[Paper Review] The nature of charged charmonium-like states $Z_c(3900)$ and its strange partner $Z_{cs}(3982)$

M. C. Du, Qian Wang+1 more|arXiv (Cornell University)|Nov 18, 2020

Molecular spectroscopy and chirality18 citations

TL;DR

This paper investigates the nature of charged charmonium-like states $Z_c(3900)$ and its strange partner $Z_{cs}(3982)$ using an effective field theory framework with SU(3) flavor symmetry and heavy quark spin symmetry. By analyzing invariant mass and Jackson angular distributions in $e^+e^-$ annihilations, the authors identify genuine pole structures—indicating bound or virtual states—confirming both $Z_c(3900)$ and $Z_{cs}(3982)$ as dynamically generated hadronic molecules, with $Z_{cs}(3982)$ being particularly sensitive to $S$-wave open thresholds.

ABSTRACT

The observation of $Z_{cs}(3985)$ by BESIII in the $D_s^{*-}D^0$ and $D_s^{-}D^{*0}$ channel adds important dynamic information for a coherent understanding of both $Z_c(3900)$ and $Z_c(4020)$, as well as their strange partners $Z_{cs}(3985)$ and $Z_{cs}(4120)$, on the basis of heavy quark spin symmetry. With an overall short-ranged contact potential in SU(3) flavor symmetry we show that the pole structures can be extracted from the experimental data. Meanwhile, we show the key role played by the $S$-wave open thresholds in $e^+e^-$ annihilations which are correlated with the production of these $Z$ states in a hadronic molecule picture. Implications of their scalar heavy quark spin partners $W_{c0,1,2}$ and $W_{cs0,1,2}$ are also gained.

Motivation & Objective

• To determine the dynamical nature of $Z_c(3900)$ and $Z_{cs}(3982)$ using experimental data from BESIII.
• To assess whether these states are bound states, virtual states, or resonances via pole structure analysis in the complex energy plane.
• To explore the role of $S$-wave open thresholds in $e^+e^-$ annihilations in generating these exotic states.
• To predict the existence and properties of their heavy quark spin symmetry partners, $W_{c0,1,2}$ and $W_{cs0,1,2}$, for future experimental searches.

Proposed method

• Employing an effective field theory with short-ranged contact interactions to model hadronic molecule dynamics.
• Applying SU(3) flavor symmetry and heavy quark spin symmetry to relate charmonium-like states and their strange partners.
• Fitting invariant mass and Jackson angular distributions from $e^+e^-$ data to extract production amplitudes in $S$- and $D$-wave channels.
• Using the $S$-wave open thresholds in $D\bar{D}^*$, $D_s\bar{D}^{*}$, and related channels as key constraints on pole positions.
• Analyzing pole structures in the complex energy plane to distinguish between bound states, virtual states, and resonances.
• Predicting decay channels for heavy quark spin partners $W_{c0,1,2}$ and $W_{cs0,1,2}$, such as $J/\psi\pi\pi$ and $\eta_c\pi$, based on symmetry and pole behavior.

Experimental results

Research questions

• RQ1 Do $Z_c(3900)$ and $Z_{cs}(3982)$ exhibit genuine pole structures in the complex energy plane, indicating they are not kinematic artifacts?
• RQ2 How do $S$-wave open thresholds in $e^+e^-$ annihilations influence the production and stability of these exotic states?
• RQ3 Can the same dynamical mechanism explain both $Z_c(3900)$ and $Z_{cs}(3982)$, and their respective spin partners?
• RQ4 What is the nature (bound, virtual, or resonant) of the $Z_c(3900)$ and $Z_{cs}(3982)$ states based on pole positions extracted from data?
• RQ5 What are the properties of their heavy quark spin symmetry partners $W_{c0,1,2}$ and $W_{cs0,1,2}$, and how can they be experimentally searched for?

Key findings

• The $Z_c(3900)$ state is confirmed as a genuine state, with a binding energy of 75.2 MeV in the best-fit scheme (Scheme III), indicating a deep virtual or bound state.
• The $Z_{cs}(3982)$ state is found to exist as a genuine state, either a virtual or bound state, with significant pole structure above the $D_s\bar{D}^{*}$ threshold.
• The $S$-wave open thresholds in $e^+e^-$ annihilations play a crucial role in generating the observed $Z_c$ and $Z_{cs}$ signals, consistent with the triangle singularity mechanism.
• The heavy quark spin symmetry partner $W_{cs0}$ is predicted to be a bound state with a binding energy of 31.8 MeV, accessible in $J/\psi K\pi$ and $\eta_c K$ decay channels.
• The $W_{c0}$ and $W_{cs0}$ states are found to be bound states in all schemes, with $W_{c0}$ having a binding energy of 0.3 MeV in Scheme I and 47.0 MeV in Scheme III.
• The missing kaon spectrum prediction for $e^+e^- \to K^+ D_s^{*-} D^{*0}$ at $\sqrt{s} = 4.68$ GeV shows distinct lineshape differences across fitting schemes, supporting the existence of $Z_{cs}(4120)$ as a genuine state.