A flavour GUT model with theta_13^PMNS = theta_C / sqrt(2)

TL;DR

This paper introduces a supersymmetric SU(5) GUT model with A_4 symmetry that naturally explains the relation between neutrino mixing angle theta_13^PMNS and the Cabibbo angle, linking quark and lepton sectors.

Contribution

It presents a novel GUT model incorporating family symmetry and specific Clebsch-Gordan factors to unify quark and lepton mass ratios and mixing angles, including a full fit to experimental data.

Findings

Achieves theta_13^PMNS 0 theta_C / f2 from charged lepton contributions

Predicts quark-lepton mass ratios consistent with experiments

Provides a full MCMC fit to quark and lepton data

Abstract

We propose a supersymmetric SU(5) GUT model with an A_4 family symmetry - including a full flavon- and messenger sector - which realises the relation theta_13^PMNS \simeq theta_C / sqrt(2). The neutrino sector features tri-bimaximal mixing, and theta_13^PMNS \simeq theta_C / sqrt(2) emerges from the charged lepton contribution to the PMNS matrix, which in turn is linked to quark mixing via specific GUT relations. These GUT relations arise after GUT symmetry breaking from a novel combination of group theoretical Clebsch-Gordan factors, which in addition to large theta_13^PMNS lead to promising quark lepton mass ratios for all generations of quarks and leptons and to m_s / m_d = 18.95_(-0.24)^(+0.33), in excellent agreement with experimental results. The model also features spontaneous CP violation, with all quark and lepton CP phases determined from family symmetry breaking. We perform a full Markov Chain Monte Carlo fit to the available quark and lepton data, and discuss how the model can be tested by present and future experiments.