Triminimal Parametrization of Quark Mixing Matrix

TL;DR

This paper introduces a new, simple triminimal parametrization of the quark mixing matrix based on quark-lepton complementarity and tri-bimaximal lepton mixing, offering fast convergence and practical utility.

Contribution

It presents a novel triminimal parametrization of the CKM matrix rooted in quark-lepton complementarity and tri-bimaximal lepton mixing, enhancing simplicity and convergence.

Findings

Derived a new parametrization with three small angles and a CP phase.

Established relations between quark and lepton mixing parametrizations.

Discussed deviations from quark-lepton complementarity.

Abstract

Starting from a new zeroth order basis for quark mixing (CKM) matrix based on the quark-lepton complementarity and the tri-bimaximal pattern of lepton mixing, we derive a triminimal parametrization of CKM matrix with three small angles and a CP-violating phase as its parameters. This new triminimal parametrization has the merits of fast convergence and simplicity in application. With the quark-lepton complementary relations, we derive relations between the two unified triminimal parametrizations for quark mixing obtained in this work and for lepton mixing obtained by Pakvasa-Rodejohann-Weiler. Parametrization deviating from quark-lepton complementarity is also discussed.