Unified parametrization of quark and lepton mixing matrices in tri-bimaximal pattern

TL;DR

This paper introduces a unified parametrization of quark and lepton mixing matrices based on quark-lepton complementarity within a tri-bimaximal pattern, simplifying the expression of physical quantities like CP violation.

Contribution

It presents a novel combined parametrization of quark and lepton mixing matrices using QLC and tri-bimaximal pattern, enhancing understanding of fermion mixing.

Findings

Simplified expression for the Jarlskog parameter of CP violation.

Unified parametrization links quark and lepton mixing matrices.

Application to physical quantities demonstrates the approach's effectiveness.

Abstract

Parametrization of the quark and lepton mixing matrices is the first attempt to understand the mixing of fermions. In this work, we parameterize the quark and lepton matrices with the help of quark-lepton complementarity (QLC) in a tri-bimaximal pattern of lepton mixing matrix. In this way, we combine the parametrization of the two matrices with each other. We apply this new parametrization to several physical quantities, and show its simplicity in the expression of, e.g., the Jarlskog parameter of CP violation.