In this work, we distinguish the isospin unambiguously to construct the diquark-diquark-antiquark type five-quark currents with the isospin $I=\frac{ 1}{ 2}$, and study the $uudc\bar{ c}$ pentaquark states with the QCD sum rules systematically for the first time. Then we obtain the mass spectrum of the diquark-diquark-antiquark type $uudc\bar{ c}$ pentaquark states with the isospin-spin-parity $IJ^P=\frac{ 1}{ 2}{ \frac{ 1}{ 2}}^-$, $\frac{ 1}{ 2}{ \frac{ 3}{ 2}}^-$ and $\frac{ 1}{ 2}{ \frac{ 5}{ 2}}^-$, and make possible assignments of the $P_c(4312)$, $P_c(4337)$, $P_c(4380)$, $P_c(4440)$ and $P_c(4457)$. As a byproduct, we obtain the lowest hidden-charm pentaquark state which lies just above the $\bar{ D}\Lambda_c$ threshold.
Categories: hep-ph