Unification and Texture Universality: The Essence of Hermiticity

TL;DR

This paper proposes a unified theoretical framework for fermion masses using a specific symmetry group, revealing that certain mass matrices have a Hermitian texture, which simplifies understanding their structure.

Contribution

It introduces a novel symmetry-based model unifying Dirac seesaw mechanisms and demonstrates the Hermitian texture of down-type quark and neutrino mass matrices.

Findings

Mass matrices can be described with three universal parameters.

Down-type quark and light neutrino mass matrices exhibit Hermitian textures.

The framework preserves natural Yukawa coupling values.

Abstract

A unified framework sheltering the type-I Dirac seesaw, based on the $\Delta(27) \times Z_7 \times Z_{5} \times Z_4 \times Z_3$ symmetry, is proposed, preserving the naturalness of Yukawa couplings. It helps to visualize mass matrices within the lepton and quark sectors in terms of \textit{three universal parameters}: $\Sigma_1$, $\Sigma_2$, and $\Sigma_3$, highlighting that the down-type quark and light neutrino mass matrices exhibit a \textit{Hermitian} texture.