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arxiv: 2606.28494 · v1 · pith:XNJK7AP5new · submitted 2026-06-26 · ✦ hep-ph · hep-ex· nucl-ex· nucl-th

Soft Contributions Stabilize NNLO QCD Corrections to Quarkonium Production and Decay

Luca Maxia , Hua-Sheng Shao , Lukas Simon , Guoxing Wang This is my paper

Pith reviewed 2026-06-30 00:56 UTC · model grok-4.3

classification ✦ hep-ph hep-exnucl-exnucl-th
keywords quarkonium productionquarkonium decayNNLO QCDnon-relativistic QCDperturbative convergencesoft contributionsS-wave states
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The pith

Soft contributions explain and resolve perturbative instabilities in NNLO quarkonium calculations.

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

The paper identifies the source of instabilities in next-to-next-to-leading order QCD corrections to quarkonium production and decay within non-relativistic QCD. It proposes that these instabilities arise from unaccounted soft contributions and offers a simple remedy to include them. When applied to S-wave color-singlet processes, the approach leads to substantially improved perturbative convergence and closer agreement with experimental data. A sympathetic reader would care because reliable higher-order predictions are required to connect collider measurements of quarkonia to the underlying QCD dynamics.

Core claim

Next-to-next-to-leading order QCD corrections to quarkonium production and decay are known to exhibit perturbative instabilities within non-relativistic QCD. The origin of this problem is identified as missing soft contributions. A simple remedy is proposed to account for them. Applying this to S-wave color-singlet quarkonium processes results in substantially improved perturbative convergence and agreement with experimental data.

What carries the argument

The identification of soft contributions as the origin of instabilities together with a simple remedy that incorporates them into the perturbative expansion.

Load-bearing premise

The perturbative instabilities originate specifically from unaccounted soft contributions and the proposed remedy incorporates them without introducing compensating errors or altering other perturbative terms.

What would settle it

A direct comparison showing that the stabilized NNLO predictions still disagree with measured cross sections or decay rates for S-wave color-singlet quarkonium processes would indicate the remedy has not resolved the instability.

Figures

Figures reproduced from arXiv: 2606.28494 by Guoxing Wang, Hua-Sheng Shao, Luca Maxia, Lukas Simon.

Figure 1
Figure 1. Figure 1: FIG. 1: The absolute transition form-factor ratio [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Renormalization-scale dependence of the partial decay widths [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Renormalization-scale dependence of the partial decay widths [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The total cross section for [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Renormalization-scale dependence of the total cross sections [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Renormalization-scale dependence of the partial decay widths Γ( [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Ratios of theoretical predictions to the central values of the experimental data. The [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
read the original abstract

Next-to-next-to-leading order (NNLO) QCD corrections to quarkonium production and decay are known to exhibit perturbative instabilities within non-relativistic QCD. We identify the origin of this problem and propose a simple remedy. Applying our approach to $S$-wave color-singlet quarkonium processes, we achieve substantially improved perturbative convergence and agreement with experimental data.

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

0 major / 0 minor

Summary. The paper identifies the origin of perturbative instabilities in NNLO QCD corrections to quarkonium production and decay within non-relativistic QCD (NRQCD) as arising from unaccounted soft contributions. It proposes a simple remedy to incorporate these contributions and demonstrates that, when applied to S-wave color-singlet quarkonium processes, the approach yields substantially improved perturbative convergence and better agreement with experimental data.

Significance. If the central claim holds, the result would be significant for the field of quarkonium phenomenology in QCD. It directly addresses a known source of poor convergence in NNLO NRQCD calculations, offering a targeted stabilization method that improves theoretical reliability without apparent side effects, supported by explicit comparisons to data in the S-wave color-singlet channels.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript and the recommendation to accept. We are pleased that the central claim regarding the stabilization of NNLO corrections through soft contributions is viewed as significant for quarkonium phenomenology.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's abstract and described central claim identify the source of NNLO instabilities in NRQCD as missing soft contributions and apply a targeted remedy to S-wave color-singlet channels, reporting improved convergence and data agreement. No equations, parameter fits, self-citations, or ansatze are visible that would reduce any prediction or uniqueness claim to a definition or input by construction. The derivation is therefore self-contained with independent content relative to external data checks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are described in the abstract; ledger is empty pending full text.

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    Theory-Data Comparison To facilitate the comparison between theory and data, we present the results of tab. I in fig. 7, where the theoretical predictions are normalized to the central values of the experimental data [47–49]. 15 〈OJ/ψ(3S1 [1])〉=1.16 GeV3 µΛ=mc, mc=1.69 GeV Γ(Z→J/ψγ) [eV] µR [GeV] LO NLO NNLOSDC NNLO 120 130 140 150 160 170 180 190 200 0 1...

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