The interplay between grand unified and flavour symmetries in a Pati-Salam x S4 model

TL;DR

This paper constructs a Pati-Salam x S4 model combining grand unified and flavour symmetries, explaining fermion mass relations and neutrino predictions, while addressing new Higgs and RG running challenges.

Contribution

It develops a novel model integrating Pati-Salam and S4 symmetries, providing insights into fermion masses and neutrino properties with predictive power.

Findings

Explains relations between quark and lepton masses

Predicts neutrino sector observables

Identifies new complications in Higgs and RG analysis

Abstract

Both discrete flavour symmetries and Grand Unified symmetries explain apparent structures in the mass sector of the Standard Model. A model that combines both symmetries is therefore very appealing. We construct a model with the $S_4$ flavour symmetry and the Pati-Salam unification. We show that this model can indeed explain many observable relations between the masses of the quarks and leptons and that it is predictive in the neutrino sector. However, the combination of the two symmetries leads to new complications in the Higgs sector and in the running of the renormalisation group equations.