Strange Pentaquark Molecules in QCD Sum Rules

In this article, we systematically construct hidden- and open-strange pentaquarks in the hadronic molecular picture to search for possible partners of hadronic molecular state multiplets in the strange quark sector using QCD sum rules. Within this picture, 21 distinct currents are constructed with $J^P=1\mathrm{/}{2}^{-}$ and $3\mathrm{/}{2}^{-}$. There is no bound state found from $J^P=1\mathrm{/}{2}^{-}$ currents, while three of them from $J^P=3\mathrm{/}{2}^{-}$ currents are bound-state solutions consistent with the $\mathrm{\Lambda }(2050)3\mathrm{/}{2}^{-}$, $\mathrm{\Xi }(2250)$, and $N(2120)3\mathrm{/}{2}^{-}$ states, which can be identified as $\mathrm{\Lambda }\phi$, $\mathrm{\Xi }\phi$, and $\mathrm{\Sigma }{K}^{\ast }$ hadronic molecular states, respectively. Other constructions are interpreted as hadronic molecular states composed of excited states with the same quantum numbers, and some of these exhibit mass values that align with known resonances listed in the RPP(PDG). Our numerical results indicate that $\mathrm{\Lambda }(2050)3\mathrm{/}{2}^{-}$ and $\mathrm{\Xi }(2250)$ should be the multiplet partner of each other. Additionally, although $\mathrm{\Sigma }{K}^{\ast }$ bound state was identified under this framework, no corresponding partner states were found within the context of the currents we constructed. Alternative constructions may offer new possibilities for identifying such states.