Simple parametrization of neutrino mixing matrix

TL;DR

This paper introduces simple, Wolfenstein-like parametrizations of the neutrino mixing matrix using the smallest mixing angle as an expansion parameter, connecting neutrino and quark mixing via quark-lepton complementarity.

Contribution

It presents novel parametrizations of the neutrino mixing matrix based on the smallest mixing angle, utilizing the triminimal approach in both CK and KM schemes, linking to quark mixing parameters.

Findings

New Wolfenstein-like parametrizations for neutrino mixing.

Connection established between neutrino and quark mixing parameters.

Shared features with the Wolfenstein parametrization of quark mixing.

Abstract

We propose simple forms of neutrino mixing matrix in analogy with the Wolfenstein parametrization of quark mixing matrix, by adopting the smallest mixing angle $\theta_{13}$ as a measure of expansion parameters with the tribimaximal pattern as the base matrix. The triminimal parametrization technique is utilized to expand the mixing matrix under two schemes, i.e., the standard Chau-Keung (CK) scheme and the original Kobayashi-Maskawa (KM) scheme. The new parametrizations have their corresponding Wolfenstein-like parametrizations of quark mixing matrix, and therefore they share the same intriguing features of the Wolfenstein parametrization. The newly introduced expansion parameters for neutrinos are connected to the Wolfenstein parameters for quarks via the quark-lepton complementarity.