Dependence of the Quark-Lepton Complementarity on Parametrizations of the CKM and PMNS Matrices

TL;DR

This paper investigates how the quark-lepton complementarity relations depend on different parametrizations of the CKM and PMNS matrices, identifying conditions under which they hold exactly or approximately.

Contribution

It systematically analyzes all angle-phase parametrizations to determine where QLC relations are valid and explores the impact of small mixing angles and radiative corrections.

Findings

QLC relations approximately hold in five parametrizations

Vanishing small mixing angles ensure exact QLC relations in those parametrizations

Sensitivity of QLC relations to radiative corrections is discussed

Abstract

The quark-lepton complementarity (QLC) is very suggestive in understanding possible relations between quark and lepton mixing matrices. We explore the QLC relations in all the possible angle-phase parametrizations and point out that they can approximately hold in five parametrizations. Furthermore, the vanishing of the smallest mixing angles in the CKM and PMNS matrices can make sure that the QLC relations exactly hold in those five parametrizations. Finally, the sensitivity of the QLC relations to radiative corrections is also discussed.