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

Abstract

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 $0.33sin\gamma$, and about $0.45sin\gamma$ 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.

Comments: 12 pages, latex, 1 figure, submitted to Phis. Lett. B