$1/(M_{R})_{33}$ expansion of the type-I seesaw mechanism and partial $Z_{2}$ symmetry for TM$_{1,2}$ mixing

TL;DR

This paper explores an expansion of the type-I seesaw mechanism focusing on the inverse of the (3,3) element of the right-handed neutrino mass matrix, revealing conditions for matrices and a partial Z2 symmetry that explains large neutrino mixing.

Contribution

It introduces a novel expansion approach of the type-I seesaw mechanism using the inverse of a specific matrix element, linking partial Z2 symmetry to neutrino mixing and hierarchy.

Findings

Conditions for M_R and m_D matrices are derived.

Partial Z2 symmetry leads to large neutrino mixing.

Hierarchical m_D is compatible with large mixing.

Abstract

We consider an expansion of the type-I seesaw mechanism by the inverse of the 3-3 matrix element $1/(M_{R})_{33}$ of the mass matrix of right-handed neutrinos $M_{R}$. Conditions of such a situation are obtained for $M_{R}$ and the Dirac mass matrix $m_{D}$. In this case, a partial $Z_{2}$ symmetry such as $S m_{D} P_{} = \pm m_{D} P_{}$ with a projection matrix $P_{} = {\rm diag} ( 1, 1, 0)$ leads to an approximate $Z_{2}$ symmetry by $S$ for the neutrino mass matrix $m_{\nu}$. Such a partial $Z_{2}$ symmetry is desirable in the context of unified theories because it allows hierarchical $m_{D}$ and the large mixing of $m_{\nu}$ simultaneously.