Flavor Mixing Democracy and Minimal CP Violation

TL;DR

This paper proposes a unified flavor mixing parametrization for quarks and leptons, linking mixing angles and CP violation to mass hierarchies, and introduces a simple neutrino mixing model predicting observable CP violation effects.

Contribution

It introduces a unique flavor mixing parametrization that relates mixing angles and CP phases to mass hierarchies, and proposes a neutrino mixing ansatz with testable CP violation predictions.

Findings

Quark mixing angles are close to the Cabibbo angle with minimal CP phase.

Lepton mixing angles are large and the CP phase is minimal in the proposed parametrization.

Predicted CP violation in neutrinos could be a few percent for certain mixing angles.

Abstract

We point out that there is a unique parametrization of quark flavor mixing in which every angle is close to the Cabibbo angle \theta_C \simeq 13^\circ with the CP-violating phase \phi_q around 1^\circ, implying that they might all be related to the strong hierarchy among quark masses. Applying the same parametrization to lepton flavor mixing, we find that all three mixing angles are comparably large (around \pi/4) and the Dirac CP-violating phase \phi_l is also minimal as compared with its values in the other eight possible parametrizations. In this spirit, we propose a simple neutrino mixing ansatz which is equivalent to the tri-bimaximal flavor mixing pattern in the \phi_l \to 0 limit and predicts \sin\theta_13 = 1/\sqrt{2} \sin (\phi_l/2) for reactor antineutrino oscillations. Hence the Jarlskog invariant of leptonic CP violation J_l = (\sin\phi_l)/12 can reach a few percent if \theta_13 lies in the range 7^\circ \leq \theta_13 \leq 10^\circ.