The hadronic coupling constants of the lowest hidden-charm pentaquark state with the QCD sum rules in rigorous quark-hadron duality

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