Predictions for the unitarity triangle angles in a new parametrization

Abstract

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 θ I + i sin θ U. Such a V depends on three real parameters including the parameter θ. It is interesting that a value of θ = p/4 is required to fit the available data on the CKM-matrix including CP-violation. Predictions of this fit for the angles α, β and γ for the unitarity triangle corresponding to V₁₁V₁₃+V₂₁V₂₃+V₃₁V₃₃ = 0, are given. For θ = p/4, we obtain α = 88.46°, β = 45.046° and γ = 46.5°. 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 2β= 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.