Estimating of CP Violation in $B_{c}\rightarrow B K^{0}+B {\bar{K}}^0\rightarrow B π^{\pm} e^{\mp} ν_{e}$ Decays
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| Formato: | Preprint |
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2025
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| _version_ | 1866918207717113856 |
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| author | Cheng, Xiao-Dong Weng, Zhen-Lu Fan, Ying-Ying Wang, Ru-Min |
| author_facet | Cheng, Xiao-Dong Weng, Zhen-Lu Fan, Ying-Ying Wang, Ru-Min |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19123 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Estimating of CP Violation in $B_{c}\rightarrow B K^{0}+B {\bar{K}}^0\rightarrow B π^{\pm} e^{\mp} ν_{e}$ Decays Cheng, Xiao-Dong Weng, Zhen-Lu Fan, Ying-Ying Wang, Ru-Min High Energy Physics - Phenomenology 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. |
| title | Estimating of CP Violation in $B_{c}\rightarrow B K^{0}+B {\bar{K}}^0\rightarrow B π^{\pm} e^{\mp} ν_{e}$ Decays |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2505.19123 |