Interplay between $\mu$-$\tau$ reflection symmetry, four-zero texture and universal texture

Abstract

In this letter, we consider exact $\mu -\tau$ reflection symmetries for quarks and leptons. Fermion mass matrices are assumed to be four-zero textures for charged fermions $f=u,d,e$ and a symmetric matrix for neutrinos ${\nu }_L$. By a bi-maximal transformation, all the mass matrices lead to $\mu -\tau$ reflection symmetric forms, which seperately satisfy $T_u{m}_{u,\nu }^{\ast }{T}_u=m_{u,\nu }$ and $T_d{m}_{d,e}^{\ast }{T}_d=m_{d,e}$. Reconciliation between the $\mu -\tau$ reflection symmetries and observed $\sin {\theta }_{13}$ predicts ${\delta }_{CP}\simeq 203^{\circ }$. Moreover, imposition of universal texture $(m_f{)}_{11}=0$ for $f=u,d,\nu ,e$ predicts the normal hierarchy with the lightest neutrino mass $|m_1|=6.26$ or $2.54$ meV.

5 pages, substantially modified, the final version published in PLB