Quasi-two-body decays Bc+ → χc0,c1 [ρ(K*) →] ππ(Kπ) in the PQCD approach
Abstract
We study the quasi-two-body decays Bc+ → χc0,c1 [ρ(K*) →] π+π0(K0π+) in the perturbative QCD framework at leading order. The ππ and Kπ pairs are produced via the P-wave resonances ρ(770), ρ(1450), ρ(1700), and K*(892), parametrized by the Gounaris-Sakurai and relativistic Breit-Wigner models. The ρ channels, dominated by the ρ(770) resonance, yield ℬ(Bc+ → χc0 π+π0) = 7.33 × 10−4 and ℬ(Bc+ → χc1 π+π0) = 1.02 × 10−3, with constructive ρ interference making the coherent total ∼ 26%--30% larger than the ρ(770) contribution alone. The Cabibbo-suppressed Kπ channels yield branching ratios roughly a factor of five below those of the ππ modes, ℬ(Bc+ → χc0 K0π+) = 1.49 × 10−4 and ℬ(Bc+ → χc1 K0π+) = 1.94 × 10−4, the Cabibbo suppression being only partially compensated by the narrow K*(892) resonance and the normalization factor NK*=1.48. For χc1 modes, fL ≈ 93% dominates and decreases with increasing resonance mass. The ratio Rχc1/χc0ππ ≈ 1.38 reflects the common resonant ρ production mechanism shared by χc0 and χc1, with the charmonium decay-constant hierarchy and phase space determining the relative yield of P-wave charmonia. The analogous ratio in the Cabibbo-suppressed Kπ channel, Rχc1/χc0Kπ ≈ 1.30, is consistent with this value, confirming that the spin ratio is governed by charmonium-side dynamics.
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BibTeX
@misc{deng2026quasitwobody,
title = {{Quasi-two-body decays $B_c^+ \to χ_c0,c1 [ρ(K^*) \to] ππ(Kπ)$ in the PQCD approach}},
author = {Jun Deng and Xian-Qiao Yu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.23163},
eprint = {2607.23163},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.23163},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quasi-two-body decays B_c^+ → χ_c0,c1 [ρ(K^*) →] ππ(Kπ) in the PQCD approach
AU - Jun Deng
AU - Xian-Qiao Yu
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2607.23163
UR - https://arxiv.org/abs/2607.23163
AB - We study the quasi-two-body decays B_c^+ → χ_c0,c1 [ρ(K^*) →] π^+π^0(K^0π^+) in the perturbative QCD framework at leading order. The ππ and Kπ pairs are produced via the P-wave resonances ρ(770), ρ(1450), ρ(1700), and K^*(892), parametrized by the Gounaris-Sakurai and relativistic Breit-Wigner models. The ρ channels, dominated by the ρ(770) resonance, yield ℬ(B_c^+ → χ_c0 π^+π^0) = 7.33 × 10^−4 and ℬ(B_c^+ → χ_c1 π^+π^0) = 1.02 × 10^−3, with constructive ρ interference making the coherent total ∼ 26%--30% larger than the ρ(770) contribution alone. The Cabibbo-suppressed Kπ channels yield branching ratios roughly a factor of five below those of the ππ modes, ℬ(B_c^+ → χ_c0 K^0π^+) = 1.49 × 10^−4 and ℬ(B_c^+ → χ_c1 K^0π^+) = 1.94 × 10^−4, the Cabibbo suppression being only partially compensated by the narrow K^*(892) resonance and the normalization factor N_K^*=1.48. For χ_c1 modes, f_L ≈ 93% dominates and decreases with increasing resonance mass. The ratio R_χ_c1/χ_c0^ππ ≈ 1.38 reflects the common resonant ρ production mechanism shared by χ_c0 and χ_c1, with the charmonium decay-constant hierarchy and phase space determining the relative yield of P-wave charmonia. The analogous ratio in the Cabibbo-suppressed Kπ channel, R_χ_c1/χ_c0^Kπ ≈ 1.30, is consistent with this value, confirming that the spin ratio is governed by charmonium-side dynamics.
ER -