Analysis of

In this article, we construct the diquark–diquark–antiquark type interpolating currents, and we study the masses and pole residues of the $$J^P={\frac{3}{2}}^-$$ and $${\frac{5}{2}}^+$$ hidden charm pentaquark states in detail with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension-10 in the operator product expansion. In the calculations, we use the formula $$\mu =\sqrt{M^2_{P_c}-(2{\mathbb {M}}_c)^2}$$ to determine the energy scales of the QCD spectral densities. The present predictions favor assigning $$P_c(4380)$$ and $$P_c(4450)$$ to be the $${\frac{3}{2}}^-$$ and $${\frac{5}{2}}^+$$ pentaquark states, respectively