Nearest-Neighbour-Interactions from a minimal discrete flavour symmetry within SU(5) Grand Unification

TL;DR

This paper explores a minimal Z_4 flavor symmetry within SU(5) Grand Unification, demonstrating its role in shaping fermion mass matrices, suppressing proton decay, and aligning with experimental neutrino data.

Contribution

It identifies Z_4 as the minimal discrete symmetry capable of producing NNI mass matrices in an SU(5) GUT framework with two Higgs doublets.

Findings

Z_4 symmetry enforces NNI structure in quark and charged lepton mass matrices.

Only two neutrino mass textures fit experimental data under this symmetry.

Z_4 symmetry suppresses proton decay via color Higgs triplet exchange.

Abstract

A flavour symmetry based on Z_4 is analysed in the context of SU(5) Grand Unification with the standard fermionic content plus three right-handed neutrinos. The role of Z_4 is to forbid some Yukawa couplings of up- and down-quarks to Higgs scalars such that the quark mass matrices M_u, M_d have Nearest-Neighbour-Interaction (NNI) structure, once they are generated through the electroweak symmetry breaking. It turns out in this framework that Z_4 is indeed the minimal discrete symmetry and its implementation requires the introduction of at least two Higgs quintets, which leads to a two Higgs doublet model at low energy scale. Due to the SU(5) unification, it is shown that the charged lepton mass matrix develops also NNI form. However, the effective neutrino mass matrix exhibits a non parallel pattern, in the framework of the type-I seesaw mechanism. Analysing all possible zero textures allowed by gauge-horizontal symmetry SU(5) x Z_4, it is seen that only two patterns are in agreement with the leptonic experimental data and they could be further distinguished by the light neutrino mass spectrum hierarchy. It is also demonstrated that Z_4 freezes out the possibility of proton decay through exchange of colour Higgs triplets at tree-level.