In this article, we tentatively assign the $P_c(4312)$ to be the $\bar{D}\Sigma_c$ pentaquark molecular state with the spin-parity $J^P={\frac{1}{2}}^-$, and discuss the factorizable and non-factorizable contributions in the two-point QCD sum rules for the $\bar{D}\Sigma_c$ molecular state in details to prove the reliability of the single pole approximation in the hadronic spectral density. We study its two-body strong decays with the QCD sum rules, special attentions are paid to match the hadron side with the QCD side of the correlation functions to obtain solid duality. We obtain the partial decay widths $\Gamma\left(P_c(4312)\to \eta_c p\right)=0.255\,{\rm{MeV}}$ and $\Gamma\left(P_c(4312)\to J/\psi p\right)=9.296^{+19.542}_{-9.296}\,\,{\rm{MeV}}$, which are compatible with the experimental value of the total width, and support assigning the $P_c(4312)$ to be the $\bar{D}\Sigma_c$ pentaquark molecular state.

中文翻译：

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用 QCD 和规则分析作为五夸克分子态的 $P_c(4312)$ 的强衰变

在本文中，我们暂时将 $P_c(4312)$ 指定为 $\bar{D}\Sigma_c$ 五夸克分子态，自旋奇偶性 $J^P={\frac{1}{2}}^ -$，并详细讨论 $\bar{D}\Sigma_c$ 分子态的两点 QCD 求和规则中可分解和不可分解的贡献，以证明强子谱密度中单极近似的可靠性。我们用QCD和规则研究了它的二体强衰变，特别注意将强子侧与相关函数的QCD侧匹配以获得固体对偶性。我们得到部分衰减宽度 $\Gamma\left(P_c(4312)\to \eta_c p\right)=0.255\,{\rm{MeV}}$ 和 $\Gamma\left(P_c(4312)\to J /\psi p\right)=9.296^{+19.542}_{-9.296}\,\,{\rm{MeV}}$，与总宽度的实验值兼容，