Large CP Asymmetries in $B^{\pm }\to {\eta }_c({\chi }_{c0}){\pi }^{\pm }$ from ${\eta }_c({\chi }_{c0})$ Width

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