Predictions for the unitarity triangle angles in a new parametrization

摘要

A new approach to the parametrization of the CKM matrix, V, is considered in which V is written as a linear combination of the unit matrix I and a nondiagonal matrix U which causes inter-generational-mixing, that is V = cos theta I + i sin theta U. Such a V depends on three real parameters including the parameter theta. It is interesting that a value of theta = pi/4 is required to fit the available data on the CKM-matrix including CP-violation. Predictions of this fit for the angles alpha, beta and gamma for the unitarity triangle corresponding to V11V13* + V21V23* + V31V33* = 0, are given. For theta = pi/4, we obtain alpha = 88.46degrees, beta = 45.046degrees and gamma = 46.5degrees. These values are just about in agreement, within errors, with the present data. It is very interesting that the unitarity triangle is expected to be approximately a right-angle, isosceles triangle. Our prediction sin 20 = 1 is in excellent agreement with the value 0.99 +/- 0.15 +/- 0.05 reported by the Belle collaboration at the Lepton-Photon 2001 meeting. [References: 30]