Possible open-charmed pentaquark molecule $$\varOmega _c(3188)$$ Ω c ( 3188 ) – the $$D \varXi $$ D Ξ bound state – in the Bethe–Salpeter formalism

We study the S-wave $$D\varXi $$ bound state in the Bethe–Salpeter formalism in the ladder and instantaneous approximations. With the kernel generated by the hadronic effective Lagrangian, two open-charmed bound states, which quantum numbers are $$I=0$$ , $$J^P=(\frac{1}{2})^-$$ and $$I=1$$ , $$J^P=(\frac{1}{2})^-$$ , respectively, are predicted as new candidates of hadronic pentaquark molecules in our formalism. If existing, they could contribute to the broad 3188 MeV structure near the five new narrow $$\varOmega _c$$ states observed recently by the LHCb Collaboration.