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 $\bar{ D}\Sigma_c$, $\bar{ D}\Sigma_c^*$, $\bar{ D}^*\Sigma_c$ and $\bar{ D}^*\Sigma_c^*$ 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 $\bar{ D}\Sigma_c$, $\bar{ D}\Sigma_c^*$, $\bar{ D}^*\Sigma_c$ and $\bar{ D}^*\Sigma_c^*$ pentaquark states with the isospin $I=\frac{ 1}{ 2}$, respectively. The corresponding $\bar{ D}\Sigma_c$, $\bar{ D}\Sigma_c^*$, $\bar{ D}^*\Sigma_c$ and $\bar{ D}^*\Sigma_c^*$ 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.
Categories: hep-ph