Study of $B_c \to χ_{cJ}\ (P, V)$ decays in the improved perturbative QCD formalism

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Main Authors: Liu, Xin, Li, Hsiang-nan, Xiao, Zhen-Jun
Format: Preprint
Published: 2025
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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
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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