Almost exact diagonal reflection symmetries and three-zero texture

Abstract

In this paper, we consider the three-zero texture with diagonal reflection symmetries in the SM. The three-zero texture has two less assumptions ((Mu)11,(Mν)11≠0) than the universal four-zero texture of mass matrices (Mf)11=(Mf)13,31=0 for f=u,d,ν,e. The texture allows diagonal reflection symmetries to be almost exact and d-e unification. They reproduce the CKM and MNS matrices with accuracies of O(10−4) and O(10−3). By using perturbative approximations of the diagonalization, two relations with good accuracy for quark mass and mixing are obtained. Although this calculation is done in a special basis, it is a general result in a sense, because other textures and generalized CP symmetries exist by some weak basis transformation.By assuming a d-e unified relation (Md∼Me), we obtain the lightest neutrino mass m1≃2.12−5.64[meV] and the effective mass of the double beta decay |mee|≃1.23−2.15[meV].