Analysis of the strong decays of Pc(4312) as a pentaquark molecular state with QCD sum rules

In this article, we tentatively assign begin{document}$P_c(4312)$end{document} to be the begin{document}$bar{D}Sigma_c$end{document} pentaquark molecular state with the spin-parity begin{document}$J^P={frac{1}{2}}^-$end{document}, and discuss the factorizable and non-factorizable contributions in the two-point QCD sum rules for the begin{document}$bar{D}Sigma_c$end{document} molecular state in detail 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, and special attention is paid to match the hadron side with the QCD side of the correlation functions to obtain solid duality. We obtain the partial decay widths begin{document}$Gammaleft(P_c(4312)to eta_c pright)=0.255,,{rm{MeV}}$end{document} and begin{document}$Gammaleft(P_c(4312)to J/psi pright)=9.296^{+19.542}_{-9.296},,{rm{MeV}}$end{document}, which are compatible with the experimental value of the total width, and support assigning begin{document}$P_c(4312)$end{document} to be the begin{document}$bar{D}Sigma_c$end{document} pentaquark molecular state.