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