Hadronic coupling constants of the lowest hidden-charm pentaquark state,using QCD sum rules with rigorous quark-hadron duality

In this article, we illustrate how to calculate the hadronic coupling constants of the pentaquark states with QCD sum rules based on rigorous quark-hadron quality. We then study the hadronic coupling constants of the lowest diquark-diquark-antiquark type hidden-charm pentaquark state with spin-parity \begin{document}$ J^P = {\dfrac{1}{2}}^- $\end{document} in detail, and calculate the partial decay widths. The total width \begin{document}$ \Gamma(P_c) = 14.32\pm3.31\rm{MeV} $\end{document} is compatible with the experimental value \begin{document}$ \Gamma_{P_c(4312)} = 9.8\pm2.7^{+ 3.7}_{- 4.5} \rm{ MeV} $\end{document} from the LHCb collaboration, and favors assigning the \begin{document}$ P_c(4312) $\end{document} to be the \begin{document}$ ud]uc]\bar{c} $\end{document} pentaquark state with \begin{document}$ J^P = {\dfrac{1}{2}}^- $\end{document}. The hadronic coupling constants have the relation \begin{document}$ |G_{PD^-\Sigma_c^{++}}| = \sqrt{2}|G_{P\bar{D}^0\Sigma_c^+}|\gg $\end{document}\begin{document}$ |G_{P\bar{D}^0\Lambda_c^+}| $\end{document}, and favor the hadronic dressing mechanism. The \begin{document}$ P_c(4312) $\end{document} may have a diquark-diquark-antiquark type pentaquark core with the typical size of the \begin{document}$ qqq $\end{document}-type baryon states. The strong couplings to the meson-baryon pairs \begin{document}$ \bar{D}\Sigma_c $\end{document} lead to some pentaquark molecule components, and the \begin{document}$ P_c(4312) $\end{document} may spend a rather large time as the \begin{document}$ \bar{D}\Sigma_c $\end{document} molecular state.