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The paper shows that low-energy J/ψ–π and J/ψ–K scattering is dominated by soft-gluon exchange, with scattering-length upper bounds of −0.0021 fm and −0.028 fm that rule out bound states in either channel.

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2026-08-03 08:06 UTC pith:AXG6VTXM

load-bearing objection Useful dispersive determination of J/ψπ and J/ψK scattering lengths, but the gluon-dominance claim for the K channel hinges on an unproven polarizability inequality. the 3 major comments →

arxiv 2601.18103 v3 pith:AXG6VTXM submitted 2026-01-26 hep-ph

Low-energy scattering of the J/psi π and J/psi K system

Jiang Yan , Xiong-Hui Cao , Meng-Lin Du , Feng-Kun Guo This is my paper
classification hep-ph
keywords J/psi scatteringscattering lengthchiral perturbation theorychromopolarizabilitydispersion relationsmulti-gluon exchangecoupled channelsquarkonium
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper aims to determine how weakly the charmonium state J/ψ interacts with pions and kaons at low energies. It derives upper bounds on the S-wave scattering lengths — a_{J/ψπ} ≲ −0.0021 fm and a_{J/ψK} ≲ −0.028 fm — where a negative sign signals weak attraction too shallow to bind. The central quantitative finding is that the J/ψ–K interaction is about thirteen times stronger than J/ψ–π, a direct consequence of the strange quark mass breaking chiral symmetry. Comparing two possible interaction mechanisms, the paper concludes that multi-gluon exchange (treated through correlated ππ and K K̄ exchanges) dominates over open-charm coupled-channel rescattering by orders of magnitude.

Core claim

The paper's central claim is that the threshold S-wave scatterings of π and K off J/ψ are both weak and attractive, with upper bounds a_{J/ψπ} ≤ −0.0021 fm and a_{J/ψK} ≤ −0.028 fm, and that the J/ψK channel is moderately enhanced by the strange quark's explicit chiral symmetry breaking. It further claims that this scattering arises predominantly from soft-gluon exchange — implemented as correlated ππ and K K̄ exchanges resummed through dispersion relations — while the alternative mechanism, coupling to open-charm channels such as D D̄* and D* D̄_s, contributes at the 10^{-6} fm level and is negligible. Along the way the paper corrects an earlier claim in the literature: the symmetry-breakin

What carries the argument

The argument rests on three connected pieces. (1) A chiral effective Lagrangian for charmonium–pseudoscalar interactions whose symmetry-breaking c_m term mixes the bare charmonium fields; a rotation diagonalizes the mass matrix and yields the physical J/ψ and ψ' with corrected couplings. (2) The crossed-channel amplitudes J/ψJ/ψ→P P̄, expressed through low-energy constants tied to chromopolarizabilities, with ππ–K K̄ rescattering included via a Muskhelishvili–Omnès dispersion relation. (3) Crossing symmetry, which maps the s=0 crossed amplitude to the near-threshold J/ψP amplitude, giving the scattering length. The quantitative comparison to the coupled-channel mechanism uses previously fitt

Load-bearing premise

The numerical upper bounds rest on the assumption that J/ψ's diagonal chromopolarizability α11 is at least the off-diagonal value 1.18 GeV^{-3} — imported from quark-model wave-function overlap arguments, not derived here — so if α11 is actually smaller, the bounds lose their meaning.

What would settle it

A lattice QCD calculation of the J/ψπ and J/ψK S-wave scattering lengths at physical quark masses: if either |a_{J/ψK}| comes out well below 0.028 fm (e.g., less than 0.01 fm) or the sign is repulsive, the paper's central claim fails. Likewise, an independent determination of α11 below 1.18 GeV^{-3} would falsify the assumed input.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Neither J/ψπ nor J/ψK supports a hadronic bound state: the scattering lengths are far too small in magnitude.
  • The J/ψK scattering length is about thirteen times larger than J/ψπ's, quantifying how the strange-quark mass relaxes chiral suppression.
  • The soft-gluon (multi-gluon) exchange mechanism, not open-charm rescattering, sets the size of J/ψ–light-meson cross sections at low energies.
  • Together with earlier work on J/ψ–nucleon scattering, the result suggests multi-gluon exchange may universally dominate light-hadron scattering off charmonia.
  • Lattice QCD can confront these upper bounds directly at physical pion mass.

Where Pith is reading between the lines

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

  • If the same reasoning carries over to bottomonia, the much smaller chromopolarizabilities of Υ states could flip the balance toward coupled-channel contributions; that is testable by analogous lattice calculations.
  • The paper does not reconcile the abstract's quoted bounds (−0.0037 and −0.049 fm) with Eq. (25) (−0.0021 and −0.028 fm); a reader should settle which numbers are final before using them.
  • The diagonalization correction to the c_m term affects other charmonium dipion transitions, so re-analysis of ψ'→J/ψππ data with the corrected Lagrangian may shift extracted chromopolarizabilities.
  • Because the bounds scale linearly with α11, a future precision measurement of the J/ψ chromopolarizability would immediately tighten or loosen the quoted limits.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper studies S-wave J/ψπ and J/ψK scattering at threshold using dispersion relations. Starting from an effective chiral Lagrangian for charmonia and pseudoscalar mesons, the authors show that the explicit chiral symmetry-breaking c_m term induces ψ–ψ′ mixing and that after diagonalization the physical-basis contact term remains nonzero. They construct the crossed-channel amplitudes J/ψJ/ψ → P\bar{P}, incorporate ππ–K\bar{K} rescattering through a coupled-channel Muskhelishvili–Omnès formalism, and relate the J/ψP threshold amplitudes to these crossed amplitudes via crossing symmetry. The main numerical results are the upper bounds a_{J/ψπ} ≲ −0.0021 fm and a_{J/ψK} ≲ −0.028 fm (Eq. (25)), obtained under the assumption α11 ≥ 1.18 GeV^{-3}. These are compared with coupled-channel open-charm contributions (Eq. (26)), leading to the conclusion that soft-gluon exchange dominates both channels and that J/ψK is moderately enhanced by explicit chiral symmetry breaking.

Significance. If the bounds are correct, they provide a sharp, testable prediction for charmonium–light-meson interactions and would extend the authors' earlier conclusion on J/ψ–nucleon scattering to the pion and kaon channels, with implications for J/ψ suppression in heavy-ion collisions and for future lattice QCD calculations. The paper has genuine methodological strengths: the crossing relation (Eq. (23)) is clearly stated, the use of a coupled-channel Omnès matrix is well motivated, and the algebraic dependence of the scattering length on the chromopolarizability is transparent. However, the numerical results are not self-contained: the central values and the qualitative dominance claim are conditional on external inputs—most importantly α11 ≳ 1.18 GeV^{-3} from a quark-model argument—and the manuscript does not propagate uncertainties or reconcile two different sets of numbers quoted in the abstract and in the body. These issues must be addressed before the quantitative claims can be accepted.

major comments (3)
  1. [Abstract vs. Eq. (25)] The abstract states a_{J/ψπ} ≲ −0.0037 fm and a_{J/ψK} ≲ −0.049 fm, while Eq. (25) in the full text gives −0.0021 fm and −0.028 fm. The discrepancy is a factor of about 1.76 in both channels and is not merely cosmetic: the paper advertises precise upper bounds. The authors must identify which set of values is correct, explain the origin of the factor (e.g., different input for α11 or a different numerical evaluation), and ensure the abstract, body, and summary are internally consistent. This is a load-bearing issue because the central quantitative claim is not unambiguously defined.
  2. [§3.1, Eq. (25)] The numerical bounds scale linearly with the diagonal chromopolarizability α11 through Eqs. (16)–(18), and the paper adopts α11 ≳ 1.18 GeV^{-3} solely from the quark-model wave-function overlap argument in Ref. [26]. This inequality is neither derived nor tested here. The previous lattice-based extraction α11 = (1.6 ± 0.8) GeV^{-3} [37] is compatible with this lower bound, but the older estimates α11 ≈ 0.2 GeV^{-3} [1,2,31] would reduce |a_{J/ψK}| by roughly a factor of six, moving it below the upper edge of the coupled-channel interval in Eq. (26). Because the qualitative conclusion of gluon dominance depends on this input, the authors should either (i) provide an explicit derivation or robust test of the inequality α11 ≥ α12, (ii) present the sensitivity of Eq. (25) to α11 over the full range of published estimates, or (iii) weaken the dominance claim accordingly. No uncertainty propag
  3. [§3.2, Eqs. (25)–(26)] The conclusion that 'both J/ψπ and J/ψK scatterings are predominantly governed by the soft-gluon exchange mechanism' is not robust to the uncertainties in the inputs. For J/ψK, the coupled-channel upper bound is a_{J/ψK}^{CC} ∈ [−0.01, −8.9×10^{-6}] fm; the upper edge, −0.01 fm, is only a factor of ~2.8 smaller in magnitude than the gluon-exchange bound −0.028 fm. Given that the latter uses the extreme lower bound of α11, any reasonable error bar could close this gap. The comparison in the text treats Eqs. (25) and (26) as if they were sharp inequalities, but they are not: Eq. (25) is conditional on an unproven α11 inequality and Eq. (26) carries a large uncertainty from C12/δ12. The authors should state explicitly the conditions under which the dominance conclusion holds and quantify how much α11 would need to change to reverse it.
minor comments (4)
  1. [§3.1, Fig. 3] The caption of Fig. 3 states that α11 = α12 is taken for definiteness, but the numerical bounds in Eq. (25) adopt α11 ≥ 1.18 GeV^{-3}. Please clarify how the figure relates to the final bounds and why this choice is representative.
  2. [§2, Eq. (8)] The notation for the rotated coefficients in Eqs. (9)–(11) is clear, but it would help to spell out that the physical-state labels in Eq. (8) correspond to J/ψ and ψ′ after diagonalization. The footnote about the commutator [M², C_m] is somewhat terse; consider expanding it slightly.
  3. [§3.1, Eq. (15)] The variable s is used both as the Mandelstam variable and as a generic squared mass variable; this is standard but could be stated explicitly. Also, the inputs m_π = 139.57 MeV and m_K = 496 MeV are not isospin-averaged masses; please specify the convention.
  4. [Uncertainty propagation] The paper would be much improved by a short table collecting input values (α12, κ, α11, C12, δ12) with their quoted uncertainties and the resulting ranges for a_{J/ψP}. Currently, the reader cannot see how the final numbers depend on the input errors.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

All new content is a calculation using previously introduced low-energy constants and dispersion inputs; no new particles, forces, or conserved quantities are introduced.

free parameters (4)
  • α11 (J/ψ chromopolarizability) = ≥1.18 GeV^-3 (assumed lower bound; numerical reference value 1.18)
    Controls the overall size of the soft-gluon exchange amplitude; final bounds computed at α11=|α12|.
  • |α12| (off-diagonal chromopolarizability) = 1.18 ± 0.01 ± 0.05 GeV^-3 (fit to ψ'→J/ψππ in Ref. [23])
    Used to set the lower bound on α11 via α11≥α12.
  • κ (gluonic structure parameter) = 0.26 ± 0.01 ± 0.01 (fit in Ref. [23])
    Appears in the relation between LECs and chromopolarizabilities, Eqs. (16)-(18), and influences the amplitude through ~c2.
  • Coupled-channel parameters (C12, δ12, etc.) = from BESIII fits in Ref. [49]
    Determine the open-charm loop contributions to the scattering lengths in Eq. (26).
axioms (5)
  • domain assumption The chiral Lagrangian Eq. (1) correctly describes low-energy charmonium-light-meson interactions in the heavy-quark and chiral expansions.
    Used throughout Sec. 2; no derivation from QCD.
  • domain assumption Crossing symmetry (Eq. 23) connects the J/ψJ/ψ→P anti-P amplitude at s=0 to the J/ψP threshold amplitude.
    Assumes the Omnès solution is reliable at s=0 and that neglected left-hand cuts (Zc(3900) exchange) are unimportant.
  • domain assumption The unitarity relation Eq. (20) with only ππ-K anti-K intermediate states and the Omnès representation Eq. (22) describe the final-state interactions.
    Standard dispersive framework; neglects other inelastic channels and higher partial waves.
  • domain assumption α11 ≥ |α12|, based on the quark-model wave-function overlap argument of Ref. [26].
    Load-bearing for the numerical upper bounds; not proven within this paper.
  • domain assumption The LEC-to-chromopolarizability relations in Eqs. (16)-(18) from Refs. [27-30] are valid.
    Needed to express the amplitude in terms of α's.

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We investigate the low-energy interactions between the charmonium state $J/\psi$ and the light pseudoscalar mesons ($\pi$ and $K$) within the framework of dispersion relations. We demonstrate that the symmetry-breaking terms in the chiral Lagrangian induce mixing between the bare charmonium fields, necessitating a diagonalization procedure to correctly identify the physical $J/\psi$ and $\psi'$ states. Using the resulting diagonalized Lagrangian, we construct the crossed-channel amplitudes for $J/\psi J/\psi \to {\cal P}\bar{\cal P}$ and incorporate the $\pi\pi$ and $K\bar{K}$ rescattering effects through dispersion relations. This framework is used consistently both in the phenomenological extraction of the transition parameters from $\psi' \to J/\psi\pi\pi$ and in the continuation of the crossed amplitudes to the near-threshold $J/\psi{\cal P}~({\cal P}=\pi,K)$ region. As a result, we determine both the scattering lengths and the effective ranges. We obtain the upper-bound estimates $a_{J/\psi\pi}\lesssim -0.0037$~fm and $a_{J/\psi K}\lesssim -0.049$~fm, where the negative sign indicates an attractive interaction without a bound state in our convention. Our results show that the $J/\psi K$ interaction is moderately enhanced relative to the pion channel, driven by explicit chiral symmetry breaking. Furthermore, a quantitative comparison of the coupled-channel mechanism, where $J/\psi\pi$ and $J/\psi K$ couple to open-charm channels, reveals that both $J/\psi\pi$ and $J/\psi K$ scatterings are predominantly governed by the soft-gluon exchange mechanism.

Figures

Figures reproduced from arXiv: 2601.18103 by Feng-Kun Guo, Jiang Yan, Meng-Lin Du, Xiong-Hui Cao.

Figure 1
Figure 1. Figure 1: Unitary relation for the scattering amplitudes of pro [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Real (blue solid) and imaginary (red dashed) parts of the [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Real (blue solid) and imaginary (red dashed) parts of the [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

discussion (0)

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