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