Possible open-charmed pentaquark molecule $\Omega_c(3188)$ --- the $D \Xi$ bound state --- in the Bethe-Salpeter formalism

TL;DR

This paper predicts two new open-charmed pentaquark molecules as $D ext{Xi}$ bound states using the Bethe-Salpeter formalism, potentially explaining a broad structure near observed $ ext{Omega}_c$ states.

Contribution

It introduces a Bethe-Salpeter approach with hadronic effective Lagrangian to predict new pentaquark molecular states with specific quantum numbers.

Findings

Prediction of two $D ext{Xi}$ bound states with specific quantum numbers.

Potential explanation for the broad structure near $ ext{Omega}_c(3188)$.

Application of the Bethe-Salpeter formalism in this context.

Abstract

We study the $S$-wave $D\Xi$ 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 $\Omega_c$ states observed recently by the LHCb Collaboration.