Study of $B_c \to χ_{cJ}\ (P, V)$ decays in the improved perturbative QCD formalism
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2025
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| _version_ | 1866909738278584320 |
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| author | Liu, Xin Li, Hsiang-nan Xiao, Zhen-Jun |
| author_facet | Liu, Xin Li, Hsiang-nan Xiao, Zhen-Jun |
| contents | Motivated by the recent LHCb measurements of the ratios between the branching ratios (BRs), $R_{χ_{c2}/J/ψ} \equiv {\rm BR}(B_c^+ \to χ_{c2} π^+)/{\rm BR}(B_c^+ \to J/ψπ^+)$ and $R_{χ_{c1}/χ_{c2}} \equiv {\rm BR}(B_c^+ \to χ_{c1} π^+)/{\rm BR}(B_c^+ \to χ_{c2} π^+)$, we analyze the decays $B_c^+ \to χ_{cJ} (P, V)^+$ in the improved perturbative QCD (iPQCD) formalism, where $χ_{cJ}$ denotes the $p$-wave charmonia with $J=0, 1, 2$, and $P (V)$ denotes the pseudoscalars $π$ and $K$ (the vectors $ρ$ and $K^*$). Our results $R_{χ_{c2}/J/ψ} = 0.32 \pm 0.05$ and $R_{χ_{c1}/χ_{c2}}= 0.11 \pm 0.01$ at leading order in the strong coupling $α_s$ agree well with the data within uncertainties. The result $R_{χ_{c0}/J/ψ} \equiv {\rm BR}(B_c^+ \to χ_{c0} π^+)/{\rm BR}(B_c^+ \to J/ψπ^+) = 0.17 \pm 0.02$ is lower than $1.41^{+0.50}_{-0.45}$ inferred by the $B_c^+ \to χ_{c0} π^+$ measurement. The large longitudinal polarization fractions imply that these components dominate the $B_c^+ \to χ_{c1,c2} ρ^+$ BRs. A peculiar constructive (destructive) interference between the twist-2 and twist-3 contributions is identified in the $B_c^+\to χ_{c1} ρ^+$ ($B_c^+\to χ_{c1} π^+$) mode, but not in the corresponding ones with $χ_{c0,c2}$ mesons. Inputting the BRs of the strong decays $χ_{c0,c2} \to π^+ π^- / K^+ K^-$ and $χ_{cJ} \to π^+π^-(π^+ π^-/K^+K^-)$ reported by the BESIII Collaboration, we obtain those of $B_c^+ \to χ_{cJ} (ρ, π)^+$ followed by secondary decay chains under the narrow-width approximation. All the above iPQCD predictions can be confronted by more precise experiments in the future to deepen our understanding of QCD dynamics in $B_c\toχ_{cJ}$ transitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20605 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Study of $B_c \to χ_{cJ}\ (P, V)$ decays in the improved perturbative QCD formalism Liu, Xin Li, Hsiang-nan Xiao, Zhen-Jun High Energy Physics - Phenomenology High Energy Physics - Experiment Motivated by the recent LHCb measurements of the ratios between the branching ratios (BRs), $R_{χ_{c2}/J/ψ} \equiv {\rm BR}(B_c^+ \to χ_{c2} π^+)/{\rm BR}(B_c^+ \to J/ψπ^+)$ and $R_{χ_{c1}/χ_{c2}} \equiv {\rm BR}(B_c^+ \to χ_{c1} π^+)/{\rm BR}(B_c^+ \to χ_{c2} π^+)$, we analyze the decays $B_c^+ \to χ_{cJ} (P, V)^+$ in the improved perturbative QCD (iPQCD) formalism, where $χ_{cJ}$ denotes the $p$-wave charmonia with $J=0, 1, 2$, and $P (V)$ denotes the pseudoscalars $π$ and $K$ (the vectors $ρ$ and $K^*$). Our results $R_{χ_{c2}/J/ψ} = 0.32 \pm 0.05$ and $R_{χ_{c1}/χ_{c2}}= 0.11 \pm 0.01$ at leading order in the strong coupling $α_s$ agree well with the data within uncertainties. The result $R_{χ_{c0}/J/ψ} \equiv {\rm BR}(B_c^+ \to χ_{c0} π^+)/{\rm BR}(B_c^+ \to J/ψπ^+) = 0.17 \pm 0.02$ is lower than $1.41^{+0.50}_{-0.45}$ inferred by the $B_c^+ \to χ_{c0} π^+$ measurement. The large longitudinal polarization fractions imply that these components dominate the $B_c^+ \to χ_{c1,c2} ρ^+$ BRs. A peculiar constructive (destructive) interference between the twist-2 and twist-3 contributions is identified in the $B_c^+\to χ_{c1} ρ^+$ ($B_c^+\to χ_{c1} π^+$) mode, but not in the corresponding ones with $χ_{c0,c2}$ mesons. Inputting the BRs of the strong decays $χ_{c0,c2} \to π^+ π^- / K^+ K^-$ and $χ_{cJ} \to π^+π^-(π^+ π^-/K^+K^-)$ reported by the BESIII Collaboration, we obtain those of $B_c^+ \to χ_{cJ} (ρ, π)^+$ followed by secondary decay chains under the narrow-width approximation. All the above iPQCD predictions can be confronted by more precise experiments in the future to deepen our understanding of QCD dynamics in $B_c\toχ_{cJ}$ transitions. |
| title | Study of $B_c \to χ_{cJ}\ (P, V)$ decays in the improved perturbative QCD formalism |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment |
| url | https://arxiv.org/abs/2505.20605 |