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

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