在PQCD方法中B_c^+→χ_{c0,c1}[ρ(K*)→]ππ(Kπ)的准两体衰变
Quasi-two-body decays $B_c^+ \to χ_{c0,c1} [ρ(K^*) \to] ππ(Kπ)$ in the PQCD approach
- School of Physical Science and Technology, Southwest University（西南大学物理科学与技术学院）
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AI总结：
研究B_c^+→χ_{c0,c1}[ρ(K*)→]ππ(Kπ)准两体衰变，在微扰QCD框架下，通过P波共振产生ππ和Kπ对，给出各通道分支比等结果，表明共振ρ产生重塑P波粲偶素相对产率，且R_{K/π}在χ_{c0}和χ_{c1}中一致。
AI中文摘要：
我们在微扰QCD框架下的主导阶研究准两体衰变B_c^+→χ_{c0,c1}[ρ(K*)→]π^+π^0(K^0π^+)。ππ和Kπ对通过P波共振ρ(770)、ρ(1450)、ρ(1700)和K*(892)产生，由Gounaris-Sakurai和相对论Breit-Wigner模型参数化。主导的ρ(770)通道给出B(B_c^+→χ_{c0}π^+π^0)=3.24×10^-3和B(B_c^+→χ_{c1}π^+π^0)=4.19×10^-3，ρ的相长干涉贡献约25%。Kπ通道被Cabibbo压低到10^-6。对于χ_{c1}模式，f_L≈94%占主导且随共振质量增加而减小。R_{χ_{c1}/χ_{c0}}^{ππ}≈1.30与两体结果~4.7不同，表明共振ρ产生显著重塑了P波粲偶素的相对产率。R_{K/π}≈2×10^-3在χ_{c0}和χ_{c1}中一致。
英文摘要：
We study the quasi-two-body decays $B_c^+ \to χ_{c0,c1} [ρ(K^*) \to] π^+π^0(K^0π^+)$ 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 $\mathcal{B}(B_c^+ \to χ_{c0} π^+π^0) = 7.33 \times 10^{-4}$ and $\mathcal{B}(B_c^+ \to χ_{c1} π^+π^0) = 1.02 \times 10^{-3}$, with constructive $ρ$ interference making the coherent total $\sim 26\%$--$30\%$ 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, $\mathcal{B}(B_c^+ \to χ_{c0} K^0π^+) = 1.49 \times 10^{-4}$ and $\mathcal{B}(B_c^+ \to χ_{c1} K^0π^+) = 1.94 \times 10^{-4}$, 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, $f_L \approx 93\%$ dominates and decreases with increasing resonance mass. The ratio $R_{χ_{c1}/χ_{c0}}^{ππ} \approx 1.38$ 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, $R_{χ_{c1}/χ_{c0}}^{Kπ} \approx 1.30$, is consistent with this value, confirming that the spin ratio is governed by charmonium-side dynamics.
