Asymmetric tribimaximal texture

Abstract

We construct a texture where the seesaw matrix is diagonalized by the tribimaximal (TBM) matrix with a phase. All angles of the Cabibbo-Kobayashi-Maskawa matrix and Pontecorvo-Maki-Nakagawa-Sakata matrix are consistent with particle data group values, and the mass relations of quarks and charged leptons extrapolated to the grand unified theory scale are satisfied, including the Gatto relation. The novel ingredient is the asymmetry of the down-quark and charged lepton Yukawa matrices. Explaining the reactor angle requires a $\overline{)\mathrm{CP}}$ phase in the TBM matrix, resulting in the Jarlskog-Greenberg invariant at $|J|=0.028$, albeit with an undetermined sign. While $SO(10)$ restrains the right-handed neutrino Majorana matrix, the neutrino masses are left undetermined.