Magic square and Dirac flavor neutrino mass matrix

TL;DR

This paper explores the compatibility of the magic square texture with Dirac neutrino mass matrices, finding partial similarities and a preference for normal mass ordering.

Contribution

It extends the concept of magic square textures from Majorana to Dirac neutrinos, analyzing their compatibility and implications for neutrino mass ordering.

Findings

Magic square features appear approximately in Dirac neutrino mass matrices.

Magic squares favor normal mass ordering over inverted.

Partial structural similarities between magic squares and Dirac neutrino textures.

Abstract

The magic texture is one of the successful textures of the flavor neutrino mass matrix for the Majorana type neutrinos. The name "magic" is inspired by the nature of the magic square. We estimate the compatibility of the magic square with the Dirac, instead of the Majorana, flavor neutrino mass matrix. It turned out that some parts of the nature of the magic square are appeared approximately in the Dirac flavor neutrino mass matrix and the magic squares prefer the normal mass ordering rather than the inverted mass ordering for the Dirac neutrinos.