Study of isospin eigenstates of the pentaquark states with strangeness

In the present work, we construct eight color singlet-singlet type five-quark currents with strangeness to study the pentaquark states of $\bar{D}\Xi^{\prime}$, $\bar{D}\Xi_c^{*}$, $\bar{D}^{*}\Xi_c^{\prime}$ and $\bar{D}^{*}\Xi_c^{*}$ via the QCD sum rules. The considered states are isospin eigenstates with isospin quantum number $I=1$ or $I=0$. Numerical results show that the central value of the masses extracted from the Borel platforms with high isospin are slightly above the thresholds of the meson and baryon constituents and the low isospin ones are a few dozens of $\rm{MeV}$ below, what's more, the present study supports the assignment of $P_{cs}(4459)$ as $\bar{D}\Xi_c^{*}$ molecular state with the $IJ^P=0(\frac{3}{2})^-$. Technically, besides the analyses of the uncertainties of the masses and pole residues, detailed discussion about the contribution of vacuum condensates proportional to the mass of $s$ quark are conducted which may present a reference for the technical application of QCD sum rules in the future work.