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arxiv: 2606.09768 · v1 · pith:UERDOIAZnew · submitted 2026-06-08 · ✦ hep-ph · hep-ex· hep-lat· nucl-th

Dispersive analysis of the boldsymbol{J/psi to γ π⁰ π⁰} process

Bai-Long Hoid , Igor Danilkin , Anna Testa , Marc Vanderhaeghen This is my paper

Pith reviewed 2026-06-27 15:47 UTC · model grok-4.3

classification ✦ hep-ph hep-exhep-latnucl-th
keywords dispersive analysisJ/psi radiative decaypi pi scatteringMuskhelishvili-Omnes representationphase ambiguityunitarity constraintsfinal-state interactionsgravitational form factors
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The pith

Dispersive analysis selects the negative solution of the BESIII 0++-2++ E1 phase ambiguity as the one compatible with unitarity in J/ψ → γ π⁰ π⁰.

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

The paper carries out a dispersive amplitude analysis of the low-energy π⁰π⁰ system produced in the radiative decay J/ψ → γ π⁰ π⁰. It incorporates the mass-independent BESIII 0++ and 2++ intensities, the total spectrum, and the measured E1 phase difference between these waves. The isoscalar S-wave is built from a coupled-channel Muskhelishvili-Omnès representation that encodes the strong final-state interactions of the f0(500) and f0(980) resonances, while the D-wave uses a single-channel ππ representation after all kinematic constraints on the helicity amplitudes have been imposed. The analysis shows that the negative solution of the BESIII phase ambiguity, once the modulo-π freedom of the production amplitudes is used, is the only one consistent with unitarity; the measured phases are reproduced by the Omnès motion alone without large extra phases. The absolute scale of the amplitudes is fixed by normalizing to the extracted branching fraction, yielding quantities ready for input into future dispersive calculations of two-pion contributions to gravitational form factors.

Core claim

We identify the negative solution of the BESIII 0++-2++ E1 phase ambiguity, after using the modulo-π freedom of production amplitudes, as the phase solution compatible with unitarity constraints, showing that the measured phase information can be accommodated with the Omnès phase motion without requiring large additional phases. By normalizing the BESIII intensities with the extracted branching fraction, we fix the absolute scale of the fitted amplitudes, making them suitable as input for future dispersive studies of two-pion contributions to gravitational form factors.

What carries the argument

Muskhelishvili-Omnès representation (coupled-channel for the S-wave, single-channel for the D-wave) with subtraction polynomials that encode smooth short-distance production of the pseudoscalar-meson pair.

If this is right

  • The fitted amplitudes carry a fixed absolute scale set by the branching fraction.
  • These amplitudes are now suitable as input for dispersive studies of two-pion contributions to gravitational form factors.
  • The measured phase information is fully accommodated by the Omnès phase motion without large additional phases.
  • Left-hand-cut effects remain numerically subleading once the subtraction polynomials are adjusted to data.
  • All kinematic constraints of the helicity amplitudes have been incorporated before transforming to the experimental E1, M2, and E3 multipoles.

Where Pith is reading between the lines

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

  • The same framework could be applied to other radiative vector-meson decays that produce two pseudoscalars, provided similar high-statistics phase information becomes available.
  • Once the absolute amplitudes are fixed, they can be inserted directly into dispersion relations that relate two-pion intermediate states to nucleon or pion gravitational form factors.
  • Resolving the phase ambiguity in this channel reduces one source of systematic uncertainty in global dispersive analyses of ππ scattering and related processes.
  • Future lattice QCD calculations of the same decay could test whether the subtraction polynomials extracted here match the short-distance behavior seen on the lattice.

Load-bearing premise

Smooth short-distance production of a pseudoscalar-meson pair is encoded in subtraction polynomials while left-hand-cut effects are estimated and found to be numerically subleading.

What would settle it

An independent measurement of the absolute 0++-2++ E1 phase difference or of the normalized intensities that contradicts the selected negative solution or the Omnès-only description would falsify the central claim.

read the original abstract

We present a dispersive amplitude analysis of the low-energy $\pi^0\pi^0$ system in the radiative decay $J/\psi\to\gamma\pi^0\pi^0$, using the mass-independent BESIII $0^{++}$ and $2^{++}$ intensities, the total spectrum, and the measured $0^{++}-2^{++}$ $E1$ phase difference. The isoscalar $S$-wave is described by a coupled-channel $\pi\pi/K\bar K$ Muskhelishvili-Omn\`es representation, which implements the strong final-state interactions associated with the $f_0(500)$ and $f_0(980)$. The $D$-wave is treated with a single-channel $\pi\pi$ Muskhelishvili-Omn\`es representation, where we identify all kinematic constraints of helicity amplitudes before transforming them to the experimental $E1$, $M2$, and $E3$ multipoles. Smooth short-distance production of a pseudoscalar-meson pair is encoded in subtraction polynomials, while left-hand-cut effects are estimated and found to be numerically subleading. We identify the negative solution of the BESIII $0^{++}-2^{++}$ $E1$ phase ambiguity, after using the modulo-$\pi$ freedom of production amplitudes, as the phase solution compatible with unitarity constraints, showing that the measured phase information can be accommodated with the Omn\`es phase motion without requiring large additional phases. By normalizing the BESIII intensities with the extracted branching fraction, we fix the absolute scale of the fitted amplitudes, making them suitable as input for future dispersive studies of two-pion contributions to gravitational form factors.

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

1 major / 0 minor

Summary. The manuscript presents a dispersive amplitude analysis of the radiative decay J/ψ → γ π⁰ π⁰ at low energies. It employs Muskhelishvili-Omnès representations for the isoscalar S-wave (coupled ππ/KK) and D-wave (single-channel ππ), incorporating BESIII data on 0++ and 2++ intensities, the total spectrum, and the E1 phase difference. The analysis identifies the negative solution to the BESIII phase ambiguity as the one compatible with unitarity after using modulo-π freedom, with subtraction polynomials encoding short-distance production and left-hand cuts estimated as numerically subleading. The amplitudes are normalized to the branching fraction for future use in gravitational form factor studies.

Significance. If the numerical subdominance of left-hand cuts is confirmed, the result is significant for providing a unitarity-respecting amplitude that resolves the phase ambiguity without large additional phases and supplies absolute-normalized amplitudes for dispersive analyses of two-pion contributions to gravitational form factors. The approach builds on standard techniques in the field and the explicit treatment of kinematic constraints in the D-wave is a positive aspect.

major comments (1)
  1. [Abstract (amplitude construction paragraph)] Abstract (amplitude construction paragraph): The estimation that left-hand-cut effects are numerically subleading lacks a rigorous a-priori bound or systematic variation once the absolute normalization (via branching fraction) and modulo-π freedom are imposed. If these cuts contribute at a level comparable to the subtraction constants or alter the effective production phase, the argument for compatibility of the negative E1 phase solution without additional free phases would require revision. This is central to the main claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of our work and for highlighting the importance of a rigorous treatment of left-hand cuts. We address the single major comment below and propose revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: Abstract (amplitude construction paragraph): The estimation that left-hand-cut effects are numerically subleading lacks a rigorous a-priori bound or systematic variation once the absolute normalization (via branching fraction) and modulo-π freedom are imposed. If these cuts contribute at a level comparable to the subtraction constants or alter the effective production phase, the argument for compatibility of the negative E1 phase solution without additional free phases would require revision. This is central to the main claim.

    Authors: We agree that the current numerical estimation of left-hand-cut (LHC) effects, while based on explicit comparison of dispersive integrals with and without approximate LHC contributions from known singularities, does not constitute a rigorous a-priori bound and has not been systematically varied after fixing the absolute normalization via the branching fraction and exploring the modulo-π freedom. In the revised manuscript we will add a new subsection (in Sec. 3) that performs such variations: we will recompute the LHC estimates for both phase solutions, rescale the subtraction polynomials to the measured branching fraction, and explicitly scan the modulo-π choices. We will report the resulting changes to the effective production phases and confirm that the preference for the negative E1 solution remains stable within the quoted uncertainties. This revision directly addresses the referee’s concern while preserving the central claim. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The amplitude construction relies on established Muskhelishvili-Omnès representations implementing unitarity for final-state interactions (S-wave coupled-channel, D-wave single-channel), with subtraction polynomials fitted to intensities and left-hand cuts estimated numerically as subleading. Phase ambiguity resolution uses the modulo-π freedom of production amplitudes to select the solution compatible with Omnès motion, without requiring large additional phases; this is a choice among discrete options rather than a fitted input renamed as prediction. Absolute scale is fixed externally by the branching fraction. No self-definitional reductions, load-bearing self-citations, or ansatze smuggled via prior author work are present that would make the central claim equivalent to its inputs by construction. The analysis is self-contained against external unitarity constraints and data.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The analysis rests on standard dispersion relations and prior resonance parameters from literature; new elements are the application to this decay and the phase choice. Subtraction polynomials are adjusted to data.

free parameters (1)
  • coefficients of subtraction polynomials
    Encode smooth short-distance production of the pseudoscalar pair; adjusted to match BESIII intensities.
axioms (2)
  • standard math Amplitudes obey analyticity, unitarity, and crossing symmetry
    Foundation for Muskhelishvili-Omnès representations invoked throughout the amplitude construction.
  • domain assumption Left-hand-cut effects are numerically subleading
    Stated after estimation in the amplitude modeling section.

pith-pipeline@v0.9.1-grok · 5867 in / 1465 out tokens · 25215 ms · 2026-06-27T15:47:58.365760+00:00 · methodology

discussion (0)

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Reference graph

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