Correlating lepton mixing angles and mixing matrix with Wolfenstein parameters

TL;DR

This paper establishes a novel correlation between lepton and quark mixing angles, expressing the PMNS matrix in terms of Wolfenstein parameters, and deduces a hierarchical structure similar to the CKM matrix.

Contribution

It introduces a new relation linking lepton mixing angles to the Wolfenstein parameter, enabling a Wolfenstein-like parametrization of the PMNS matrix.

Findings

Lepton mixing angles are related to the Wolfenstein parameter λ.

The PMNS matrix can be parametrized by λ, A, and δ.

Bimaximal mixing pattern emerges at leading order.

Abstract

Inspired by a new relation $\theta_{13}^{\rm PMNS}={\theta_C}/{\sqrt{2}}$ observed from the relatively large $\theta_{13}^{\rm PMNS}$, we find that the combination of this relation with the quark-lepton complementarity and the self-complementarity results in correlations of the lepton mixing angles with the quark mixing angles. We find that the three mixing angles in the PMNS matrix are all related to the Wolfenstein parameter $\lambda$ in the quark mixing, so they are also correlated. Consequently, the PMNS matrix can be parameterized by $\lambda$, A, and a Dirac CP-violating phase $\delta$. Such parametrizations for the PMNS matrix have the same explicitly hierarchical structure as the Wolfenstein parametrization for the CKM matrix in the quark mixing, and the bimaximal mixing pattern is deduced at the leading order. We also discuss implications of these phenomenological relations in parametrizations.