AI 中文总结
本研究分析BaBar和Belle的B→χc1πK数据，寻找JPC=0++和2++的同位矢量D*D*分子，通过拟合衰变振幅并解析延拓T矩阵找极点，得到虚态极点结果，张量虚态与手征有效场论预测一致，还预测了角分布用于自旋鉴别和检验再散射，助力建立D(*)D(*)分子多重态谱。
AI 中文摘要
建立 $D^{(\ast)}\bar{D}^{(\ast)}$ 系统近阈值的自旋-同位矢量多重态谱，是检验 $X(3872)$、$Z_c(3900)$ 和 $Z_c(4020)$ 分子解释的核心。在此背景下，同位矢量道尤为重要，因为相关结构具有明确的奇特强子特征。本研究分析BaBar和Belle实验的 $B\to\chi_{c1}\pi K$ 数据，寻找可能的 $J^{PC}=0^{++}$ 和 $2^{++}$ 同位矢量 $D^\ast\bar{D}^\ast$ 分子。三体衰变振幅包含有效非共振项、中间K介子共振以及 $\chi_{c1}\pi$–$D^\ast\bar{D}^\ast$ 耦合道再散射。对每个数据集，在三种场景下同时拟合 $\chi_{c1}\pi$ 和 $K\pi$ 的不变质量分布：无再散射、$J=0$ 再散射、$J=2$ 再散射。随后将拟合得到的耦合道 $T$ 矩阵解析延拓以寻找极点。对于 $J^{PC}=0^{++}$ 情况，BaBar和Belle的拟合分别给出相对于 $D^\ast\bar{D}^\ast$ 阈值的虚极点为 $-2.15^{+2.10}_{-6.41}$ MeV 和 $-18.40^{+8.58}_{-13.70}$ MeV；对于 $J^{PC}=2^{++}$，对应的虚极点分别位于 $-3.42^{+2.37}_{-4.29}$ MeV 和 $-4.26^{+1.34}_{-1.69}$ MeV。张量虚态极点与手征有效场论的预测一致，该理论还预测了 $W_{c1}$ 的存在，它是 $X(3872)$ 的同位旋伙伴。由于仅靠不变质量分布无法区分总自旋 $J$，本研究还预测了角分布：$\cos\theta_{\chi_{c1}\pi}$ 分布是直接的自旋鉴别器，而 $\cos\theta_{K\pi}$ 分布可进一步检验再散射贡献。未来对这些预测的测量将有助于建立 $D^{(\ast)}\bar{D}^{(\ast)}$ 分子多重态谱。
英文摘要
Establishing the near-threshold spin-isospin multiplet spectrum of $D^{(\ast)}\bar D^{(\ast)}$ systems is central to testing molecular interpretations of the $X(3872)$, $Z_c(3900)$, and $Z_c(4020)$. The isovector channels are particularly important in this context, as the associated structures would have a clear exotic character. In this work, we analyze the BaBar and Belle data on $B\toχ_{c1}πK$ to search for possible isovector $D^\ast\bar D^\ast$ molecules with $J^{PC}=0^{++}$ and $2^{++}$. The three-body decay amplitude includes an effective nonresonant term, intermediate kaon resonances, and $χ_{c1}π$--$D^\ast\bar D^\ast$ coupled-channel rescattering. For each data set, the $χ_{c1}π$ and $Kπ$ invariant-mass distributions are fitted simultaneously under three scenarios: without rescattering and with either $J=0$ or $J=2$ rescattering. We then analytically continue the fitted coupled-channel $T$ matrices to search for poles. For the case of $J^{PC}=0^{++}$, the BaBar and Belle fits yield virtual poles at $-2.15^{+2.10}_{-6.41}$ MeV and $-18.40^{+8.58}_{-13.70}$ MeV, respectively, relative to the $D^\ast\bar D^\ast$ threshold. For $J^{PC}=2^{++}$, the corresponding virtual poles are located at $-3.42^{+2.37}_{-4.29}$ MeV and $-4.26^{+1.34}_{-1.69}$ MeV, respectively. The tensor virtual-state pole is consistent with a prediction from chiral effective field theory, which also predicts the existence of $W_{c1}$, an isospin partner of $X(3872)$. Since the invariant-mass distributions alone cannot distinguish total spin $J$, we also predict angular distributions. The $\cosθ_{χ_{c1}π}$ distribution provides a direct spin discriminator, while the $\cosθ_{Kπ}$ distribution further tests the rescattering contribution. The measurements of these predictions would help establish the $D^{(\ast)}\bar D^{(\ast)}$ molecular multiplet spectrum in the future.
Comments15 pages, 5 figures
