Exploring inconsistencies with the Cabibbo-Kobayashi-Maskawa model

Abstract

A small upper-bound is obtained for the CP phase $\delta$ in a CKM matrix, $|\sin\delta| \le 0.44$ based on CP independent data on $|V_{ub}/V_{cb}|$ alone. Potential inconsistencies with the CKM model in existing data which need a theory beyond the standard model to overcome emerge in the analysis using this CKM matrix. In addition, all CP asymmetry measurables for the $B_d- \bar B_d$ system are expressed solely by the CP phases in the decay amplitudes. Remarkably the CP asymmetry of the bench mark process $B_d\to \psi K_S$ equals sin$2\delta$. This will soon be measured by BaBar and Belle to confront the above upper-bound.