Unified triminimal parametrizations of quark and lepton mixing matrices

TL;DR

This paper explores unified triminimal parametrizations of quark and lepton mixing matrices, comparing different basis matrices and showing how these can improve convergence and unify various parametrization approaches.

Contribution

It introduces a unified framework for quark and lepton mixing matrices using triminimal parametrizations based on different basis matrices, including tri-bimaximal mixing.

Findings

Triminimal expansion around tri-bimaximal mixing converges faster.

Unified description of various parametrizations for quark and lepton sectors.

Conversion between triminimal and Wolfenstein-like parametrizations is possible.

Abstract

We present a detailed study on triminimal parametrizations of quark and lepton mixing matrices with different basis matrices. We start with a general discussion on the triminimal expansion of the mixing matrix and on possible unified quark and lepton parametrization using quark-lepton complementarity (QLC). We then consider several interesting basis matrices and compare the triminimal parametrizations with the Wolfenstein-like parametrizations. The usual Wolfenstein parametrization for quark mixing is a triminimal expansion around the unit matrix as the basis. The corresponding QLC lepton mixing matrix is a triminimal expansion around the bimaximal basis. Current neutrino oscillation data show that the lepton mixing matrix is very well represented by the tri-bimaximal mixing. It is natural to take it as an expanding basis. The corresponding zeroth order basis for quark mixing in this case makes the triminimal expansion converge much faster than the usual Wolfenstein parametrization. The triminimal expansion based on tri-bimaximal mixing can be converted to the Wolfenstein-like parametrizations discussed in the literature. We thus have a unified description between different kinds of parametrizations for quark and lepton sectors: the standard parametrizations, the Wolfenstein-like parametrizations, and the triminimal parametrizations.