Estimating of CP Violation in $B_{c}\rightarrow B K^{0}+B {\bar{K}}^0\rightarrow B π^{\pm} e^{\mp} ν_{e}$ Decays

TL;DR

This work analyzes CP violation in cascade decays of $B_c$ mesons that proceed via $c$-quark transitions with a spectator $b$ quark, focusing on final states involving $K^0$ or ${\bar K}^0$ and subsequent semileptonic kaon decays. It decomposes CP observables into kaon-mixing, direct $B_c$-decay, and a novel interference contribution arising from $K^0$-$\bar{K}^0$ mixing dynamics, and computes branching fractions and CP asymmetries using factorization, kaon mixing parameters, and hadronic form factors. The study finds ${\mathcal{A}}_{CP}^{pm}$ of order $10^{-4}$ and ${\mathcal{A}}_{CP}^{mp}$ of order $10^{-3}$, with ${\mathcal{A}}_{CP,int}^{pm}$ often dominating ${\mathcal{A}}_{CP}^{pm}$ and ${\mathcal{A}}_{CP,mix}^{mp}$ dominating ${\mathcal{A}}_{CP}^{mp}$; ${\mathcal{A}}_{CP}^{pp}$ and ${\mathcal{A}}_{CP}^{mm}$ are largely governed by $K^0-\bar{K}^0$ mixing. Numerical results indicate branching fractions up to several ×10^{-6} and that several channels could be marginally observable at the LHC and HL-LHC, motivating future experimental tests of these CP-violating effects.

Abstract

In this paper, we investigate the CP asymmetries ${\mathcal A}_{CP}^{pm}$ and ${\mathcal A}_{CP}^{mp}$ in $B_{c}^{\pm}\rightarrow B^{\pm} K^{0}+B^{\pm} {\bar{K}}^0\rightarrow B^{\pm} π^{\pm} e^{\mp} ν_{e}$ and $B_{c}^{\pm}\rightarrow B^{\pm} K^{0}+B^{\pm} {\bar{K}}^0\rightarrow B^{\pm} π^{\mp} e^{\pm} ν_{e}$ decays, both of them consist of three parts: the indirect CP violations in $K^0 -\bar{K}^0$ mixing $A_{CP,mix}^{pm}$ and $A_{CP,mix}^{mp}$, the direct CP violations in $B_{c}$ decay $A_{CP,dir}^{pm}$ and $A_{CP,dir}^{mp}$, the new CP violation effects $A_{CP,int}^{pm}$ and $A_{CP,int}^{mp}$, which originate from the interference between the amplitude of the $B_{c}^{-}\rightarrow B^{-} K^{0} ({\bar{K}}^0) \rightarrow B^{-} π^{-} e^{+} ν_{e}(π^{+} e^{-} \barν_{e})$ decay with the difference between the oscillating effect of $K^0\rightarrow {\bar{K}}^0$ and that of ${\bar{K}}^0\rightarrow K^0 $. The strong phase differences of the direct CP asymmetries $A_{CP,dir}^{pm}$ and $A_{CP,dir}^{mp}$ arising from $K^0-\bar{K}^0$ mixing parameters. ${\mathcal A}_{CP}^{pm}$ and ${\mathcal A}_{CP}^{mp}$ are of the order $\mathcal{O}(10^{-4})$ and $\mathcal{O}(10^{-3})$, respectively. The new CP violation effect ${\mathcal A}_{CP,int}^{pm}$ plays a dominant role in ${\mathcal A}_{CP}^{pm}$, the CP asymmetry ${\mathcal A}_{CP}^{mp}$ is dominated by the indirect CP violation ${\mathcal A}_{CP,mix}^{mp}$, so the CP asymmetry ${\mathcal A}_{CP}^{pm}$ provides an ideal place to study the new CP violation effect. We derive another two asymmetry observables ${\mathcal A}_{CP}^{pp}$ and ${\mathcal A}_{CP}^{mm}$, which are dominated by $K^0-\bar{K}^0$ mixing. The observables ${\mathcal A}_{CP}^{pm}$, ${\mathcal A}_{CP}^{mp}$, ${\mathcal A}_{CP}^{pp}$ and ${\mathcal A}_{CP}^{mm}$ are hopefully to be marginally observed at the LHC experiment and the HL-LHC experiment.

Figures (2)

• Figure 1: Quark diagrams for the $B_c^+\rightarrow B^{+} \bar{K}^{0}$ and $B_c^+\rightarrow B^{+} K^{0}$ decays.
• Figure 2: Quark diagrams for the $B_c^-\rightarrow B^{-} K^{0}$ and $B_c^-\rightarrow B^{-} \bar{K}^{0}$ decays.