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arxiv: 2604.09485 · v1 · submitted 2026-04-10 · ✦ hep-ph

Recognition: unknown

Threshold Top-Quark Pair-Production: Cross Sections and Key Uncertainties

Maria Vittoria Garzelli , Giovanni Limatola , Sven-Olaf Moch , Matthias Steinhauser , Oleksandr Zenaiev
Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:50 UTC · model grok-4.3

classification ✦ hep-ph
keywords top quarkpair productionthresholdLHCnon-relativistic QCDcross sectionuncertaintiestoponium
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0 comments X

The pith

Non-relativistic QCD predicts an excess of 4.15 pb in top-quark pair production near threshold at the 13 TeV LHC.

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

The paper computes the top-quark pair invariant-mass distribution close to threshold using the non-relativistic QCD framework and evaluates its theoretical uncertainties from multiple sources. It finds that the integral of this distribution between 340 and 350 GeV reaches 11.67 pb with uncertainties of roughly 12 percent. Subtracting the result from a standard fixed-order generator leaves a 4.15 pb excess that the authors attribute to quasi-bound toponium formation. A sympathetic reader would care because this excess offers a concrete, measurable signature that current LHC experiments could test, potentially revealing threshold dynamics that fixed-order calculations miss.

Core claim

In the non-relativistic QCD framework, top-quark pair production near threshold receives additional contributions from color-singlet and octet Green's functions that describe quasi-bound toponium states. At 13 TeV center-of-mass energy the integral of the invariant-mass distribution from 340 to 350 GeV equals 11.67 pb with asymmetric uncertainties of +1.43 pb and -1.47 pb. Subtracting the POWHEG-BOX prediction yields an excess of 4.15 pb carrying the same uncertainty envelope.

What carries the argument

The non-relativistic QCD framework with color-singlet and octet Green's functions, which models the threshold enhancement from quasi-bound toponium formation beyond fixed-order QCD.

If this is right

  • LHC analyses can directly search for the predicted 4.15 pb excess in the top-pair invariant-mass spectrum near 345 GeV.
  • Uncertainties in the prediction are comparable in size to those in standard fixed-order calculations but arise from different sources including Green's functions.
  • The excess size scales with variations in the top-quark mass and the strong coupling constant.
  • Implications for ATLAS and CMS top-pair measurements near threshold can be quantified using the reported numbers.

Where Pith is reading between the lines

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

  • Confirmation of the excess would open a route to study toponium-like states in hadron collisions rather than only in electron-positron machines.
  • The same Green's function approach could be adapted to predict threshold enhancements in other heavy-quark systems such as bottom-quark pairs.
  • Improved experimental resolution in the invariant-mass spectrum would allow separation of the threshold peak from the smooth continuum background.
  • Reducing the uncertainty on the top-quark mass would shrink the dominant theoretical error and sharpen the predicted excess.

Load-bearing premise

The non-relativistic QCD framework together with the modeling of color-singlet and octet Green's functions correctly captures the formation of quasi-bound toponium near threshold.

What would settle it

A high-precision measurement of the top-quark pair invariant-mass distribution at the LHC that finds the 340-350 GeV integral outside the reported 11.67 +1.43/-1.47 pb range or shows no excess above the POWHEG-BOX result.

Figures

Figures reproduced from arXiv: 2604.09485 by Giovanni Limatola, Maria Vittoria Garzelli, Matthias Steinhauser, Oleksandr Zenaiev, Sven-Olaf Moch.

Figure 1
Figure 1. Figure 1: FIG. 1: Cross section in the [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: , this behaviour remains essentially unchanged when varying the hard scale µR,0 = µF,0 = mt by overall multiplicative factors as demonstrated in [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Cross section in the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Left panel: NRQCD predictions for [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Cross section in the [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Left panel: predictions for [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Cross section in the [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Left panel: predictions for [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Cross section in the [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Left panel: predictions for [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Left panel: NRQCD NLO predictions for [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Predictions for [PITH_FULL_IMAGE:figures/full_fig_p017_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: NLO NRQCD (light-blue and pink bands) predictions for [PITH_FULL_IMAGE:figures/full_fig_p018_14.png] view at source ↗
read the original abstract

We study theoretical uncertainties in predicting top-quark pair-production near threshold at the LHC using the non-relativistic QCD framework. We include variations in the top-quark mass and width, the strong coupling $\alpha_s$, renormalization and factorization scales, and parton distribution functions, as well as uncertainties from the color-singlet and octet Green's functions that describe quasi-bound toponium formation. These uncertainties are compared with those from standard fixed-order QCD predictions, and implications for ATLAS and CMS analyses are discussed. For the LHC at 13 TeV center-of-mass energy, the integral of the top-quark pair invariant-mass distribution from 340 to 350 GeV is 11.67 pb with ${}^{+1.43}_{-1.47}$ pb uncertainty. The corresponding excess after subtracting the POWHEG-BOX result is 4.15 pb with the same uncertainties.

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 / 1 minor

Summary. The manuscript studies theoretical uncertainties in top-quark pair production near threshold at the LHC within the non-relativistic QCD (NRQCD) framework. It incorporates variations of the top-quark mass and width, α_s, renormalization and factorization scales, PDFs, and uncertainties arising from color-singlet and octet Green's functions that model quasi-bound toponium formation. The central results are the integrated cross section of 11.67 pb (+1.43/-1.47 pb) over the 340–350 GeV invariant-mass window at 13 TeV and the 4.15 pb excess obtained after subtracting the POWHEG-BOX prediction; implications for ATLAS and CMS analyses are discussed.

Significance. If the Green's-function uncertainty procedure is shown to be robust, the work would provide a concrete, numerically explicit estimate of threshold enhancements that could inform LHC measurements and help quantify the difference between NRQCD and standard fixed-order/MC tools. The explicit comparison to POWHEG-BOX and the inclusion of multiple standard uncertainty sources constitute a useful benchmark for the community.

major comments (1)
  1. [Abstract] Abstract: the quoted uncertainty band of +1.43/-1.47 pb is stated to arise in part from variations of the color-singlet and octet Green's functions, yet the manuscript provides no explicit description of the variation procedure (ranges, correlation assumptions, or independent treatment of binding potential and width smearing). Without this, it is not possible to verify that the band exhausts plausible non-perturbative or higher-order relativistic corrections to the threshold Green's function, which directly affects the reliability of both the 11.67 pb central value and the 4.15 pb excess.
minor comments (1)
  1. [Abstract] The abstract refers to implications for ATLAS and CMS but does not cite specific experimental papers or analyses that have already examined the threshold region.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the constructive comment on the need for greater transparency in the Green's function uncertainty procedure. We address the point below and will revise the manuscript to include the requested details.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the quoted uncertainty band of +1.43/-1.47 pb is stated to arise in part from variations of the color-singlet and octet Green's functions, yet the manuscript provides no explicit description of the variation procedure (ranges, correlation assumptions, or independent treatment of binding potential and width smearing). Without this, it is not possible to verify that the band exhausts plausible non-perturbative or higher-order relativistic corrections to the threshold Green's function, which directly affects the reliability of both the 11.67 pb central value and the 4.15 pb excess.

    Authors: We agree that the current manuscript does not provide a sufficiently explicit account of the Green's function variation procedure. In the revised version we will insert a dedicated paragraph (likely in Section 3 or a new subsection of the results) that specifies: (i) the numerical ranges adopted for the binding-potential parameters in both singlet and octet channels, (ii) the independent smearing applied to the top-quark width, (iii) the correlation assumptions used when combining singlet and octet contributions, and (iv) the quadrature or envelope prescription employed to obtain the final asymmetric uncertainty. This addition will allow readers to reproduce and assess the robustness of the quoted band and the 4.15 pb excess relative to POWHEG-BOX. revision: yes

Circularity Check

0 steps flagged

No circularity in NRQCD threshold cross-section computation

full rationale

The paper computes the near-threshold top-pair invariant-mass integral directly within the NRQCD framework by evaluating the Green's functions with explicit variations of input parameters (top mass, width, α_s, scales, PDFs) and separate uncertainty bands from color-singlet/octet Green's functions. The quoted 11.67 pb central value and ±1.43/1.47 pb band are outputs of this forward calculation, not quantities defined by or fitted to the uncertainty parameters themselves. The excess relative to POWHEG-BOX is an external subtraction, not an internal redefinition. No equation reduces the reported result to its own inputs by construction, no self-citation supplies a load-bearing uniqueness theorem, and no ansatz is smuggled via prior work. The derivation therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central numerical claims rest on the applicability of non-relativistic QCD near threshold and on standard QCD inputs whose central values are chosen by hand or taken from prior fits; no new entities are postulated.

free parameters (2)
  • renormalization and factorization scales
    Central values chosen by hand and then varied to estimate uncertainty; directly affect the quoted cross section.
  • top-quark mass and width
    Input parameters varied around nominal values; the integral result depends on the chosen central mass.
axioms (1)
  • domain assumption Non-relativistic QCD framework is valid for describing top-quark pair production near threshold
    Invoked to justify use of color-singlet and octet Green's functions for quasi-bound toponium.

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