Towards modeling the short-range interactions of hidden/open charm pentaquark molecular states

Abstract

The hadronic $\Sigma_c^{(*)}\bar{D}^{(*)}$ and $\Sigma_c^{(*)}{D}^{(*)}$ interactions are revisited, with a focus on their short-range parts, motivated by a tension between the interpretations of $P_{c\bar{c}}(4312)$, $P_{c\bar{c}}(4440)$, and $P_{c\bar{c}}(4457)$ in effective field theory (EFT) frameworks and the one-boson-exchange (OBE) model. While the three states can be interpreted as $\Sigma_c\bar{D}^{(*)}$ molecular states within EFT frameworks, this is not feasible in the single-channel OBE model with consistent cutoff. In this work, the possibility to reconcile OBE model with EFTs by refitting the $\rho$-, $\omega$- and $\sigma$-exchange interaction is explored and ruled out. It is pointed out that the problem in OBE arises from the strong short-range spin-dependent one-pion-exchange (OPE) interaction and the fixed signs of other short-range interactions in OBE model also prevent the cancellation. To address this issue, the short-range subtraction strategies within the OBE model are revisited. Two subtraction schemes are explored: removing the delta-function from all interactions and eliminating it only from the pseudoscalar-meson-exchange component. These schemes favor different spin assignments for $P_{c\bar{c}}(4440)$ and $P_{c\bar{c}}(4457)$. Though solving the problem, there is no clear dynamical picture to support the subtraction schemes. We propose a new quark-exchange mechanism motivated by the Pauli principle. Different from the two subtraction schemes in OBE, the quark-exchange mechanism offers an explanation grounded in microscopic dynamics. It is shown that the spin-dependent quark-exchange interaction cancels those from OPE. The differences in the predictions for the spin, isospin, and open-charm partner states of the experimental $P_{c\bar{c}}$ states offer a way to distinguish between the subtracted OBE model and the OBE model with quark-exchange contributions.