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 $V=\cos \theta I+i\sin \theta U$. Such a $V$ depends on 3 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 $V_{11}{V}_{13}^{\ast }+V_{21}{V}_{23}^{\ast }+V_{31}{V}_{33}^{\ast }=0$, are given. For $\theta$=$\pi /4$, we obtain $\alpha =88.46^{\circ }$, $\beta =45.046^{\circ }$ and $\gamma =46.5^{\circ }$. 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 $\sin 2\beta =1$ 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.

Comments: 11 pages, latex, no figures