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arxiv: 1907.01400 · v2 · pith:PDVOEZANnew · submitted 2019-07-02 · ✦ hep-ph

Constraining gluon PDFs with quarkonium production

Melih Arslan Ozcelik This is my paper

Pith reviewed 2026-05-25 11:17 UTC · model grok-4.3

classification ✦ hep-ph
keywords gluon PDFsquarkonium productioneta_c hadroproductionNLO QCDpositivity constraintsparton distribution functionslow-scale PDFsheavy quark production
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The pith

Positivity of the NLO eta_c hadroproduction cross section constrains the x-dependence of gluon PDFs at low scales.

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

The paper explores how requiring the transverse-momentum-integrated cross section for eta_c production in hadron collisions to remain positive when computed at next-to-leading order in the strong coupling can limit the allowed shapes of gluon parton distribution functions at small momentum fractions and low scales. If a trial gluon PDF makes the perturbative result negative, that PDF is excluded because a physical cross section cannot be negative. A sympathetic reader would care because gluon distributions at low scales remain loosely determined by existing data sets, and quarkonium production supplies an independent handle on their x-dependence. The method therefore offers a way to reduce uncertainties in predictions for gluon-initiated processes at modest energies.

Core claim

The positivity of the P_T-integrated eta_c-hadroproduction cross-section computed at NLO in alpha_s can set up constraints on the x-dependence of gluon PDFs at low scales.

What carries the argument

The positivity requirement on the NLO perturbative cross section for eta_c hadroproduction, which filters gluon PDF shapes that would produce a negative result.

If this is right

  • Gluon PDF parametrizations that drive the NLO eta_c cross section negative are disallowed at low scales.
  • The resulting bounds target the small-x region where other constraints are weak.
  • The positivity filter can be incorporated into global PDF determinations to tighten gluon uncertainties.
  • The approach applies specifically to the P_T-integrated cross section rather than differential distributions.

Where Pith is reading between the lines

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

  • The same positivity test could be applied to other hidden-flavor states such as J/psi or chi_c to generate additional constraints.
  • If future data on eta_c production at moderate energies disagree with the NLO-allowed PDFs, the method would need refinement for non-perturbative contributions.
  • This technique may help address discrepancies in small-x gluon densities that affect predictions for forward physics at hadron colliders.

Load-bearing premise

The next-to-leading-order perturbative result stays positive and close enough to the true cross section that its positivity directly translates into reliable PDF constraints without being overturned by higher-order terms or non-perturbative effects.

What would settle it

An explicit NNLO calculation that yields a negative cross section for a gluon PDF shape allowed by the NLO positivity condition, or a global fit showing that PDFs excluded by the condition fit all other data better than those allowed by it.

Figures

Figures reproduced from arXiv: 1907.01400 by Melih Arslan Ozcelik.

Figure 2
Figure 2. Figure 2: K-factor at y = 0 as a function of √ s and with different PDF choices. Default scale choice used µR = µF = 2mc = 3GeV (left). Alternative scale choice used µR = mc = 1.5GeV, µF = 2mc = 3GeV (right). Above, in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
read the original abstract

We explore how the positivity of the P_T-integrated eta_c-hadroproduction cross-section computed at NLO in alpha_s can set up constraints on the x-dependence of gluon PDFs at low scales.

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 explores how the positivity of the P_T-integrated eta_c hadroproduction cross-section, computed at NLO in alpha_s, can be used to derive constraints on the x-dependence of gluon PDFs at low scales.

Significance. If the central assumption holds, the approach would provide a novel positivity-based constraint on low-x gluons complementary to existing fits. However, the result is exploratory and its utility depends on demonstrating that NLO positivity survives higher-order and non-perturbative corrections, which is not quantified in the available text.

major comments (1)
  1. [abstract] The central claim (abstract) requires that the NLO positivity condition directly translates into reliable PDF constraints. This is load-bearing but rests on the untested assumption that NNLO corrections and NRQCD long-distance matrix elements do not overturn the sign or magnitude at low scales where alpha_s is large; the manuscript provides no numerical estimate or robustness test of this assumption.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for the careful reading and constructive comments on our exploratory study. We address the major comment below.

read point-by-point responses

  1. Referee: [abstract] The central claim (abstract) requires that the NLO positivity condition directly translates into reliable PDF constraints. This is load-bearing but rests on the untested assumption that NNLO corrections and NRQCD long-distance matrix elements do not overturn the sign or magnitude at low scales where alpha_s is large; the manuscript provides no numerical estimate or robustness test of this assumption.

    Authors: We agree that the manuscript provides no numerical estimate or robustness test of NNLO corrections or NRQCD matrix-element variations, and that this is a genuine limitation for claiming reliable PDF constraints. The abstract and title frame the work as exploratory (using 'explore how ... can set up constraints'), not as a definitive result. The NLO positivity condition is a necessary (though not necessarily sufficient) requirement that already restricts the allowed x-dependence of low-scale gluon PDFs; we view it as a first-step constraint that can be refined once higher-order results become available. We will revise the abstract and add an explicit caveats paragraph in the conclusions to emphasize the untested higher-order assumption and the indicative nature of the bounds. revision: partial

standing simulated objections not resolved
  • Quantitative numerical estimate or robustness test of NNLO corrections and NRQCD long-distance matrix elements on the sign of the cross section (requires new higher-order calculations beyond the scope of the present work).

Circularity Check

0 steps flagged

No circularity: positivity constraint is an external physical condition applied to PDFs

full rationale

The paper's central claim is that positivity of the NLO P_T-integrated eta_c cross section imposes constraints on gluon PDF x-dependence. This is a one-way application of a perturbative result (computed independently of any specific PDF parametrization) to bound allowed PDF shapes. No step reduces a prediction to a fitted input by construction, no self-citation chain carries the load-bearing premise, and the positivity requirement is not defined in terms of the PDFs it constrains. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no information on free parameters, axioms, or invented entities can be extracted.

pith-pipeline@v0.9.0 · 5533 in / 979 out tokens · 24675 ms · 2026-05-25T11:17:24.674995+00:00 · methodology

discussion (0)

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Reference graph

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