord{\left/{\vphantom {{{\theta_{\text{Cabibbo}}}} {\left( {3\sqrt 2 } \right) \sim 0.05}}} \right.} {\left( {3\sqrt 2 } \right) \sim 0.05}} $\end{document}, which should be observable in planned long baseline experiments.