Unitarity boomerangs of quark and lepton mixing matrices

Understand

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.