Unitarity boomerangs of quark and lepton mixing matrices

Abstract

The most popular way to present mixing matrices of quarks (CKM) and leptons (PMNS) is the parametrization with three mixing angles and one CP-violating phase. There are two major options in this kind of parametrizations, one is the original Kobayashi-Maskawa (KM) matrix, and the other is the Chau-Keung (CK) matrix. In a new proposal by Frampton and He, a unitarity boomerang is introduced to combine two unitarity triangles, and this new presentation displays all four independent parameters of the KM parametrization in the quark sector simultaneously. In this paper, we study the relations between KM and CK parametrizations, and also consider the quark-lepton complementarity (QLC) in the KM parametrization. The unitarity boomerang is discussed in the situation of the CK parametrization for comparison with that in the KM parametrization in the quark sector. Then we extend the idea of unitarity boomerang to the lepton sector, and check the corresponding unitarity boomerangs in the two cases of parametrizations.

18 latex pages, 4 figures. Version accepted for publication in PLB

References in corpus (8)

• Phenomenology with Massive Neutrinos
• Quark-Lepton Complementarity in Unified Theories
• Quark lepton complementarity and renormalization group effects
• The Seesaw Mechanism in Quark-Lepton Complementarity
• Triminimal Parametrization of Quark Mixing Matrix
• Unitarity Boomerang
• Unified parametrization of quark and lepton mixing matrices in tri-bimaximal pattern
• Unified triminimal parametrizations of quark and lepton mixing matrices

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• A prediction of neutrino mixing matrix with CP violating phase
• On Leptonic Unitary Triangles and Boomerangs
• Hunting for New Physics with Unitarity Boomerangs
• The $\alpha$, $\beta$ and $\gamma$ parameterizations of CP violating CKM phase
• Simple parametrization of neutrino mixing matrix
• The $\beta$ angle as the CP violating phase in the CKM matrix