Signal for CP violation in $B^{\pm} \to P {\bar P} π^{\pm}$ decays

Abstract

We analyze the partial rate asymmetry in $B^{\pm} \to P {\bar P} π^{\pm}$ decays ($ P = π^+, K ^+, π^0, η$) which results from the interference of the nonresonant decay amplitude and the resonant amplitude for $B^{\pm} \to χ_{c0} π^{\pm} $ followed by the decay $χ_{c0} \to P {\bar P} $. The CP violating phase $γ$ can be extracted from the measured asymmetry. We find that the partial rate asymmetry for $B^\pm \to π^+ π^- π^\pm$ is $0.33~sin γ$, while for $B^\pm \to K^+ K^-π^\pm$ it amounts $0.45~ sin γ$.