Distinguishing between the twin b-flavored unitarity triangles on a circular arc

摘要

With the help of the generalized Wolfenstein parametrization of quark flavor mixing and CP violation, we calculate fine differences between the twin b-flavored unitarity triangles defined by V-ub* V-ud + V-cb* V-cd + V-tb* V-td = 0 and V-ud* V-td + V-us* V-ts + V-ub* V-tb = 0 in the complex plane. We find that apexes of the rescaled versions of these two triangles, described respectively by (rho) over bar + i (eta) over bar = - (V-ub* V-ud) / ( V-cb* V-cd) and = (rho) over tilde + i (eta) over tilde = - (V-ub* V-tb) / (V-us* V-ts), are located on a circular arc whose center and radius are given by O = (0.5, 0.5 cot alpha) and R = 0.5 csc alpha with alpha being their common inner angle. The small difference between ((rho) over bar ,(eta) over bar) and ((rho) over tilde, (eta) over tilde) is characterized by (rho) over tilde - (rho) over bar similar to(eta) over tilde - (eta) over bar similar to O(lambda(2)) with lambda similar or equal to 0.22 being the Wolfenstein expansion parameter, and these two apexes are insensitive to the two-loop renormalization-group running effects up to the accuracy of O(lambda(4)). Some comments are also made on similar features of three pairs of the rescaled unitarity triangles of lepton flavor mixing and CP violation. (C) 2020 The Authors. Published by Elsevier B.V.