The CP violating asymmetry in $B^{\pm} \to M {\bar M} π^{\pm}$ decays

Abstract

We analyze the asymmetry in the partial widths for the decays $B^{\pm} \to M {\bar M} π^{\pm}$ ($ M = π^+, K ^+, π^0, η$), which results from the interference of the nonresonant decay amplitude with the resonant amplitude for $B^{\pm} \to χ_{c0} π^{\pm} $ followed by the decay $χ_{c0} \to M {\bar M} $. The CP violating phase $γ$ can be extracted from the measured asymmetry. We find that the partial width asymmetry for $B^\pm \to π^+ π^- π^\pm$ is about $0.33~sin γ$, and about $0.45~ sin γ$ for $B^\pm \to K^+ K^-π^\pm$, while it is somewhat smaller for $B^\pm \to π^0 π^0 π^\pm$ and $B^\pm \to ηηπ^\pm$. Potential sources of uncertainties in these results, primarily coming from poorly known input parameters, are discussed.