Phenomenology of Trimaximal mixing with one texture equality

TL;DR

This paper investigates specific neutrino mass matrix textures with one texture equality that are compatible with trimaximal mixing patterns TM1 and TM2, analyzing their implications for neutrino parameters and symmetries.

Contribution

It identifies which textures are compatible with current data and explores their implications and group-theoretic motivations.

Findings

Seven textures compatible with TM1 mixing.

Six textures compatible with TM2 mixing.

Implications for neutrino mass scale and CP phases.

Abstract

We study neutrino mass matrices with one texture equality and the neutrino mixing matrix having either its first (TM$_1$) or second (TM$_2$) column identical to that of the tribimaximal mixing matrix. We found that out of total fifteen possible neutrino mass matrices with one texture equality, only seven textures are compatible with $TM_1$ mixing and six textures are compatible with $TM_2$ mixing in the light of the current neutrino oscillation data. These textures have interesting implications for the presently unknown parameters such as the neutrino mass scale, effective Majorana neutrino mass, the atmospheric mixing and the Dirac- and Majorana-type CP violating phases. We, also, present the $S_{3}$ group motivation for some of these textures.