Universal Mass Matrix and Leptonic $\theta_{13}$ Angle

TL;DR

This paper proposes a universal mixing hypothesis at high energy scales linking quark and lepton sectors, which predicts the leptonic mixing angle θ13 and CP phase with narrow allowed ranges, providing insights into neutrino mixing.

Contribution

It introduces a universal mass matrix framework at high energy scales that relates quark and lepton mixing matrices, predicting the leptonic θ13 angle and CP phase.

Findings

Predicted θ13 range: 0.036 to 0.048

Predicted CP phase δ: 6° to 12°

Narrow allowed regions for leptonic mixing parameters

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 $6^\circ<\delta <12^\circ$.