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

We study CP asymmetries in $B^{\pm}\to hπ^{\pm}$ decays, where the hadronic states $h=ρρ, K\Kbarπ$, $π^+π^-K^+K^-$, etc., and $h=π^+π^-, K^+K^-, 2(π^+π^-)$, etc., are taken on the resonances $η_c$ and $χ_{c0}$, respectively. The relatively large $η_c$ and $χ_{c0}$ 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.

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