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

TL;DR

This paper investigates CP violation in non-leptonic $B_c$ decays to excited states, predicting sizable CP asymmetries in specific channels and estimating the required event numbers for detection.

Contribution

It applies an improved Bethe-Salpeter method to calculate hadronic matrix elements for excited state decays, providing new predictions for CP violation effects in these channels.

Findings

Some decay modes have large branching ratios around 10^{-3}

CP violation effects are most detectable in specific decay channels

Detection of CP asymmetry requires at least 10^7 $B_c$ events

Abstract

We study the CP violation in two-body nonleptonic decays of $B_c$ 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: $B_c\to c\bar c(2S, 2P)+\bar cq(1S, 1P)$, $B_c\to c\bar c(1S)+\bar cq(2S, 2P)$, $B_c\to c\bar c(1P)+\bar cq(2S)$, $B_c\to c\bar c(1D)+\bar cq(1S, 1P)$, and $B_c\to c\bar c(3S)+\bar cq(1S)$. 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 $10^{-3}$. The CP violation effect in $B_c \rightarrow \eta_c(1S)+D(2S)$, $B_c \rightarrow \eta_c(1S)+D_0^{*}(2P)$, and $B_c \rightarrow J/\psi+D^{*}(2S)$ are most likely to be found. If the detection precision of the CP asymmetry in such channels can reach the $3\sigma$ level, at least $10^7$ $B_c$ events are needed.