Analysis of the $P_{cs}(4338)$ and related pentaquark molecular states via the QCD sum rules

In this work, we tentatively identify the $P_{cs}(4338)$ as the $\bar{D}{\mathrm{\Xi }}_c$ molecular state, and distinguish the isospins of the current operators to explore the $\bar{D}{\mathrm{\Xi }}_c$, $\bar{D}{\mathrm{\Lambda }}_c$, ${\bar{D}}_s{\mathrm{\Xi }}_c$, ${\bar{D}}_s{\mathrm{\Lambda }}_c$, ${\bar{D}}^{\ast }{\mathrm{\Xi }}_c$, ${\bar{D}}^{\ast }{\mathrm{\Lambda }}_c$, ${\bar{D}}_s^{\ast }{\mathrm{\Xi }}_c$ and ${\bar{D}}_s^{\ast }{\mathrm{\Lambda }}_c$ molecular states without strange, with strange and with double strange in the framework of the QCD sum rules in details. The present explorations favor identifying the $P_{cs}(4338)$ ($P_{cs}(4459)$) as the $\bar{D}{\mathrm{\Xi }}_c$ (${\bar{D}}^{\ast }{\mathrm{\Xi }}_c$) molecular state with the spin-parity $J^P={\frac{1}{2}}^{-}$ (${\frac{3}{2}}^{-}$) and isospin $(I,I_3)=(0,0)$, the observation of their cousins with the isospin $(I,I_3)=(1,0)$ in the $J\mathrm{/}\psi {\mathrm{\Sigma }}^0\mathrm{/}{\eta }_c{\mathrm{\Sigma }}^0$ invariant mass distributions would decipher their inner structures.