Narrow Results

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.

We show a matrix decomposition of flavor mass matrix for Dirac neutrinos $M$ by sum as $M=M^{\prime }+M^0$ where $M^{\prime }$ 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 the so-called normal ordering of neutrino masses is favored over the inverted ordering in the context of magic square.