Magic square and three-zero textures for Dirac neutrinos

TL;DR

This paper explores a novel matrix decomposition for Dirac neutrino mass matrices, combining magic square properties with three-zero textures, and finds that normal mass ordering is favored in this framework.

Contribution

It introduces a new decomposition method for Dirac neutrino mass matrices using magic square features and three-zero textures, highlighting a preference for normal mass ordering.

Findings

Normal ordering of neutrino masses is favored.

The matrix decomposition combines magic square properties with three-zero textures.

The approach provides new insights into neutrino mass structure.

Abstract

We show a matrix decomposition of flavor mass matrix for Dirac neutrinos $M$ by sum as $M=M'+M^0$ where $M'$ obeys the feature of the magic square and $M^0$ is three-zero texture. The favorable three-zero textures in the context of magic square are explored. It turned out that so-called the normal ordering of neutrino masses is favored over the inverted ordering in the context of magic square.