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

Abstract

The hadronic ${\Sigma }_c^{(\ast )}{\bar{D}}^{(\ast )}$ and ${\Sigma }_c^{(\ast )}{D}^{(\ast )}$ 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 ${\Sigma }_c{\bar{D}}^{(\ast )}$ 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.

18 pages, 12 figures. Accepted version by PRD

References in corpus (29)

• Multiquark Resonances
• Pentaquark and Tetraquark states
• Observation of a narrow pentaquark state, $P_c(4312{)}^{+}$, and of two-peak structure of the $P_c(4450{)}^{+}$
• Prediction of narrow $N^{\ast }$ and ${\Lambda }^{\ast }$ resonances with hidden charm above 4 GeV
• Emergence of a complete heavy-quark spin symmetry multiplet: seven molecular pentaquarks in light of the latest LHCb analysis
• Strong LHCb evidence supporting the existence of the hidden-charm molecular pentaquarks
• A survey of heavy-heavy hadronic molecules
• X(3872) and Other Possible Heavy Molecular States
• Is X(3872) {\sl Really} a Molecular State?
• Is X(3872) a molecule?
• Study of $P_c(4457)$, $P_c(4440)$, and $P_c(4312)$ in a quasipotential Bethe-Salpeter equation approach
• Heavy quark spin symmetric molecular states from ${\bar{D}}^{(\ast )}{\Sigma }_c^{(\ast )}$ and other coupled channels in the light of the recent LHCb pentaquarks
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• Anatomy of the newly observed hidden-charm pentaquark states: $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$
• Isospin breaking decays as a diagnosis of the hadronic molecular structure of the $P_c(4457)$
• Spectrum of the strange hidden charm molecular pentaquarks in chiral effective field theory
• Probing the long-range structure of the $T_{cc}^{+}$ with the strong and electromagnetic decays
• Isospin breaking, coupled-channel effects, and X(3872)
• Hidden-charm and hidden-bottom molecular pentaquarks in chiral perturbation theory
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• Deuteron-like states composed of two doubly charmed baryons
• New strange pentaquarks
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