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 non-diagonal matrix $U$ which causes intergenerational-mixing, that is $V=\cosθI+i\sinθU$. Such a $V$ depends on 3 real parameters including the parameter $θ$. It is interesting that a value of $θ=π/4$ 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 $V_{11}V^*_{13} + V_{21} V^*_{23} +V_{31}V^*_{33} =0$, are given. For $θ$=$π/4$, we obtain $α=88.46^\circ$, $β=45.046^\circ$ and $γ=46.5^\circ$. 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-angled, isosceles triangle. Our prediction $\sin 2β= 1$ is in excellent agreement with the value $0.99\pm 0.15\pm 0.05$ reported by the Belle collaboration at the Lepton-Photon 2001 meeting.