Analysis of the hidden-charm pentaquark molecular states with strangeness and without strangeness via the QCD sum rules

In this article, we investigate the $\bar{D}{\mathrm{\Sigma }}_c$, $\bar{D}{\mathrm{\Xi }}_c^{\mathrm{\prime }}$, $\bar{D}{\mathrm{\Sigma }}_c^{\ast }$, $\bar{D}{\mathrm{\Xi }}_c^{\ast }$, ${\bar{D}}^{\ast }{\mathrm{\Sigma }}_c$, ${\bar{D}}^{\ast }{\mathrm{\Xi }}_c^{\mathrm{\prime }}$, ${\bar{D}}^{\ast }{\mathrm{\Sigma }}_c^{\ast }$ and ${\bar{D}}^{\ast }{\mathrm{\Xi }}_c^{\ast }$ pentaquark molecular states with strangeness and without strangeness via the QCD sum rules at length, pay much attention to the light flavor $SU(3)$ breaking effects, and make predictions for new pentaquark molecular states besides assigning the $P_c(4312)$, $P_c(4380)$, $P_c(4440)$, $P_c(4457)$ and $P_{cs}(4459)$ self-consistently. We can search for those pentaquark molecular states in the decays of the ${\mathrm{\Lambda }}_b^0$, ${\mathrm{\Xi }}_b^0$ and ${\mathrm{\Xi }}_b^{-}$ in the future. Furthermore, we discuss the higher dimensional vacuum condensates in details.