Isospin eigenstates of the color singlet-singlet type pentaquark states

Abstract

In this article, we construct the color singlet-singlet type five-quark currents with the isospins $(I,I_3)=(\frac{1}{2},\frac{1}{2})$ and $(\frac{3}{2},\frac{1}{2})$ unambiguously to explore the $\bar{D}{\Sigma }_c$, $\bar{D}{\Sigma }_c^{\ast }$, ${\bar{D}}^{\ast }{\Sigma }_c$ and ${\bar{D}}^{\ast }{\Sigma }_c^{\ast }$ pentaquark states via the QCD sum rules for the first time, where the $\bar{D}$, ${\Sigma }_c$, $\cdots$ represent the color-singlet clusters having the same quantum numbers as the corresponding physical mesons or baryons. The numerical results support assigning the $P_c(4312)$, $P_c(4380)$, $P_c(4440)$ and $P_c(4457)$ as the $\bar{D}{\Sigma }_c$, $\bar{D}{\Sigma }_c^{\ast }$, ${\bar{D}}^{\ast }{\Sigma }_c$ and ${\bar{D}}^{\ast }{\Sigma }_c^{\ast }$ pentaquark states with the isospin $I=\frac{1}{2}$, respectively. The corresponding $\bar{D}{\Sigma }_c$, $\bar{D}{\Sigma }_c^{\ast }$, ${\bar{D}}^{\ast }{\Sigma }_c$ and ${\bar{D}}^{\ast }{\Sigma }_c^{\ast }$ pentaquark states with the isospin $I=\frac{3}{2}$ have slightly larger masses, the observations of the higher pentaquark candidates in the $J/\psi \Delta$ invariant mass spectrum would shed light on the nature of the $P_c$ states, and make contributions in distinguishing the scenarios of color antitriplet-antitriplet-antitriplet type and color singlet-singlet type pentaquark states.