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arxiv: 2605.19546 · v1 · pith:4UNITGWSnew · submitted 2026-05-19 · ✦ hep-ph · hep-ex

Top Pair Threshold Revisited

Torbj\"orn Sj\"ostrand , Valery A. Khoze , Christian T. Preuss This is my paper

Pith reviewed 2026-05-20 05:54 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords top quark pair productionthreshold regionnon-relativistic Green's functionttbar cross sectionLHC observationsMonte Carlo event generationbelow-threshold production
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0 comments X

The pith

The non-relativistic Green's function formalism, updated for Monte Carlo use, predicts a below-threshold ttbar cross section of about 6.5 pb that matches LHC observations.

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

The paper revives a theoretical approach first used more than 35 years ago to describe top quark pair production near the energy threshold. It adapts the non-relativistic Green's function method into a consistent form that handles both above-threshold and below-threshold regimes and works with event generators. When practical updates are added for current LHC energies, the calculation produces a below-threshold cross section on the order of 6.5 picobarns. This value lines up with the excess signals reported by the CMS and ATLAS experiments. The resulting code has been added to the Pythia generator to support direct comparisons with data.

Core claim

The non-relativistic Green's function formalism, revived and combined with practical prescriptions for current LHC conditions, unifies the above- and below-threshold behavior of ttbar production and yields a below-threshold cross section of the order of 6.5 pb that is comparable with the CMS and ATLAS numbers.

What carries the argument

The non-relativistic Green's function formalism that unifies above- and below-threshold ttbar production and supports Monte Carlo event generation.

If this is right

  • The formalism supplies a single framework for simulating ttbar production both above and below threshold in Monte Carlo generators.
  • It produces a concrete below-threshold cross section value of order 6.5 pb that can be compared directly with LHC data.
  • The updated implementation is released publicly inside Pythia so experimental analyses can test it against full event samples.
  • The approach avoids treating the threshold region solely through continuum perturbative calculations.

Where Pith is reading between the lines

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

  • Similar Green's function techniques could be explored for threshold production of other heavy particles where non-relativistic effects matter.
  • Future higher-luminosity LHC runs may provide the statistics needed to test whether the formalism continues to hold at greater precision.
  • The method offers a way to reduce reliance on purely perturbative calculations in the threshold region for background estimates.

Load-bearing premise

The non-relativistic Green's function formalism remains accurate for top pair production near threshold under current LHC conditions without dominant higher-order or non-perturbative effects.

What would settle it

A precision measurement of the ttbar cross section in the region just below the pair production threshold that differs substantially from 6.5 pb would challenge the central prediction.

Figures

Figures reproduced from arXiv: 2605.19546 by Christian T. Preuss, Torbj\"orn Sj\"ostrand, Valery A. Khoze.

Figure 1
Figure 1. Figure 1: Threshold βt behaviour of pure phase space, and corrected by the Coulomb factors or replaced by the Green’s functions, for a narrow or wide energy range, respectively. Thus the scale is minimal at threshold, E = 0, where Q2 = mtΓt ≈ (15 GeV)2 . In this case the default is a second-order running αs with αs(m2 Z ) = 0.118, unlike the LO ME choices, but can easily be changed. The resulting threshold behaviour… view at source ↗
Figure 2
Figure 2. Figure 2: Green’s functions with corrected argument [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Decomposition of the colour singlet Green’s function, as described in the text. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of the standard Green’s function expression using Γ [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Decomposition of the colour octet Green’s function, as described in the text. [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Production cross section as a function of (a,b) threshold energy [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Colour singlet fraction of t¯t production. Note that the q¯q-only and gg-octet options give vanishing singlet rates [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Narrow-Green scenario (a) t and ¯t pair mass and (b) individual masses. For E < 0 events the newly selected m′ t1 and m′ t2 are used, also in the “all” sample. 140 150 160 170 180 190 200 mt (GeV) 10 3 10 2 10 1 10 0 10 1 d /d mt (p b/G e V) max(m0 t1 , m0 t2 ), only decrease min(m0 t1 , m0 t2 ), only decrease max(m0 t1 , m0 t2 ), may increase min(m0 t1 , m0 t2 ), may increase 0.0 0.2 0.4 0.6 0.8 1.0 t 0 5… view at source ↗
Figure 9
Figure 9. Figure 9: Below-threshold (E < 0) properties: (a) larger and smaller of the newly selected m′ t1 and m′ t2 masses, and (b) the resulting βt , eq. (2). Comparison of the two scenarios described in the text. of the events are located in the peak region, which more closely agrees, so overall effects are modest. Notably the average βt is only moderately smaller. Cross sections for E < 0 only differ at the per cent level… view at source ↗
Figure 10
Figure 10. Figure 10: (a) mb distribution and (b) colour singlet fraction for the basic hard process, with showers added, or also with multiparton interactions and colour reconnection. Results are for 107 events, lower than in other figures owing to the larger generation time for (almost) complete events than for only the hard process. peaks in [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Two distributions for a 350 GeV e+e − collider with bremsstrahlung included, (a) threshold energy E and (b) invariant t¯t mass mb . In (a) the Coulomb, narrow-Green and both-broad curves overlap for E > 0. 4 Electroweak production studies In addition to the gg → t¯t and q¯q → g ∗ → t¯t QCD production processes, a third possibility for hadron colliders is the q¯q → γ ∗/Z 0 → t¯t electroweak process. Its cr… view at source ↗
Figure 12
Figure 12. Figure 12: The t¯t cross section in e+e − collisions as a function of the collision energy ECM, in (a) without QED initial-state bremsstrahlung and in (b) with it. energy dependence of this cross section, without and with bremsstrahlung. Without it, the cross section enhancement approximately 2 GeV below the t¯t threshold is clearly visible, but this peak almost completely disappears when bremsstrahlung is included,… view at source ↗
Figure 13
Figure 13. Figure 13: Ratio R of the QED t¯t to µ +µ − cross sections in e+e − collisions, as further described in the text. around or below 347 GeV there. But one should note the non-negligible scale dependence, and also ambiguities in the top mass definition, so overall agreement is quite encouraging. 5 Decay studies One of the key tools in the experimental isolation of a signal is the pseudoscalar nature of t¯t states near … view at source ↗
Figure 14
Figure 14. Figure 14: Angular correlations in near-threshold pseudoscalar [PITH_FULL_IMAGE:figures/full_fig_p023_14.png] view at source ↗
read the original abstract

Recently the CMS and ATLAS collaborations have found evidence for an unexpectedly large ttbar cross section in the threshold region, with an excess of the order of 5-10 pb relative to continuum perturbative calculations. A convenient approach to the theoretical study of this region, unifying the above- and below-threshold behaviour, is the non-relativistic Green's function formalism. It was first applied to top production more than 35 years ago, well before the discovery of the top. We therefore revive and dissect the old formalism, and put it back together in a more consistent form, suited for Monte Carlo event generation. Combined with some practical prescriptions, it can be applied to current conditions. As an example, the below-threshold cross section comes out to be of the order of 6.5 pb, i.e. comparable with the CMS and ATLAS numbers. The new code is publicly available in the Pythia event generator so can be used for more detailed comparisons.

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

2 major / 0 minor

Summary. The paper revives the non-relativistic Green's function formalism for ttbar production near threshold (originally applied more than 35 years ago), updates it into a consistent form suitable for Monte Carlo event generation, and combines it with practical prescriptions for current LHC conditions. As an example application, it reports that the below-threshold cross section is of the order of 6.5 pb, comparable to the 5-10 pb excess observed by CMS and ATLAS relative to continuum perturbative calculations. The updated implementation is made publicly available in the Pythia event generator.

Significance. If the updated formalism and unspecified practical prescriptions can be shown to keep higher-order QCD corrections, relativistic effects, and non-perturbative contributions sub-dominant, the work would supply a unified description of above- and below-threshold ttbar production and facilitate detailed comparisons through the public Pythia code. The open availability of the implementation is a concrete strength for reproducibility and community testing.

major comments (2)
  1. [Abstract] Abstract: the headline numerical result that the below-threshold cross section 'comes out to be of the order of 6.5 pb' is presented without derivation details, error estimates, or validation against benchmarks or data; this is load-bearing for the claim of comparability with the CMS/ATLAS excess and cannot be assessed from the given information.
  2. [Abstract] Abstract and formalism update: the result depends on 'some practical prescriptions' for adapting the 1980s Green's function to LHC conditions, yet no explicit matching procedure, relation to data, or estimate of residual higher-order/non-perturbative effects is provided; without this, the 6.5 pb value cannot be shown to be robust rather than an artifact of the adaptation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and for recognizing the potential of the updated non-relativistic Green's function formalism together with the public Pythia implementation. We address the two major comments point by point below. Where the concerns are valid, we indicate the revisions that will be made to strengthen the presentation without altering the core results or scope of the work.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline numerical result that the below-threshold cross section 'comes out to be of the order of 6.5 pb' is presented without derivation details, error estimates, or validation against benchmarks or data; this is load-bearing for the claim of comparability with the CMS/ATLAS excess and cannot be assessed from the given information.

    Authors: The 6.5 pb figure is presented in the abstract as an illustrative example of applying the revived and updated formalism to below-threshold ttbar production at the LHC. The full derivation, including the consistent reformulation of the Green's function and its embedding in a Monte Carlo framework, is provided in the body of the manuscript. We agree that the abstract, as a concise summary, does not contain derivation details, quantitative error estimates, or explicit benchmark comparisons. To improve accessibility, we will revise the abstract to state explicitly that the result is an order-of-magnitude estimate obtained from the updated formalism and to direct readers to the relevant sections describing the calculation and its relation to the original 1980s implementation. Comprehensive error estimates and data validation lie beyond the scope of this formalism-focused paper but can be performed by users of the public code. revision: partial

  2. Referee: [Abstract] Abstract and formalism update: the result depends on 'some practical prescriptions' for adapting the 1980s Green's function to LHC conditions, yet no explicit matching procedure, relation to data, or estimate of residual higher-order/non-perturbative effects is provided; without this, the 6.5 pb value cannot be shown to be robust rather than an artifact of the adaptation.

    Authors: The practical prescriptions consist of the technical adaptations required to render the non-relativistic Green's function suitable for modern Monte Carlo event generation, including a smooth matching onto the perturbative continuum above threshold and incorporation of parton-shower effects. These adaptations are described in the manuscript to enable direct use of the formalism. We acknowledge that greater explicitness would help demonstrate robustness. In the revised manuscript we will expand the relevant section to detail the matching procedure, to recall the power-counting arguments that keep higher-order QCD and relativistic corrections sub-dominant near threshold, and to provide order-of-magnitude estimates for non-perturbative contributions informed by existing quarkonium literature. This will clarify that the 6.5 pb result follows from the updated formalism rather than from arbitrary choices. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation revives external historical formalism

full rationale

The paper revives a non-relativistic Green's function formalism first applied to top production more than 35 years ago (pre-dating the top quark discovery) and combines it with practical prescriptions for Monte Carlo event generation under current LHC conditions. The below-threshold cross section of order 6.5 pb is presented as an example output from this approach, shown to be comparable to CMS/ATLAS observations. No equations or steps in the provided text reduce the central result to a self-definition, a fitted parameter renamed as prediction, or a load-bearing self-citation chain. The historical formalism provides independent external content, and the prescriptions are described as adaptations rather than tuned fits that force the numerical output by construction. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of the revived non-relativistic formalism plus unspecified practical prescriptions; no explicit free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption Non-relativistic Green's function formalism remains valid and sufficient for ttbar threshold region under current collider conditions.
    Invoked as the unifying approach for above- and below-threshold behavior.

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discussion (0)

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Reference graph

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