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arXiv 1608.02537hep-ph
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电子正电子湮没中的$P$波耦合沟道效应

$P$-wave coupled channel effects in electron-positron annihilation

Meng-Lin Du, Ulf-G. Meißner, Qian Wang

备注：
15 pages, 2 figures
发表信息：
Phys. Rev. D 94, 096006 (2016)
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摘要：

本文系统地研究了$e^+e^-$湮灭中$D\bar{D}$、$D\bar{D}^*+c.c.$和$D^*\bar{D}^*$阈值引起的$P$波耦合通道效应.我们提供了一个探索性的研究，通过解决Lippmann-Schwinger方程的短程接触势在重夸克极限。这些接触势可以从$e^+e^-$湮灭中的$P$波相互作用中提取出来，然后用于研究可能的等单线态$P$波强子分子。特别地，这样的研究可以提供关于具有量子数$J^{PC}=1^{-+}$的奇异候选物的信息。在$D\bar{D}$、$D\bar{D}^*+c.c.$和$D^*\bar{D}^*$阈值的质量区域中，存在两个夸克模型裸态，即$ψ(3770)$和$ψ(4040)$，它们分别被指定为$(1^3D_1)$和$(3^1S_1)$态。通过对$e^+e^-\to D\bar{D}$、$D\bar{D}^*+c.c.$、$D^*\bar{D}^*$的截面进行整体拟合，确定了各通道的物理耦合常数，并提取了$ψ(3770)$和$ψ(4040)$的极点位置。重夸克自旋对称性（HQSS）极限下的比值的偏离反映了$D$和$D^*$之间的质量分裂引起的HQSS破缺效应。除了这两个极点之外，我们还发现了一个比$D\bar{D}^*+c.c.$阈值高出几MeV的极点，这可能与BABAR和Belle早些时候观察到的所谓$G(3900)$有关。通过高光度实验测量$D^*\bar{D}^*$通道中的角分布，可以进一步检查这种情况。

英文摘要：

$P$-wave coupled channel effects arising from the $D\bar{D}$, $D\bar{D}^*+c.c.$, and $D^*\bar{D}^*$ thresholds in $e^+e^-$ annihilations are systematically studied. We provide an exploratory study by solving the Lippmann-Schwinger equation with short-ranged contact potentials obtained in the heavy quark limit. These contact potentials can be extracted from the $P$-wave interactions in the $e^+e^-$ annihilations, and then be employed to investigate possible isosinglet $P$-wave hadronic molecules. In particular, such an investigation may provide information about exotic candidates with quantum numbers $J^{PC}=1^{-+}$. In the mass region of the $D\bar{D}$, $D\bar{D}^*+c.c.$, and $D^*\bar{D}^*$ thresholds, there are two quark model bare states, i.e. the $ψ(3770)$ and $ψ(4040)$, which are assigned as $(1^3D_1)$ and $(3^1S_1)$ states, respectively. By an overall fit of the cross sections of $e^+e^-\to D\bar{D}$, $D\bar{D}^*+c.c.$, $D^*\bar{D}^*$, we determine the physical coupling constants to each channel and extract the pole positions of the $ψ(3770)$ and $ψ(4040)$. The deviation of the ratios from that in the heavy quark spin symmetry (HQSS) limit reflects the HQSS breaking effect due to the mass splitting between the $D$ and the $D^*$. Besides the two poles, we also find a pole a few MeV above the $D\bar{D}^*+c.c.$ threshold which can be related to the so-called $G(3900)$ observed earlier by BABAR and Belle. This scenario can be further scrutinized by measuring the angular distribution in the $D^*\bar{D}^*$ channel with high luminosity experiments.

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