Bayesian analysis of the constraints on gamma from B --> K pi rates and CP asymmetries in the flavour-SU(3) approach

Abstract

The relation between the branching ratios and direct CP asymmetries of B --> 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 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 |gamma - 90 deg| > 21 deg 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_c) and neutral (R_n) B --> K pi decays are also presented.