Interplay between exact μ − τ reflection symmetries, four-zero texture and universal texture

Abstract

In this letter, we consider exact μ−τ 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 νL. By a bi-maximal transformation, all the mass matrices lead to μ−τ reflection symmetric forms, which separately satisfy Tumu,ν⁎Tu=mu,ν and Tdmd,e⁎Td=md,e.Reconciliation between the μ−τ reflection symmetries and observed sin⁡θ13 predicts δCP≃sin−1⁡[memμc13s23s13]≃203∘. Moreover, imposition of universal texture (mf)11=0 for f=u,d,ν,e predicts the normal hierarchy with the lightest neutrino mass |m1|=6.26 or 2.54 meV.