B and B_s decays into three pseudoscalar mesons and the determination of the angle gamma of the unitarity triangle

Abstract

We reconsider two classical proposals for the determination of the angle gamma of the unitarity triangle: B^\pm => chi_{c0} \pi^\pm => \pi^+\pi^-\pi^\pm and B_s => rho^0 K_S => \pi^+ \pi^- K_S. We point out the relevance, in both cases, of non resonant amplitudes, where the \pi^+ \pi^- pair is produced by weak decay of a B^* (J^P=1^-) or B_0 (J^P=0^+) off-shell meson. In particular, for the B decay channel, the inclusion of the B_0 pole completes some previous analyses and confirms their conclusions, provided a suitable cut in the Dalitz plot is performed; for the B_s decay the inclusion of the B^*, B_0 amplitudes enhances the role of the tree diagrams as compared to penguin amplitudes, which makes the theoretical uncertainty related to the B_s => rho^0 K_S decay process less significant. While the first method is affected by theoretical uncertainties, the second one is cleaner, but its usefulness will depend on the available number of events to perform the analysis.