Possible open-charmed pentaquark molecule ${\mathrm{\Omega }}_c(3188)$ --- the $D\mathrm{\Xi }$ bound state --- in the Bethe-Salpeter formalism

We study the $S$-wave $D\mathrm{\Xi }$ 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 eV structure near the five new narrow ${\mathrm{\Omega }}_c$ states observed recently by the LHCb Collaboration.