Bayesian analysis of the constraints on γ from B → Kπ rates and CP asymmetries in the flavour-SU ( 3 ) approach

The relation between the branching ratios and direct CP asymmetries of B → Kπ decays and the angle γ 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 flavour-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 |γ − 90◦| > 21 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 γ. Predictions for the ratios of charged (Rc) and neutral (Rn) B → Kπ decays are also presented.