Neutrino Mixing based on Mass Matrices with a $2 \leftrightarrow 3$ Symmetry

TL;DR

This paper systematically investigates lepton mass matrices with a $2 ightarrow 3$ symmetry broken only by phases, exploring different symmetry scenarios and their implications for neutrino phenomenology without relying on explicit parameter values.

Contribution

It introduces a comprehensive analysis of lepton mass matrices with $2 ightarrow 3$ symmetry broken by phases, considering different symmetry implementations and their effects on neutrino masses.

Findings

Neutrino seesaw mass matrix can obey $2 ightarrow 3$ symmetry even if $M_R$ does not.

Different symmetry scenarios lead to distinct phenomenological implications.

The approach does not depend on explicit parameter values, allowing broad applicability.

Abstract

Under the assumption that the $2\leftrightarrow 3$ symmetry is broken only through phases, we give a systematical investigation of possible lepton mass matrix forms without referring to the explicit parameter values. The two types of the $2\leftrightarrow 3$ symmetry are investigated: one is that the left- and right-handed fields $(f_L, f_R)$ obey the symmetry, and another one is that only $f_L$ obeys the symmetry. In latter case, in spite of no $2\leftrightarrow 3$ symmetry in the Majorana mass matrix $M_R$ for $\nu_R$, the neutrino seesaw mass matrix still obey the $2\leftrightarrow 3$ symmetry. Possible phenomenologies are discussed.