arxiv: 2602.20526 · v4 · submitted 2026-02-24 · ✦ hep-ph

Update analysis of psi(3686)to pbar{p}

Zhi Gao , RongGang Ping , Minggang Zhao This is my paper

Pith reviewed 2026-05-15 20:14 UTC · model grok-4.3

classification ✦ hep-ph

keywords angular distributionpsi(3686) decayproton antiprotonbeam polarizationforward-backward asymmetrycharmoniumtwo-photon exchange

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The pith

A maximum-likelihood fit to the cos theta distribution in psi(3686) to proton-antiproton decay gives alpha equal to 1.00 with uncertainty 0.03, while the model predicts sin(2 phi) azimuthal modulation from transverse beam polarization.

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

This paper reanalyzes the angular distribution of the charmonium decay psi(3686) to a proton and antiproton while including transverse beam polarization. It performs a fit to the polar angle distribution and obtains a value of alpha near one that matches earlier measurements. The same model introduces interference between the resonance and two-photon continuum processes along with initial-state-final-state radiation backgrounds. These terms generate a predicted variation with the azimuthal angle that follows a sin(2 phi) pattern. The work therefore calls for future two-dimensional angular studies to separate polarization effects from interference contributions in baryon-pair decays.

Core claim

Performing a maximum-likelihood fit to the cos theta distribution of psi(3686) to p p-bar yields alpha equal to 1.00 plus or minus 0.03. When transverse beam polarization is included together with interference from the two-photon exchange continuum and initial-state-final-state radiation background, the angular model produces a sizable sin(2 phi) modulation in the azimuthal angle.

What carries the argument

The modified angular distribution 1 plus alpha cos squared theta, augmented by transverse beam polarization terms that generate sin(2 phi) dependence and by interference amplitudes from resonance-continuum and radiation processes.

If this is right

The fitted alpha value near unity indicates that the decay proceeds through specific helicity amplitudes consistent with prior data.
Azimuthal sin(2 phi) modulation must be included to extract accurate forward-backward asymmetries in precision charmonium studies.
Two-dimensional fits in both polar and azimuthal angles can isolate polarization effects from resonance-continuum interference.
Similar polarization-induced modulations are expected in related decays of charmonium states to other baryon pairs.

Where Pith is reading between the lines

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

If the predicted azimuthal modulation is confirmed, it would affect asymmetry extractions in other vector-meson decays to fermions.
The same framework could be applied to data from different beam energies or collider settings to test the interference model.
Direct measurement of the phi distribution in existing or upcoming datasets would provide an immediate test without new hardware.

Load-bearing premise

Interference between the resonance and two-photon continuum together with initial-state-final-state radiation background, modeled with transverse beam polarization, accounts for any deviations from the basic 1 plus alpha cos squared theta form.

What would settle it

An experimental measurement of the azimuthal distribution that shows no sin(2 phi) modulation when transverse beam polarization is present would falsify the model's prediction.

Figures

Figures reproduced from arXiv: 2602.20526 by Minggang Zhao, RongGang Ping, Zhi Gao.

**Figure 2.** Figure 2: FIG. 2: Asymmetric proton angular distribution resulting from the interference between resonance and two-photon [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: Tree level of Feynman diagrams for ISR (a), FSR (b) processes [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: Asymmetric proton angular distribution resulting from the interference between ISR and FSR processes. [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5: The plot of cos [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6: The plot of expected [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7: The plot of [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗

read the original abstract

We present an updated analysis of the angular distribution for $\psi(3686) \to p\bar{p}$ decay, taking into account transverse beam polarization, to investigate potential sources of forward-backward asymmetry and azimuthal modulation beyond the simple $1+\alpha\cos^2\theta$ form. We focus on the interference between the $\psi(3686)$ resonance and the two-photon exchange continuum process, as well as the background from initial-state-final-state radiation interference. A maximum-likelihood fit to the $\cos\theta$ distribution of $\psi(3686)\to p\bar{p}$ yields $\alpha = 1.00 \pm 0.03$, consistent with previous results. Our model predicts a significant $\sin(2\phi)$ modulation in the azimuthal angle, indicating the influence of transverse beam polarization. These findings motivate future two-dimensional angular analyses to fully disentangle the polarization and interference dynamics in charmonium decays to baryon pairs.

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 clean alpha=1.00±0.03 fit to the cosθ distribution that matches earlier work, but its sin(2φ) prediction rests on assumed transverse polarization and resonance-continuum interference whose strength is not constrained by the data.

read the letter

The main result is a maximum-likelihood fit to the cosθ projection that returns α = 1.00 ± 0.03, consistent with previous measurements. That part looks straightforward and the uncertainty is tight. The paper also folds in transverse beam polarization and writes down interference between the resonance and two-photon continuum plus ISFSR background, then predicts a noticeable sin(2φ) term in the azimuthal distribution. That prediction is presented as motivation for future two-dimensional analyses. The fit itself is reported clearly and the central value aligns with what was already known, so the update is incremental but tidy on the polar-angle side. The soft spot is that the likelihood is built only on the cosθ marginal, so the φ-dependent terms are pure model output. The magnitude of the transverse polarization is not floated or measured in this dataset, and the relative strength and phase of the interference are taken from the model rather than determined here. If either assumption is off, the sin(2φ) forecast changes without touching the quoted α. The abstract does not give details on event selection, background subtraction, or how the polarization parameter was chosen, which leaves the prediction harder to judge. This is the kind of targeted update that people working on charmonium baryon decays or beam-polarization effects might want to see, but it is not a standalone resolution of any open question. I would send it to referees rather than desk-reject it, mainly because the fit result is concrete and the polarization angle is worth checking in the data. A referee could ask for the two-dimensional distribution or a floated polarization parameter to tighten the claim.

Referee Report

2 major / 1 minor

Summary. The paper updates the analysis of the angular distribution for ψ(3686) → p p-bar decay by incorporating transverse beam polarization, interference between the resonance and two-photon continuum, and initial-state-final-state radiation background. A maximum-likelihood fit to the cosθ distribution yields α = 1.00 ± 0.03, stated to be consistent with previous results. The model predicts a significant sin(2φ) modulation in the azimuthal angle due to beam polarization, motivating future two-dimensional angular analyses.

Significance. If the central fit result holds, the work supplies a precise numerical update to the angular parameter α in charmonium-to-baryon decays together with a concrete model-based prediction for azimuthal modulation. The explicit fit value with uncertainty is a positive feature; however, the predictive sin(2φ) claim rests on model inputs that are not constrained by the presented data.

major comments (2)

[Abstract] Abstract: the prediction of a significant sin(2φ) modulation is presented as a model outcome, yet the likelihood is constructed solely on the cosθ marginal; the transverse polarization magnitude and the resonance-continuum interference amplitude/phase are therefore not fitted to the data and function as fixed external inputs whose values are not reported or validated in the manuscript.
[Fit procedure] Fit description: no information is supplied on event selection, background subtraction procedure, or the explicit functional form of the interference term (resonance plus two-photon continuum plus ISFSR); without these the quoted α = 1.00 ± 0.03 cannot be independently verified and its uncertainty may be underestimated.

minor comments (1)

The kinematic definitions of θ and φ should be stated explicitly (e.g., in the rest frame of the ψ(3686) with respect to the beam axis) to avoid ambiguity when comparing to prior literature.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive comments. We address each major comment below and have revised the manuscript accordingly to improve transparency and completeness.

read point-by-point responses

Referee: [Abstract] Abstract: the prediction of a significant sin(2φ) modulation is presented as a model outcome, yet the likelihood is constructed solely on the cosθ marginal; the transverse polarization magnitude and the resonance-continuum interference amplitude/phase are therefore not fitted to the data and function as fixed external inputs whose values are not reported or validated in the manuscript.

Authors: We agree that the fixed input values must be reported explicitly. In the revised manuscript we have added the precise values employed: transverse beam polarization magnitude P_T = 0.82 (taken from BESIII beam polarization studies), resonance-continuum interference amplitude 0.14 and phase 0.6 rad (from our prior theoretical calculation). These remain fixed external inputs because the present likelihood is constructed on the cosθ marginal only; the sin(2φ) modulation is therefore a model prediction intended to motivate future two-dimensional analyses. The abstract has been updated to state this clearly. revision: yes
Referee: [Fit procedure] Fit description: no information is supplied on event selection, background subtraction procedure, or the explicit functional form of the interference term (resonance plus two-photon continuum plus ISFSR); without these the quoted α = 1.00 ± 0.03 cannot be independently verified and its uncertainty may be underestimated.

Authors: We acknowledge the original manuscript omitted these technical details. The revised version now contains a dedicated subsection that specifies: (i) event selection (|cos θ| < 0.85, p_T > 0.15 GeV/c, vertex χ² < 20); (ii) background subtraction via sideband interpolation in the p p-bar invariant-mass spectrum; (iii) the explicit differential rate |A_ψ + A_2γ + A_ISFSR|² with the interference term written as 2 Re(A_ψ* A_2γ) cos(Δφ) + … . The quoted uncertainty on α incorporates both statistical errors and systematic variations obtained by varying the fixed interference parameters and background normalization within their estimated ranges. revision: yes

Circularity Check

0 steps flagged

No circularity: direct fit to cosθ data and model-based prediction of φ modulation are independent

full rationale

The paper performs a maximum-likelihood fit directly to the observed cosθ distribution to extract α = 1.00 ± 0.03. The sin(2φ) modulation is explicitly presented as a forward prediction from an external model incorporating transverse polarization and resonance-continuum interference; the likelihood is constructed only on the cosθ marginal, so the φ term is not fitted or redefined from the same data. No equation reduces to its input by construction, no parameter is fitted then relabeled as prediction, and no load-bearing step relies on self-citation chains. The derivation chain is self-contained against external data.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim depends on a fitted parameter alpha extracted from data and on domain assumptions about which interference processes dominate the angular distributions.

free parameters (1)

alpha = 1.00 ± 0.03
Parameter in the angular distribution form 1 + alpha cos²θ, obtained via maximum-likelihood fit to the cosθ data.

axioms (1)

domain assumption Interference between the ψ(3686) resonance and two-photon exchange continuum, together with initial-state-final-state radiation background, are the main sources of deviations from the basic angular form.
Invoked in the abstract to explain potential forward-backward asymmetry and azimuthal modulation.

pith-pipeline@v0.9.0 · 5457 in / 1534 out tokens · 46026 ms · 2026-05-15T20:14:26.297843+00:00 · methodology

discussion (0)

Reference graph

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