A4 × SU(5) SUSY GUT of flavour with trimaximal neutrino mixing

The recent discovery of a sizeable reactor angle θ13 by Daya Bay and RENO has ruled out exact tri-bimaximal (TB) lepton mixing. Recently two of us studied the vacuum alignment of the Altarelli-Feruglio A4 family symmetry model including additional flavons in the 1′ and 1′′ representations, leading to so-called “trimaximal” neutrino mixing and allowing a potentially large reactor angle. Here we show how such a model may arise from a Supersymmetric (SUSY) Grand Unified Theory (GUT) based on SU(5), leading to sum rule bounds \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \left| s \right| \leqslant \frac{{{\theta_C}}}{3},\left| a \right| \leqslant \frac{1}{2}\left( {r + \frac{{{\theta_C}}}{3}} \right)\left| {\cos \;\delta } \right| $\end{document} (these predictions are based upon the assumption of a Georgi-Jarlskog relation), where s, a, r parameterise the solar, atmospheric and reactor angle deviations from their TB mixing values, δ is the CP violating oscillation phase, and θC is the Cabibbo angle.