The LHCb collaboration has recently observed three pentaquark peaks, the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$. They are very close to a pair of heavy baryon-meson thresholds, with the $P_c(4312)$ located 8.9 MeV below the $\overline{D}{\mathrm{\Sigma }}_c$ threshold, and the $P_c(4440)$ and $P_c(4457)$ located 21.8 and 4.8 MeV below the ${\overline{D}}^{*}{\mathrm{\Sigma }}_c$ one. The spin-parities of these three states have not been measured yet. In this work we assume that the $P_c(4312)$ is a $J^P={\frac{1}{2}}^{-}$ $\overline{D}{\mathrm{\Sigma }}_c$ bound state, while the $P_c(4440)$ and $P_c(4457)$ are ${\overline{D}}^{*}{\mathrm{\Sigma }}_c$ bound states of unknown spin-parity, where we notice that the consistent description of the three pentaquarks in the one-boson-exchange model can indeed determine the spin and parities of the later, i.e., of the two ${\overline{D}}^{*}{\mathrm{\Sigma }}_c$ molecular candidates. For this determination we revisit first the one-boson-exchange model, which in its original formulation contains a short-range deltalike contribution in the spin-spin component of the potential. We argue that it is better to remove these deltalike contributions because, in this way, the one-boson-exchange potential will comply with the naïve expectation that the form factors should not have a significant impact in the long-range part of the potential (in particular the one-pion-exchange part). Once this is done, we find that it is possible to consistently describe the three pentaquarks, to the point that the $P_c(4440)$ and $P_c(4457)$ can be predicted from the $P_c(4312)$ within a couple of MeV with respect to their experimental location. In addition the so-constructed one-boson-exchange model predicts the preferred quantum numbers of the $P_c(4440)$ and $P_c(4457)$ molecular pentaquarks to be ${\frac{3}{2}}^{-}$ and ${\frac{1}{2}}^{-}$, respectively.

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一玻色子交换模型中Pc（4440）和Pc（4457）的自旋奇偶性

LHCb合作最近观测到了三个五夸克峰，即 $P_C（4312）$， $P_C（4440）$ 和 $P_C（4457）$。它们非常接近一对重的重子介子阈值，$P_C（4312）$ 位于8.9 MeV以下 $\overline{d}{\mathrm{\Sigma }}_C$ 阈值，以及 $P_C（4440）$ 和 $P_C（4457）$ 位于下方的21.8和4.8 MeV ${\overline{d}}^{*}{\mathrm{\Sigma }}_C$一。这三种状态的自旋奇偶性尚未测量。在这项工作中，我们假设$P_C（4312）$ 是一个 ${Ĵ}^P={\frac{\mathrm{1个}}{\mathrm{2个}}}^{-}$ $\overline{d}{\mathrm{\Sigma }}_C$ 绑定状态，而 $P_C（4440）$ 和 $P_C（4457）$ 是 ${\overline{d}}^{*}{\mathrm{\Sigma }}_C$ 未知自旋奇偶性的束缚态，在这里我们注意到，在一个玻色子交换模型中对三个五夸克的一致描述确实可以确定后一个奇偶性（即两个）的自旋和奇偶性 ${\overline{d}}^{*}{\mathrm{\Sigma }}_C$分子候选物。为了进行此确定，我们首先回顾一个玻色子交换模型，该模型在其原始公式中包含电位自旋自旋分量中的短距离三角洲型贡献。我们认为最好删除这些类似delta的贡献，因为这样一来，一次玻色子交换的潜力将符合天真的期望，即形态因素不会对该潜力的长期部分产生重大影响（特别是一小子交换部分）。完成此操作后，我们发现可以一致地描述三个五夸克，以至于$P_C（4440）$ 和 $P_C（4457）$ 可以从 $P_C（4312）$在MeV范围内就其实验位置而言。此外，如此构造的一玻色子交换模型可以预测原子的首选量子数。$P_C（4440）$ 和 $P_C（4457）$ 分子五夸克 ${\frac{3}{\mathrm{2个}}}^{-}$ 和 ${\frac{\mathrm{1个}}{\mathrm{2个}}}^{-}$， 分别。