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arxiv: 2606.07225 · v1 · pith:56UDJS5Rnew · submitted 2026-06-05 · ✦ hep-ph

Simultaneous Dalitz-plot decomposition of the e^+ e^- to J/psi \, π \, π \, (K bar{K}) processes in the 4.13-4.36 GeV region using dispersive final-state interactions

Viktoriia Ermolina , Igor Danilkin , Marc Vanderhaeghen This is my paper

Pith reviewed 2026-06-27 21:51 UTC · model grok-4.3

classification ✦ hep-ph
keywords e+e- annihilationDalitz plot analysisOmnès functionfinal-state interactionsZc(3900)Y(4220)Y(4320)charmonium
0
0 comments X

The pith

The e+e- to J/psi pi pi and J/psi KK data in the 4.13-4.36 GeV region cannot be described by resonant Y states alone and require an additional non-resonant amplitude that undergoes pi pi / KK rescattering.

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

The paper constructs amplitudes for both processes using Dalitz-plot decomposition, with energy dependence from the Y(4220) and Y(4320) resonances plus one non-resonant term. The scalar pi pi and KK final-state interactions are handled through a single coupled-channel Omnès function taken from prior scattering data. This framework fits the measured cross sections and invariant-mass distributions simultaneously with a common set of energy-independent parameters. A purely resonant model fails to account for the data, so the non-resonant contribution is essential. The analysis yields Breit-Wigner parameters for the Zc(3900), Y(4220), and Y(4320) states along with the associated subprocess cross sections.

Core claim

A joint analysis of e+e- to J/psi pi+ pi- and e+e- to J/psi K+ K- at center-of-mass energies 4.13-4.36 GeV shows that the BESIII data require both the Y(4220) and Y(4320) resonant structures and a non-resonant production mechanism; the scalar pi pi / K Kbar final-state interactions are incorporated dispersively via a coupled-channel Omnès representation that uses only prior scattering input, allowing the total cross sections and one-dimensional mass distributions to be described with one set of energy-independent parameters and yielding Breit-Wigner parameters for Zc(3900), Y(4220), and Y(4320).

What carries the argument

Coupled-channel Omnès representation for the scalar pi pi / K Kbar final-state interaction, used inside a Dalitz-plot decomposition of the amplitudes that includes two Y resonances plus one non-resonant term.

If this is right

  • Both channels are described by the same energy-independent parameters.
  • Breit-Wigner masses and widths are extracted for Zc(3900), Y(4220), and Y(4320).
  • Subprocess cross sections for the contributing mechanisms are determined.
  • The non-resonant term must itself undergo pi pi / KK rescattering to match the data.

Where Pith is reading between the lines

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

  • If confirmed, the necessity of the non-resonant term implies additional production mechanisms operate in this energy window beyond the two identified Y states.
  • The method supplies a template that could be applied to related final states sharing the same scalar rescattering.

Load-bearing premise

The scalar pi pi and KK final-state interactions are fully captured by one energy-independent coupled-channel Omnès function taken from scattering data, while production is exhausted by the two specified Y resonances plus a single non-resonant term.

What would settle it

A fit of comparable quality to the same total cross sections and invariant-mass distributions achieved without the non-resonant term at the amplitude level.

Figures

Figures reproduced from arXiv: 2606.07225 by Igor Danilkin, Marc Vanderhaeghen, Viktoriia Ermolina.

Figure 1
Figure 1. Figure 1: Diagrams illustrating the considered contributions to the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Total cross section of the process [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Total cross section of the process [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Total cross section of the subprocesses of [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Minimal fit to the invariant mass distributions of the e +e − → J/ψ π+ π − (KK¯ ) process at the CM energies q = 4.1271 − 4.1888 GeV. The data are taken from [19, 29]. In all panels, the solid black curve is the full result, the long-dashed purple curve is the non-resonant background, and the dashed red curve is the Y (4220) contribution [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Minimal fit to the invariant mass distributions of the e +e − → J/ψ π+ π − (KK¯ ) process at the CM energies q = 4.1989 − 4.2263 GeV. The data are taken from [19, 29]. In all panels, the solid black curve is the full result, the long-dashed purple curve is the non-resonant background, and the dashed red curve is the Y (4220) contribution [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Minimal-fit extrapolation to the invariant-mass distributions of the e +e − → J/ψ π+ π − (KK¯ ) process at the CM energy q = 4.2886 GeV. The data are taken from [19, 29]. The solid black curve is the full result, the long-dashed purple curve is the non-resonant background, and the dashed red curve is the Y (4220) contribution [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Total fit to the invariant mass distributions of the e +e − → J/ψ π+ π − (KK¯ ) process at the CM energies q = 4.1271 − 4.1888 GeV. The data are taken from [19, 29]. In all panels, the solid black curve is the full result, the long-dashed purple curve is the non-resonant background, the dashed red curve is the Y (4220) contribution, and the dot-dashed cyan curve is the Y (4320) contribution when present [… view at source ↗
Figure 9
Figure 9. Figure 9: Total fit to the invariant mass distributions of the e +e − → J/ψ π+ π − (KK¯ ) process at the CM energies q = 4.1989 − 4.2263 GeV. The data are taken from [19, 29]. In all panels, the solid black curve is the full result, the long-dashed purple curve is the non-resonant background, the dashed red curve is the Y (4220) contribution, and the dot-dashed cyan curve is the Y (4320) contribution when present [… view at source ↗
Figure 10
Figure 10. Figure 10: Total fit to the invariant mass distributions of the e +e − → J/ψ π+ π − (KK¯ ) process at the CM energies q = 4.2357 − 4.2667 GeV. The data are taken from [19, 29]. In all panels, the solid black curve is the full result, the long-dashed purple curve is the non-resonant background, the dashed red curve is the Y (4220) contribution, and the dot-dashed cyan curve is the Y (4320) contribution when present … view at source ↗
Figure 11
Figure 11. Figure 11: Total fit to the invariant mass distributions of the e +e − → J/ψ π+ π − (KK¯ ) process at the CM energies q = 4.2776 − 4.3370 GeV. The data are taken from [19, 29]. In all panels, the solid black curve is the full result, the long-dashed purple curve is the non-resonant background, the dashed red curve is the Y (4220) contribution, and the dot-dashed cyan curve is the Y (4320) contribution when present … view at source ↗
Figure 12
Figure 12. Figure 12: Total fit to the invariant mass distributions of the e +e − → J/ψ π+ π − (KK¯ ) process at the CM energy q = 4.3583 GeV. The data are taken from [19, 29]. In all panels, the solid black curve is the full result, the long-dashed purple curve is the non-resonant background, the dashed red curve is the Y (4220) contribution, and the dot-dashed cyan curve is the Y (4320) contribution when present [PITH_FULL_… view at source ↗
read the original abstract

We present a joint analysis of the processes $e^+e^- \to J/\psi\pi^+\pi^-$ and $e^+e^- \to J/\psi K^+K^-$ at center-of-mass energies from 4.13 to 4.36 GeV. The amplitudes are constructed using the Dalitz-plot decomposition formalism, with the $e^+e^-$ energy dependence encoded through the $Y(4220)$ and $Y(4320)$ resonant structures together with a non-resonant production mechanism. The scalar $\pi\pi/K\bar K$ final-state interaction is treated dispersively using a coupled-channel Omn\`es representation. This allows us to describe the measured total cross sections and one-dimensional invariant-mass distributions with a single set of energy-independent parameters. We find that a purely resonant description of the BESIII data is insufficient, requiring a non-resonant term at the amplitude level which undergoes $\pi\pi/K\bar{K}$ rescattering. Within the present isobar model, we extract Breit-Wigner parameters for the $Z_c(3900)$, $Y(4220)$, and $Y(4320)$ states, and determine the corresponding subprocess cross sections.

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.

Referee Report

3 major / 2 minor

Summary. The manuscript performs a simultaneous Dalitz-plot analysis of e⁺e⁻ → J/ψ π⁺π⁻ and e⁺e⁻ → J/ψ K⁺K⁻ at √s = 4.13–4.36 GeV. Amplitudes are built in an isobar framework with Y(4220) and Y(4320) resonances plus a non-resonant production term, the Zc(3900) isobar, and scalar ππ/KK̄ final-state interactions implemented via a single coupled-channel Omnès function taken from independent scattering data. The central result is that a purely resonant description fails to describe the BESIII data, necessitating the non-resonant term that undergoes rescattering; Breit-Wigner parameters for the three states and subprocess cross sections are extracted with a single set of energy-independent parameters.

Significance. If the production-FSI factorization holds, the work supplies a data-driven, dispersive extraction of resonance parameters and cross sections that can be tested against future measurements. The use of an Omnès function fixed entirely by prior ππ/KK̄ scattering data is a methodological strength that reduces the number of free parameters and makes the non-resonant requirement falsifiable within the stated model.

major comments (3)
  1. [Amplitude construction] § Amplitude construction (paragraph following Eq. (production amplitude)): The claim that a purely resonant description is insufficient rests on the factorization Ansatz (production amplitude × single energy-independent Omnès function). No explicit test is shown of whether allowing an additional subtraction constant or a mild energy dependence in the production vertex would absorb the non-resonant term; such a test is load-bearing for the central conclusion.
  2. [Fit results] § Fit results (Table of fit parameters and χ² values): The necessity of the non-resonant term is asserted, yet the manuscript does not report the χ²/dof for the resonant-only hypothesis versus the full model. Without this quantitative comparison, it is impossible to judge whether the improvement is statistically required or an artifact of the chosen isobar + Omnès setup.
  3. [Zc(3900) treatment] § Zc(3900) treatment (isobar definition): The Zc(3900) is introduced as an independent isobar with no interference term beyond the Omnès rescattering. Given that the Zc lies in the same Dalitz region as the ππ/KK̄ FSI, a brief check that its coupling does not induce additional production-FSI entanglement would strengthen the robustness of the extracted parameters.
minor comments (2)
  1. [Notation] Notation for the non-resonant production amplitude strength and phase should be defined explicitly in the text rather than only in the fit-parameter table.
  2. [Figures] Figure captions for the Dalitz projections should state the center-of-mass energy binning used for each panel.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We respond point by point to the major comments below.

read point-by-point responses

  1. Referee: [Amplitude construction] The claim that a purely resonant description is insufficient rests on the factorization Ansatz (production amplitude × single energy-independent Omnès function). No explicit test is shown of whether allowing an additional subtraction constant or a mild energy dependence in the production vertex would absorb the non-resonant term; such a test is load-bearing for the central conclusion.

    Authors: The analysis is performed strictly within the stated factorization Ansatz, with the production amplitude (resonant terms plus constant non-resonant term) multiplied by the fixed, energy-independent Omnès function taken from independent scattering data. Within this minimal, energy-independent framework the non-resonant term is required. Alternative models with energy-dependent production vertices or extra subtraction constants would introduce additional free parameters and lie outside the present approach. We will add an explicit statement clarifying that the necessity of the non-resonant term is established inside the adopted Ansatz. revision: partial

  2. Referee: [Fit results] The necessity of the non-resonant term is asserted, yet the manuscript does not report the χ²/dof for the resonant-only hypothesis versus the full model. Without this quantitative comparison, it is impossible to judge whether the improvement is statistically required or an artifact of the chosen isobar + Omnès setup.

    Authors: We agree that the χ²/dof comparison is needed for a quantitative assessment. In the revised manuscript we will report the χ²/dof values obtained for the resonant-only hypothesis and for the full model. revision: yes

  3. Referee: [Zc(3900) treatment] The Zc(3900) is introduced as an independent isobar with no interference term beyond the Omnès rescattering. Given that the Zc lies in the same Dalitz region as the ππ/KK̄ FSI, a brief check that its coupling does not induce additional production-FSI entanglement would strengthen the robustness of the extracted parameters.

    Authors: The Zc(3900) enters the Dalitz decomposition as an isobar whose contribution is multiplied by the same coupled-channel Omnès function that encodes the ππ/KK̄ FSI. Because the Omnès function is applied uniformly to the final-state pair, no additional production-FSI entanglement is generated beyond the model definition. We will insert a short clarifying paragraph in the revised text. revision: partial

Circularity Check

0 steps flagged

No significant circularity; Omnès input independent of present fit

full rationale

The amplitude is constructed as (Y(4220) + Y(4320) + non-resonant term) imes coupled-channel Omnès function, with the Omnès taken from prior independent au o3 u and au o KK u data on au o3 u and au o KK u scattering (explicitly stated as energy-independent and fixed). Resonance parameters and non-resonant strength are fitted to BESIII Dalitz distributions; the claim that a purely resonant description fails is a direct outcome of that fit, not a redefinition of the input. No equation equates a fitted quantity to itself by construction, and the Omnès is externally constrained rather than self-cited as a uniqueness theorem.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The analysis rests on several fitted resonance and background parameters plus standard dispersion relations; no new particles are postulated.

free parameters (3)
  • Breit-Wigner masses, widths and couplings for Zc(3900), Y(4220), Y(4320)
    Fitted directly to the measured cross sections and mass distributions.
  • non-resonant production amplitude strength and phase
    Introduced and fitted to account for the shortfall of the resonant-only description.
  • coupled-channel Omnès parameters
    Taken from prior scattering analyses but effectively adjusted within the joint fit.
axioms (2)
  • standard math Unitarity and analyticity of two-body scattering amplitudes
    Foundation of the coupled-channel Omnès representation.
  • domain assumption Isobar decomposition of the three-body Dalitz plot
    Assumes the amplitude factorizes into resonant isobars plus background.

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discussion (0)

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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