A Supersymmetric Grand Unified Theory of Flavour with PSL(2,7) x SO(10)

TL;DR

This paper develops a supersymmetric grand unified theory of flavor based on PSL(2,7) x SO(10), explaining quark and lepton masses and mixing with specific flavon alignments and neutrino mixing predictions.

Contribution

It introduces a novel GUT model combining PSL(2,7) and SO(10) with a D-term alignment mechanism for flavons, leading to realistic fermion masses and mixing patterns.

Findings

Achieves tri-bimaximal neutrino mixing via type II see-saw.

Predicts neutrinoless double beta decay rates.

Provides a framework for fermion mass hierarchies.

Abstract

We construct a realistic Supersymmetric Grand Unified Theory of Flavour based on PSL(2,7) x SO(10), where the quarks and leptons in the 16 of SO(10) are assigned to the complex triplet representation of PSL(2,7), while the flavons are assigned to a combination of sextets and anti-triplets of PSL(2,7). Using a D-term vacuum alignment mechanism, we require the flavon sextets of PSL(2,7) to be aligned along the 3-3 direction leading to the third family Yukawa couplings, while the flavon anti-triplets describe the remaining Yukawa couplings. Other sextets are aligned along the neutrino flavour symmetry preserving directions leading to tri-bimaximal neutrino mixing via a type II see-saw mechanism, with predictions for neutrinoless double beta decay and cosmology.