CP violation in non-leptonic $$B_c$$ decays to excited final states

Abstract We study the CP violation in two-body nonleptonic decays of $$B_c$$ B c meson. concentrate on decay channels which contain at least one excited heavy meson final states. Specifically, following are considered: $$B_c\rightarrow c{\bar{c}}(2S, 2P)+{\bar{c}}q(1S, 1P)$$ ? ¯ ( 2 S , P ) + q 1 , c{\bar{c}}(1S)+{\bar{c}}q(2S, 2P)$$ c{\bar{c}}(1P)+{\bar{c}}q(2S)$$ c{\bar{c}}(1D)+{\bar{c}}q(1S, D and c{\bar{c}}(3S)+{\bar{c}}q(1S)$$ 3 . The improved Bethe-Salpeter method is applied to calculate hadronic transition matrix element. Our results show that some modes have large branching ratios, order $$10^{-3}$$ 10 - effect $$B_c \rightarrow \eta _c(1S)+D(2S)$$ ? _c(1S)+D_0^{*}(2P)$$ 0 ? J/\psi +D^{*}(2S)$$ J / ? most likely be found. If detection precision asymmetry such can reach $$3\sigma $$ ? level, $$10^7$$ 7 events needed.