Universal Mass Matrix and Leptonic ${\theta }_{13}$ Angle

Abstract

We propose a universal mixing hypothesis between quark and lepton sectors at high energy scale (probably GUT scale) where quark-lepton universality holds. Namely in the charged lepton diagonal base, all the other mass matrices for up and down quarks and neutrinos are diagonalized by the same unitary matrix except for the phase elements. Thanks to this hypothesis, the observed values of the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix and the mixing angles ${\theta }_{12}$ and ${\theta }_{23}$ in the Maki-Nakagawa-Sakata (MNS) lepton mixing matrix can predict the unknown magnitudes of the mixing angle ${\theta }_{13}$ and of the CP violating Dirac phase $\delta$ in the MNS matrix. Their allowed regions are rather narrow, $0.036<sin{\theta }_{13}<0.048$ and $6^{\circ }<\delta <12^{\circ }$.

Comments: 8 pages, 2 figures