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REVIEW 1 major objections 4 minor 33 references

Near-threshold top-pair excesses at the LHC are mostly ordinary higher-order QCD, not a free-standing toponium signal.

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2026-07-13 02:17 UTC pith:Y3KKOGSM

load-bearing objection Public NLO+PS generators plus clean ATLAS-bin numbers that settle the size of threshold enhancement and the loosely defined toponium piece. the 1 major comments →

arxiv 2607.09539 v1 pith:Y3KKOGSM submitted 2026-07-10 hep-ph

Top-Antitop Production and Decay at Threshold at the LHC in QCD Perturbation Theory

Paolo Nason , Giovanni Pelliccioli , Emanuele Re , Luca Rottoli This is my paper
classification hep-ph
keywords top-antitop productionthreshold resummationCoulomb correctionstoponiumNLO+PS generatorsfinite top widthLHC phenomenology
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

When a top and antitop are produced with mass just above twice the top mass, Coulomb-like soft-gluon exchanges generate large corrections that can be summed to all orders. The paper builds three public NLO event generators that include those corrections and asks how large they really are once standard fixed-order QCD is already accounted for, how much of them can be labelled “toponium,” and whether the top’s finite lifetime matters. In the narrow mass window used by ATLAS the extra enhancement over ordinary NLO is only a few picobarns, the loosely defined bound-state piece is smaller still, and truncating the series at third order already captures nearly everything. Finite-width effects stay modest once the experimental resolution is coarser than the top width. The generators therefore give experiments a clean way to re-interpret the recent excess claims without double-counting or over-attributing the signal to a quasi-bound state.

Core claim

In the ATLAS threshold bin the full resummed Coulomb enhancement over a baseline NLO calculation is of order four picobarns; the contribution that can be ascribed to would-be toponium bound states is only a few picobarns; and the first three orders of the expansion already contain essentially the whole effect. Finite-width corrections remain small for any mass resolution much larger than the top width.

What carries the argument

Three NLO+PS generators (thr1, thr2, bb4l) that multiply the Born matrix element by the all-order Sommerfeld/Coulomb factor (including the discrete bound-state poles) while subtracting the pieces already present at NLO, with an approximate but inclusively consistent treatment of off-shell top virtualities.

Load-bearing premise

The Monte-Carlo treatment of finite-width effects uses a simplified recipe that matches the known inclusive formula after integration over top virtualities, but does not implement the fully differential off-shell formula derived in the appendix.

What would settle it

A high-resolution measurement of the top-pair invariant-mass spectrum below the nominal 2mt threshold (or a future e+e- threshold scan) that shows a shape or size incompatible with the thr2/bb4l predictions once the approximate off-shell recipe is replaced by the exact resolvent formula of Appendix A.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 4 minor

Summary. The paper constructs three public NLO+PS Monte Carlo generators (thr1, thr2, bb4l) that incorporate all-order Coulomb-enhanced threshold corrections (Sommerfeld factor plus bound-state poles) for ttbar production and decay near the 2mt threshold at the LHC. Using these tools the authors quantify, for the ATLAS bin (mtt < 350 GeV, p* < 50 GeV) and for coarser mtt cuts, the size of the enhancement beyond ordinary NLO/NNLO, the loosely defined bound-state contribution, and the residual impact of finite top width. They conclude that O(αs^{3}) already captures the bulk of the effect (~4 pb over baseline NLO), that the bound-state piece is a few pb, and that finite-width shifts remain at the 1–2 pb level once experimental resolution is coarser than Γt.

Significance. The work supplies concrete, publicly available generators that allow experimental analyses to include threshold resummation without double-counting NLO pieces and without treating toponium as an extra free-floating resonance. The order-by-order tables, the three-generator cross-check, the semi-analytic phase-space test (Fig. 7), and the comparison with an independent NLO-NRQCD calculation constitute a solid, falsifiable clarification of the ATLAS/CMS excess. The public codes and the explicit separation of double-top / single-top / no-top samples are particularly valuable for future LHC studies.

major comments (1)
  1. [Appendix A, Eq. (A.19)] Appendix A derives the fully differential resolvent formula (A.19) at fixed top and antitop virtualities, yet the thr2 and bb4l generators implement only an approximate recipe that recovers the inclusive Fadin–Khoze spectral density after integration over virtualities. While the authors argue (and the numerical checks support) that this is adequate for LHC-resolution observables, a short quantitative estimate of the residual error on the double-top sample below the nominal threshold would strengthen the claim that the approximation does not affect the central LHC conclusions.
minor comments (4)
  1. [Abstract / §1] In the abstract and introduction the phrase “enhanced t tbar production near threshold in the pseudoscalar channel” is repeated; a single, precise statement of the experimental claim would improve readability.
  2. [Table 3, §5] Table 3 shows a large single-top contamination in the bb4l NLO sample; a brief remark on the jet-radius dependence of the dt/st classification would help users of the generator.
  3. [§2.2] The regularisation of the δ-function contribution (Eq. 2.7) and the polynomial P(v) used for the (αs/v)^{4} term are technical but essential; a short sentence confirming numerical stability under variation of Ecut and η would be useful.
  4. A few typographical slips remain (“as as a”, “to toponium”, missing spaces around equations). A final proof-reading pass is recommended.

Circularity Check

0 steps flagged

No significant circularity: threshold resummation follows standard Fadin–Khoze NRQCD; generators implement known formulae without fitting free parameters to the ATLAS/CMS excess.

full rationale

The paper’s central claims (size of Coulomb-enhanced corrections beyond NLO/NNLO, size of the loosely defined bound-state piece, and smallness of finite-width effects for LHC-resolution bins) are obtained by implementing the textbook non-relativistic spectral density of Fadin–Khoze (eqs. 2.1–2.6, A.27–A.33) inside three independent NLO+PS generators. No free parameters are fitted to the experimental excess; the only free choices are conventional scale factors that are varied and tabulated. Self-citations to the authors’ earlier NRR paper supply intermediate formulae that are re-derived or extended here (higher-order terms, finite-width recipe of Appendix A). The approximate finite-width mapping (A.24) is acknowledged as incomplete relative to the fully differential resolvent (A.19), but that incompleteness is a technical limitation, not a circular reduction of a prediction to an input. External comparison with an independent NLO-NRQCD calculation (ref. [18]) further anchors the results. Consequently the derivation chain is self-contained against external benchmarks and exhibits no circular step that forces the quoted cross-section numbers by construction.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

The calculation inherits standard QCD, the Coulomb potential, and the classic Fadin–Khoze spectral density. Free choices are limited to technical regularisation parameters, the scale prescription for αs in the Coulomb factor, colour-channel fractions, and the approximate finite-width recipe. No new dynamical entities are postulated.

free parameters (4)
  • E_cut (delta-function regularisation) = 1 GeV (central)
    Width of the polynomial approximation to δ(E) used for bound-state terms in thr1; varied by a factor of two around 1 GeV to check stability.
  • Coulomb αs scale factor = central = 1
    Heuristic scale √(m √(E²+Γt²)) multiplied by a user factor; varied by ½ and 2 in tables. Not fitted to data.
  • Colour singlet/octet fractions in bb4l = 2/7, 5/7
    Fixed 2/7 and 5/7 ansatz for Born colour decomposition when full colour information is not re-projected.
  • Top virtuality window for dt/st/nt classification = 15 GeV
    ±15 GeV cut used to separate double-top, single-top and no-top samples; analysis choice, not a fit.
axioms (4)
  • domain assumption Non-relativistic Coulomb resummation (Sommerfeld factor + bound-state poles) correctly captures the leading (αs/v)^n threshold series for colour-singlet and colour-octet channels.
    Taken from Fadin–Khoze and used throughout §§2–3 and Appendix A.
  • ad hoc to paper After integration over top and antitop virtualities the approximate MC recipe reproduces the inclusive finite-width spectral density of refs. [3,4].
    Stated in Appendix A; full differential formula (A.19) is derived but not implemented.
  • domain assumption Landau–Yang suppression of the spin-triplet gg→tt amplitude near threshold remains valid for the off-shell kinematics used here.
    Used to explain the dominance of the spin-singlet component (Introduction and §2.1).
  • domain assumption Standard POWHEG NLO matching and Les-Houches shower interface remain valid after the Born reweighting by the threshold factor.
    Underlying framework of all three generators.

pith-pipeline@v1.1.0-grok45 · 35115 in / 2982 out tokens · 36531 ms · 2026-07-13T02:17:00.308671+00:00 · methodology

0 comments
read the original abstract

In this work we consider the production of a top-antitop pair at the LHC when the mass of the pair is relatively near to the nominal threshold, that is to say to twice the top pole mass. In this regime, enhanced perturbative corrections arise that can be computed to all orders in perturbation theory. We present three generators of the NLO+PS kind (Next-to-Leading-Order that can be interfaced to parton showers) that include these threshold enhanced effects. Using these generators we address the following questions: what is the size of enhanced non-relativistic effects that are not already present in the well known NLO and NNLO perturbative results; what is the size of the contribution from these effects that can be loosely attributed to toponium production; and to what extent the finite width of the top quark affects threshold enhanced corrections. Our generators are relevant for the recent observation of enhanced $t{\bar t}$ production near threshold in the pseudoscalar channel by the ATLAS and CMS collaborations.

discussion (0)

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Reference graph

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