Analysis of the $\bar{D}{\Sigma }_c$, $\bar{D}{\Sigma }_c^{\ast }$, ${\bar{D}}^{\ast }{\Sigma }_c$ and ${\bar{D}}^{\ast }{\Sigma }_c^{\ast }$ pentaquark molecular states with QCD sum rules

Abstract

In this article, we study the $\bar{D}{\Sigma }_c$, $\bar{D}{\Sigma }_c^{\ast }$, ${\bar{D}}^{\ast }{\Sigma }_c$ and ${\bar{D}}^{\ast }{\Sigma }_c^{\ast }$ pentaquark molecular states with the QCD sum rules by carrying out the operator product expansion up to the vacuum condensates of dimension $13$ in a consistent way. The present calculations support assigning the $P_c(4312)$ to be the $\bar{D}{\Sigma }_c$ pentaquark molecular state with $J^P={\frac{1}{2}}^{-}$, assigning the $P_c(4380)$ to be the $\bar{D}{\Sigma }_c^{\ast }$ pentaquark molecular state with $J^P={\frac{3}{2}}^{-}$, assigning the $P_c(4440/4457)$ to be the ${\bar{D}}^{\ast }{\Sigma }_c$ pentaquark molecular state with $J^P={\frac{3}{2}}^{-}$ or the ${\bar{D}}^{\ast }{\Sigma }_c^{\ast }$ pentaquark molecular state with $J^P={\frac{5}{2}}^{-}$. Special attentions are payed to the operator product expansion.

Comments: 39 pages, 46 figures