Unification and Texture Universality: The Essence of Hermiticity

Abstract

A unified framework sheltering the type-I Dirac seesaw, based on the $\Delta (27)$ group supplemented by other cyclic symmetries 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. Several phenomenological aspects, such as lepton flavour violation and nonunitarity of the lepton mixing matrix are explored. The stability of the proposed texture under renormalization group evolution is also investigated.