Large CP Asymmetries in $B^{\pm}\toη_c(χ_{c0})π^{\pm}$ from $η_c(χ_{c0})$ Width

We study CP asymmetries in $B^{\pm}\to h\pi^{\pm}$ decays, where the hadronic states $h=\rho\rho, K\Kbar\pi$, $\pi^+\pi^-K^+K^-$, etc., and $h=\pi^+\pi^-, K^+K^-, 2(\pi^+\pi^-)$, etc., are taken on the resonances $\eta_c$ and $\chi_{c0}$, respectively. The relatively large $\eta_c$ and $\chi_{c0}$ decay widths, of about 10$-$15 MeV, provide the necessary absorptive phase in the interference between the resonance (going through $b\to c\cbar d$) and the background (through $b\to u\ubar d$) contributions to the amplitude. Large asymmetries of order 10$\%$ or more are likely in some modes.