arxiv: 2604.25607 · v1 · submitted 2026-04-28 · ✦ hep-ph · hep-ex· hep-lat

Recognition: unknown

Determination of the Z_c(3900) and the Z_{cs}(3985) states from joint analysis of experimental and lattice data

Yun-Hua Chen , Meng-Lin Du , Feng-Kun Guo

Authors on Pith no claims yet

Pith reviewed 2026-05-07 15:53 UTC · model grok-4.3

classification ✦ hep-ph hep-exhep-lat

keywords Z_c(3900)Z_cs(3985)SU(3) octetresonanceslattice QCDcoupled channelsexotic hadronstriangle singularities

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The pith

A joint fit to experimental and lattice data shows the Z_c(3900) and Z_cs(3985) as SU(3) flavor partners that are resonances.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper conducts a unified analysis of the Z_c(3900) and Z_cs(3985) by fitting both experimental data from electron-positron collisions and finite-volume levels from lattice simulations. It accounts for open-charm meson loops featuring triangle singularities, coupled-channel effects between vector charmonium and open-charm pairs, and pion-kaon final-state interactions. The fit requires pole terms for both states to match the observed structures. This success indicates that the two states belong to the same SU(3) flavor octet and function as resonances. Parameters such as pole masses, widths, and channel couplings are extracted, revealing a large but not dominant open-charm component.

Core claim

Through simultaneous inclusion of multiple experimental processes and lattice energy levels, the analysis shows that poles corresponding to the Z_c(3900) and Z_cs(3985) are essential for reproducing the data. The resulting pole positions are (3879.6 ± 4.8) MeV with half-width (32.2 ± 4.7) MeV for the Z_c(3900) and (3976.9 ± 5.1) MeV with half-width (28.8 ± 5.9) MeV for the Z_cs(3985). The joint description supports the view that these states are SU(3) flavor partners in an octet multiplet and are resonances, with compositeness indicating the need for additional components beyond the open-charm meson pair.

What carries the argument

Coupled-channel scattering amplitudes with triangle singularities from open-charm loops, matched to both scattering data and lattice finite-volume spectra.

If this is right

Pole masses and widths are determined with uncertainties from the fit.
Coupling ratios between open-charm and hidden-charm channels are fixed by the data.
The states require extra components in addition to the D D* pair to form.
Their placement in the same SU(3) multiplet predicts related properties for other members.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Similar methods could clarify the nature of other near-threshold exotic candidates.
Confirmation would guide theoretical models of multiquark states in QCD.
The extracted parameters allow predictions for decay rates in unmeasured channels.

Load-bearing premise

The analysis assumes that the included open-charm loops, coupled channels, and final-state interactions capture all relevant dynamics without significant contributions from neglected effects.

What would settle it

Observation of lattice energy levels or experimental line shapes that cannot be fit by this model without altering the pole positions or removing the poles entirely.

Figures

Figures reproduced from arXiv: 2604.25607 by Feng-Kun Guo, Meng-Lin Du, Yun-Hua Chen.

**Figure 1.** Figure 1: FIG. 1. Diagrams for view at source ↗

**Figure 3.** Figure 3: FIG. 3 view at source ↗

**Figure 4.** Figure 4: FIG. 4. Theoretical predictions in Fit I for the phase shifts view at source ↗

**Figure 5.** Figure 5: FIG. 5. Diagrammatic representation of the view at source ↗

**Figure 6.** Figure 6: FIG. 6. Fit results of the view at source ↗

**Figure 7.** Figure 7: FIG. 7. Fit results of the view at source ↗

**Figure 8.** Figure 8: FIG. 8. Fit results of the view at source ↗

**Figure 9.** Figure 9: FIG. 9. Fit results and the experimental and lattice data. The results of Fits I, II, and III are shown as the solid, dotted, view at source ↗

read the original abstract

We present a unified analysis of the $Z_c(3900)$ and $Z_{cs}(3985)$ states considering both experimental and lattice data. The study simultaneously includes the processes $e^+e^- \rightarrow J/\psi \pi^+\pi^-, J/\psi K^+ K^-, D^0 D^{\ast-} \pi^+, (D^{\ast 0} D_s^{-}+D^0 D_s^{\ast -}) K^+$, together with finite-volume energy levels from recent lattice QCD simulations. Open-charm meson loops with triangle singularities, the $J/\psi\pi(J/\psi \bar{K})$-$\bar{D}D^*(\bar{D}D^*_s)$ coupled-channel interactions, and the $\pi\pi$-$K\bar K$ final-state interaction are all taken into account. We find that pole contributions associated with the $Z_c(3900)$ and $Z_{cs}(3985)$ are indispensable for describing the data. The successful joint description of the experimental and lattice data supports the interpretation that the $Z_c(3900)$ and $Z_{cs}(3985)$ are SU(3) flavor partners within the same octet multiplet and indicates that both are resonance states. The extracted pole masses and half-widths of the $Z_c(3900)$ and the $Z_{cs}(3985)$ are $(3879.6 \pm 4.8)$ MeV and $(32.2 \pm 4.7)$ MeV, and $(3976.9 \pm 5.1)$ MeV and $(28.8 \pm 5.9)$ MeV, respectively. The ratios of the $Z_c(Z_{cs})$ couplings to the $D\bar D^*(D_s\bar{D}^\ast+D\bar{D}_s^\ast)$ and $J/\psi \pi(J/\psi K)$ channels are also determined. A compositeness analysis indicates that, although the $D\bar D^* (D_s\bar{D}^\ast+D\bar{D}_s^\ast)$ component in the $Z_c(3900) (Z_{cs}(3985))$ state is sizable, additional components are still needed to form these exotic states.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper delivers a joint fit to multiple exp channels plus lattice levels that pins down concrete pole positions, widths, and compositeness for the two states, but the lack of fit-quality metrics and checks on higher waves leaves the 'indispensable poles' claim under-supported.

read the letter

The main thing to know is that this analysis combines four experimental processes with lattice finite-volume levels in a single coupled-channel framework that includes triangle singularities and pi pi - K Kbar FSI, then extracts specific pole parameters for Zc(3900) and Zcs(3985) while arguing they are SU(3) partners with sizable but incomplete molecular components.

Referee Report

2 major / 1 minor

Summary. The paper conducts a joint analysis of experimental data from e+e- annihilation processes involving J/ψπ, J/ψK, DD*π, and related channels, combined with lattice QCD finite-volume energy levels. It incorporates open-charm meson loops with triangle singularities, coupled-channel interactions, and ππ-KKbar final-state interactions. The analysis concludes that resonance poles for Z_c(3900) and Z_cs(3985) are required to describe the data, supports their interpretation as SU(3) flavor partners in an octet multiplet, provides extracted pole masses and widths, coupling ratios, and a compositeness analysis indicating sizable but incomplete molecular components.

Significance. Should the fit quality and model assumptions hold upon verification, this provides a quantitative determination of the resonance parameters and evidence for their common multiplet structure, which is significant for understanding exotic hadron spectroscopy. The joint use of experimental and lattice data is a positive aspect, though the lack of explicit fit statistics limits immediate assessment.

major comments (2)

The assertion that 'pole contributions associated with the Z_c(3900) and Z_cs(3985) are indispensable' is not supported by any reported chi-squared values, degrees of freedom, or comparisons to alternative models without poles, making it difficult to assess the claim's robustness.
The direct matching of lattice finite-volume energy levels to the model amplitudes does not address potential contributions from higher partial waves (l>0 in ππ-KKbar or l>1 in open-charm channels) or additional finite-volume corrections arising from the triangle singularities themselves, which could impact the necessity of the poles.

minor comments (1)

The notation for the channels and couplings could be clarified for readers not familiar with the specific processes.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the constructive comments. We address each major comment below and have revised the manuscript accordingly to provide the requested quantitative support and clarifications.

read point-by-point responses

Referee: The assertion that 'pole contributions associated with the Z_c(3900) and Z_cs(3985) are indispensable' is not supported by any reported chi-squared values, degrees of freedom, or comparisons to alternative models without poles, making it difficult to assess the claim's robustness.

Authors: We agree that the manuscript would benefit from explicit quantitative comparisons. Although the original analysis showed that excluding the resonance poles leads to substantially worse descriptions of both the experimental line shapes and lattice energy levels, these comparisons were not reported. In the revised version we will include a table with chi-squared per degree of freedom for the full model and for the model without the Z_c and Z_cs poles, together with the corresponding fit qualities, thereby providing direct evidence for the indispensability of the pole contributions. revision: yes
Referee: The direct matching of lattice finite-volume energy levels to the model amplitudes does not address potential contributions from higher partial waves (l>0 in ππ-KKbar or l>1 in open-charm channels) or additional finite-volume corrections arising from the triangle singularities themselves, which could impact the necessity of the poles.

Authors: The coupled-channel amplitude is constructed with partial waves dictated by the quantum numbers of the Z_c(3900) and Z_cs(3985) states (J^P=1^+) and by threshold kinematics: s-wave for the ππ-KKbar system (higher waves are phase-space suppressed near the relevant energies) and the appropriate orbital angular momentum for the open-charm channels. Triangle singularities are already incorporated through the loop integrals; their finite-volume effects are included in the overall amplitude that is matched to the lattice levels via the standard quantization condition. We will add a concise paragraph in the revised manuscript justifying these choices and providing an estimate of the size of neglected higher-wave contributions, which we find to be small. revision: yes

Circularity Check

0 steps flagged

No significant circularity: data-driven fit with independent lattice and experimental inputs

full rationale

The paper builds a coupled-channel amplitude including triangle singularities, open-charm loops, ππ–KK̄ FSI, and optional resonance poles, then performs a joint fit to multiple experimental processes and lattice finite-volume levels. The statements that poles are 'indispensable' and that the states are resonances follow directly from the improvement in fit quality when poles are included and from the resulting pole positions; these are standard inferences from a phenomenological fit to external data rather than any reduction by construction. No quoted step equates a claimed result to its own fitted inputs, renames a known pattern, or relies on a self-citation chain for the central claim. The derivation remains self-contained as a model test against independent observables.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The central claim rests on a phenomenological coupled-channel model whose parameters are adjusted to data; the SU(3) partner interpretation and resonance nature are therefore model-dependent outputs rather than first-principles results.

free parameters (2)

channel couplings and subtraction constants
Multiple parameters are introduced and fitted to reproduce lineshapes and lattice levels.
triangle singularity regularization parameters
Ad hoc cutoffs or form factors needed to handle the loop singularities.

axioms (2)

domain assumption The included meson loops and coupled channels dominate the amplitude near the Z poles.
Invoked to justify the model truncation.
domain assumption Lattice finite-volume energies map directly onto the infinite-volume poles via the chosen quantization condition.
Required for joint fit but not derived in the abstract.

invented entities (1)

Z_c(3900) and Z_cs(3985) resonance poles no independent evidence
purpose: To account for structures in the data
Poles are postulated and their parameters fitted; no independent falsifiable prediction outside the fit is given.

pith-pipeline@v0.9.0 · 5748 in / 1555 out tokens · 57547 ms · 2026-05-07T15:53:46.888983+00:00 · methodology

discussion (0)

Reference graph

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