[Paper Review] Can $Z_{cs}(3985)$ be a molecular state of $\bar{D}_s^*D$ and $\bar{D}_sD^*$ ?

Ming-Zhu Liu, Jun-Xu Lu+3 more|arXiv (Cornell University)|Nov 17, 2020

Cold Atom Physics and Bose-Einstein Condensates7 citations

TL;DR

This study investigates whether the $Z_{cs}(3985)$ resonance can be a molecular state composed of $\bar{D}_s^*D$ and $\bar{D}_sD^*$ hadrons using the one-boson-exchange model. It finds that the interaction is too weak to form bound states for $\bar{D}_sD$ and $\bar{D}_s^*D$, but allows very loosely bound $\bar{D}_s^*D^*$ states with binding energies of a few MeV, suggesting $Z_{cs}(3985)$ likely has significant compact components rather than being a pure molecular state.

ABSTRACT

We study the $Z_{cs}(3985)$ state recently observed by the BESIII Collaboration in the one-boson-exchange model, assuming that it is a $\bar{D}_s^{(*)}D^{(*)}$ molecule, which has the quark content $c\bar{c}s\bar{q}$ with $q = u$, $d$. It is shown that the one-boson-exchange potential is too weak to generate dynamcally $\bar{D}_s D$, $\bar{D}^*_s D$, and $\bar{D}_sD^*$ states, while for the case of $\bar{D}^*_s D^*$, very loosely bound states are likely, with binding energies of the order of several MeV. We conclude that, the observed $Z_{cs}(3985)$ state, if confirmed by further experiments, cannot be a pure hadronic molecular state of $\bar{D}_s D^*$ and $\bar{D}_s^*D$ and could consist of large components of compact nature.

Motivation & Objective

• To determine if the $Z_{cs}(3985)$ resonance observed by BESIII can be explained as a hadronic molecule of $\bar{D}_s^{(*)}D^{(*)}$ states.
• To assess the strength of the one-boson-exchange potential in generating bound states for various $\bar{D}_s^{(*)}D^{(*)}$ channels.
• To evaluate whether the observed $Z_{cs}(3985)$ state can be purely molecular or must include significant compact quark content.

Proposed method

• Employing the one-boson-exchange model to compute the interaction kernel between $\bar{D}_s^{(*)}D^{(*)}$ hadrons.
• Using the Bethe-Salpeter equation to solve for bound state poles in the scattering amplitude.
• Evaluating the potential strength for different channels: $\bar{D}_sD$, $\bar{D}_s^*D$, $\bar{D}_sD^*$, and $\bar{D}_s^*D^*$.
• Calculating binding energies and checking for the existence of bound states in each channel.
• Comparing the predicted binding energies with the observed mass of $Z_{cs}(3985)$ at 3985 MeV.
• Assessing the dominance of molecular vs. compact components based on binding strength and quantum numbers.

Experimental results

Research questions

• RQ1 Can the one-boson-exchange potential generate a bound state for the $\bar{D}_sD$ channel?
• RQ2 Is the $\bar{D}_s^*D$ system sufficiently bound to account for $Z_{cs}(3985)$?
• RQ3 Does the $\bar{D}_sD^*$ channel support a bound state with binding energy consistent with the observed resonance?
• RQ4 What is the binding energy of the $\bar{D}_s^*D^*$ molecular state, and is it compatible with $Z_{cs}(3985)$?
• RQ5 To what extent must the $Z_{cs}(3985)$ state include compact components if molecular states are too weakly bound?

Key findings

• The one-boson-exchange potential is too weak to generate bound states for the $\bar{D}_sD$ and $\bar{D}_s^*D$ channels.
• No significant binding is found for the $\bar{D}_sD^*$ channel under the one-boson-exchange model.
• Very loosely bound states are predicted for the $\bar{D}_s^*D^*$ channel, with binding energies on the order of several MeV.
• The binding energy of the $\bar{D}_s^*D^*$ state is too small to account for the full width or mass of $Z_{cs}(3985)$ if purely molecular.
• The observed $Z_{cs}(3985)$ resonance cannot be a pure molecular state of $\bar{D}_sD^*$ or $\bar{D}_s^*D$ due to insufficient binding.
• The results imply that $Z_{cs}(3985)$ must contain a large component of compact four-quark structure rather than being a conventional hadronic molecule.