Analysis of the ${\frac{3}{2}}^{\pm}$ pentaquark states in the diquark-diquark-antiquark model with QCD sum rules

In this article, we construct the axialvector-diquark-scalar-diquark-antiquark type and the axialvector-diquark-axialvector-diquark-antiquark type interpolating currents, and study the $J^P={\frac{3}{2}}^\pm$ hidden-charm pentaquark states with the strangeness $S=0,\,-1,\,-2,\,-3$ systematically using the QCD sum rules. The predicted masses of the pentaquark states $P_{uud}^{10\frac{1}{2}}\left({\frac{3}{2}^-}\right)$, $P_{uud}^{11\frac{1}{2}}\left({\frac{3}{2}^-}\right)$ and $P_{uud}^{11\frac{3}{2}}\left({\frac{3}{2}^-}\right)$ are compatible with the experimental value $M_{P_c(4380)}=4380\pm 8\pm 29\,\rm{MeV}$ from the LHCb collaboration, more experimental data are still needed to identify the $P_c(4380)$ unambiguously.