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.
The magic texture is one of the successful textures of the flavor neutrino mass matrix for Majorana neutrinos. In this paper, it turns out that two new types of magic texture are also consistent with the neutrino oscillation experiments, observation of cosmic microwave background radiation and neutrino less double beta decay experiments. The connection between these new magic textures and the leptogenesis scenario of the origin of baryon asymmetry of the Universe is also discussed.
We show a matrix decomposition of flavor mass matrix for Dirac neutrinos [Formula: see text] by sum as [Formula: see text] where [Formula: see text] obeys the feature of the magic square and [Formula: see text] 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.
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