Almost exact diagonal reflection symmetries and three-zero texture

In this paper, we consider a three-zero texture with diagonal reflection symmetries in the SM. The three-zero texture has two less assumptions ($(M_u{)}_{11},(M_{\nu }{)}_{11}\mathrm{\ne }0$) than the universal four-zero texture of mass matrices $(M_f{)}_{11}=(M_f{)}_{13,31}=0$ for $f=u,d,\nu ,e$. 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 $O({10}^{-3})$. Some perturbative diagonalizations yield two relations with good accuracy for quark mass and mixing. 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 ($M_d\sim M_e$), we obtain the lightest neutrino mass $m_1\simeq 2.12-5.64$[meV] and the effective mass of the double beta decay $\mathrm{\mid }{m}_{ee}\mathrm{\mid }\simeq 1.23-2.15$[meV].