The Interplay Between GUT and Flavour Symmetries in a Pati-Salam x S4 Model

TL;DR

This paper explores a model combining Pati-Salam GUT and S4 flavor symmetries, demonstrating how their interplay constrains fermion masses, mixings, and the Higgs sector, and reproduces key features of the Standard Model.

Contribution

It presents a novel integration of Pati-Salam and S4 symmetries, analyzing their combined effects on fermion mass matrices and phenomenology at high energy scales.

Findings

Reproduces quark and lepton masses and mixings within the model.

Shows the combined symmetries constrain the Higgs sector and Yukawa couplings.

Predicts the reactor mixing angle near current experimental bounds.

Abstract

Both Grand Unified symmetries and discrete flavour symmetries are appealing ways to describe apparent structures in the gauge and flavour sectors of the Standard Model. Both symmetries put constraints on the high energy behaviour of the theory. This can give rise to unexpected interplay when building models that possess both symmetries. We investigate on the possibility to combine a Pati-Salam model with the discrete flavour symmetry $S_4$ that gives rise to quark-lepton complementarity. Under appropriate assumptions at the GUT scale, the model reproduces fermion masses and mixings both in the quark and in the lepton sectors. We show that in particular the Higgs sector and the running Yukawa couplings are strongly affected by the combined constraints of the Grand Unified and family symmetries. This in turn reduces the phenomenologically viable parameter space, with high energy mass scales confined to a small region and some parameters in the neutrino sector slightly unnatural. In the allowed regions, we can reproduce the quark masses and the CKM matrix. In the lepton sector, we reproduce the charged lepton masses, including bottom-tau unification and the Georgi-Jarlskog relation as well as the two known angles of the PMNS matrix. The neutrino mass spectrum can present a normal or an inverse hierarchy, and only allowing the neutrino parameters to spread into a range of values between $\lambda^{-2}$ and $\lambda^2$, with $\lambda\simeq0.2$. Finally, our model suggests that the reactor mixing angle is close to its current experimental bound.