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

Abstract: In this article, we investigate the $\bar{D}\Sigma_c$, $\bar{D}\Xi^\prime_c$, $\bar{D}\Sigma_c^*$, $\bar{D}\Xi_c^*$, $\bar{D}^{*}\Sigma_c$, $\bar{D}^{*}\Xi^\prime_c$, $\bar{D}^{}\Sigma_c^$ and $\bar{D}^{}\Xi_c^$ 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 $\Lambda_b^0$, $\Xi_b^0$ and $\Xi_b^-$ in the future. Furthermore, we discuss the higher dimensional vacuum condensates in details.