Bayesian analysis of the constraints on $\gamma$ from $B \rightarrow K\pi$ rates and CP asymmetries in the flavor-SU(3) approach

Abstract.

The relation between the branching ratios and direct CP asymmetries of $B \rightarrow K\pi$ decays and the angle $\gamma$ of the CKM unitarity triangle is studied numerically in the general framework of the SU(3) approach, with minimal assumptions about the parameters not fixed by flavor-symmetry arguments. Experimental and theoretical uncertainties are subjected to a statistical treatment according to the Bayesian method. In this context, the experimental limits recently obtained by CLEO, BaBar and Belle for the direct CP asymmetries are translated into the bound $\vert\gamma - 90^{\circ}\vert \gt 21^{\circ}$ at the 95% C.L. A detailed analysis is carried out to evaluate the conditions under which measurements of the CP averaged branching ratios may place a significant constraint on $\gamma$. Predictions for the ratios of charged ($R_{\mathrm{c}}$) and neutral ($R_{\mathrm{n}}$) $B \rightarrow K\pi$ decays are also presented.