Analysis of the two-body strong decays of the hidden-charm pentaquark states in QCD sum rules
In the present work, we study the two-body strong decays of the hidden-charm pentaquark states with the quark content $uudc\bar c$ and the quantum numbers $I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$ in the framework of the three-point QCD sum rules. The initial pentaquark states are described by four local diquark-diquark-antiquark type interpolating currents with definite isospin. We construct the three-point correlation functions for the decay channels $P_c\to η_c p$, $J/ψp$, $Λ_c\bar D$, $Λ_c\bar D^{*}$ and $Σ_c\bar D$, and derive the corresponding QCD sum rules for the strong coupling constants. At the hadron side, the correlation functions are expressed in terms of the hadron masses, pole residues, decay constants and strong coupling constants. At the QCD side, they are calculated by carrying out the operator product expansion with the full quark propagators, where the vacuum condensates up to dimension 10 are taken into account. After matching the two representations and performing the double Borel transformations, we extract the strong coupling constants from the selected Lorentz structures. With the obtained coupling constants, we evaluate the partial decay widths and discuss the possible assignments of the corresponding pentaquark states. The numerical results indicate that two of the compact hidden-charm pentaquark states can be related to the $P_c(4312)$ and $P_c(4457)$, respectively, while the other two lower-mass states may be regarded as possible hidden-charm pentaquark candidates to be searched for in future experiments. The present results may be useful for identifying the hidden-charm pentaquark states in future experiments.