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REVIEW 3 major objections 4 minor 5 cited by

Toponium bound-state effects must be folded into new-physics amplitudes too, or the allowed region for a top-philic pseudoscalar near 2m_t is misjudged.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-03 18:51 UTC pith:7PJNWQWX

load-bearing objection Genuinely new framework for treating toponium effects in BSM threshold searches, but the one number connecting it to the data is assumed rather than derived. the 3 major comments →

arxiv 2512.03220 v2 pith:7PJNWQWX submitted 2025-12-02 hep-ph hep-ex

New physics in toponium's shadow?

Thomas Flacke , Benjamin Fuks , Dongchan Kim , Jinheung Kim , Seung J. Lee , L\'eandre Munoz-Aillaud This is my paper
classification hep-ph hep-ex
keywords toponiumtop-antitop production thresholdpseudoscalar resonanceNRQCDLHC excesstop-philic new physicsmatrix-element reweightingnon-perturbative QCD
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.

The paper argues that the recent ATLAS and CMS excesses in top-antitop production near threshold can be explained partly by Standard Model toponium formation, but remain compatible with an additional top-philic pseudoscalar. The key is that the non-perturbative toponium enhancement must be applied not only to the SM amplitude but also to the BSM amplitude and its interference with the SM. Doing so markedly reshapes the viable region of the pseudoscalar mass-coupling plane, especially for narrow resonances close to twice the top mass. The authors conclude that threshold observables cannot be used to constrain top-philic new physics without a consistent treatment of bound-state effects.

Core claim

The paper’s central claim is that the observed ATLAS and CMS enhancements in t tbar production near threshold are compatible with a top-philic pseudoscalar of mass close to 2m_t, provided the non-perturbative toponium enhancement is applied consistently to the full SM+pseudoscalar amplitude. Concretely, the authors require Δσ = σ_BSM − σ_pQCD to lie within 9.0 ± 1.3k pb for m_ttbar < 400 GeV, where σ_BSM is computed by re-weighting the coherent amplitude with the NRQCD Green’s function. They show that this treatment reshapes the excluded region in the (M_a, c_t) plane near 2m_t, where SM-BSM interference and bound-state formation overlap, and that perturbative-only or SM-only toponium treatm

What carries the argument

The central mechanism is a matrix-element re-weighting by the ratio of the NRQCD S-wave Green’s function to the free Green’s function, applied to the squared coherent SM+pseudoscalar matrix element. A modified colour-singlet projection (Eq. (9)) applies the singlet projection only to the SM block of the colour matrix, since the pseudoscalar already produces a colour-singlet t tbar pair, while preserving the SM-BSM interference terms. This combination embeds Coulombic bound-state enhancement and new-physics interference on the same footing.

Load-bearing premise

The constraint relies on the ATLAS excess of 9.0 ± 1.3 pb being defined relative to the same leading-order perturbative QCD baseline (σ_pQCD) used in this paper; if the experimental baseline already includes higher-order or partial toponium content, Δσ double-counts threshold effects and every contour shifts, and likewise the top-loop coupling κ_t is treated as real although its form factor is complex for M_a > 2m_t.

What would settle it

Compute the ATLAS excess using a next-to-leading-order or next-to-next-to-leading-order perturbative baseline (rather than the paper’s LO σ_pQCD) and re-derive the allowed band; if the excess remains 9.0 ± 1.3 pb with respect to that higher-order baseline, the paper’s central constraint and its exclusion contours change visibly. Alternatively, compare the predicted m_ttbar line shape (peak-dip structure from the pseudoscalar interfering with toponium) against the unfolded ATLAS/CMS differential spectra; a good fit with SM-only toponium would falsify the need for the pseudoscalar component.

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

If this is right

  • Existing LHC constraints that ignore toponium in the BSM amplitude are unreliable in the threshold region; reinterpretation of the data shifts the allowed (M_a, c_t) bands.
  • A pseudoscalar with mass near 2m_t and narrow width can remain viable even when perturbative-only analyses would exclude it, because the threshold enhancement amplifies its colour-singlet contribution.
  • The measured 9.0 ± 1.3 pb excess is mostly (but not fully) accounted for by SM toponium, leaving room for BSM with moderate couplings.
  • Differential observables (spin correlations, m_ttbar line shapes) can discriminate between SM-only toponium and BSM-modified toponium, motivating a combined fit.
  • Future measurements with reduced uncertainties will sharpen the viable region and could eventually rule out or confirm the pseudoscalar interpretation.

Where Pith is reading between the lines

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

  • If the top-loop form factor’s imaginary part is properly taken into account, the sign flip of interference near M_a = 2m_t may be modified; the paper’s real-κ_t treatment is a zero-width-type approximation that could shift the peak-dip structure.
  • The same re-weighting logic should apply to scalars and to s-channel colour-octet resonances, where the colour projection is different; the qualitative conclusion that non-perturbative threshold enhancement amplifies singlet BSM contributions is likely generic.
  • A direct differential fit to the ATLAS/CMS m_ttbar distributions, rather than a single bin count, could separate the SM toponium component from the pseudoscalar component, since the lineshapes differ.
  • The benchmark choice fixing κ_g via the total width ties the gluon coupling to the width; a UV completion with independent κ_g and κ_t could evade or strengthen the derived contours.

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

3 major / 4 minor

Summary. The paper studies top-antitop production near threshold in the presence of a top-philic pseudoscalar state of mass near 2m_t. It constructs an effective model with pseudoscalar couplings to gluons and top quarks, and incorporates non-relativistic QCD toponium effects by re-weighting squared matrix elements with the NRQCD Green's function. The main result is a set of allowed regions in the (M_a, c_t) plane obtained by requiring that the BSM-inclusive threshold cross section minus the authors' LO no-toponium SM prediction reproduces the ATLAS excess of 9.0 ± 1.3 pb below m_ttbar < 400 GeV, together with a high-mass constraint. The paper argues that applying toponium corrections to the full SM+BSM amplitude, rather than only to the SM part, markedly reshapes the viable parameter space, especially for narrow pseudoscalars near the top-antitop threshold.

Significance. If correct, the paper would provide a useful methodological step: it handles the toponium Green's-function resummation and the BSM amplitude in a single coherent framework, and it exposes the dangers of naive perturbative-only or SM-only-toponium treatments. The authors use public tools and provide reproducible model and generator settings, which is a strength. Their qualitative conclusion—that threshold measurements can be consistent with an additional top-philic pseudoscalar, and that the allowed region depends on how bound-state effects are applied to BSM amplitudes—is falsifiable and worth reporting. However, the quantitative contours in Fig. 3 rest on an unvalidated identification of the experimental baseline, and the treatment of the top-loop form factor as real in the on-shell region is another source of concern.

major comments (3)
  1. [§3, Eqs. (10)–(11)] The central constraint equates the ATLAS excess of 9.0 ± 1.3 pb with Δσ = σ_BSM − σ_pQCD, where σ_pQCD is the authors' leading-order, no-toponium, parton-level cross section with m_ttbar < 400 GeV. The ATLAS measurement is defined in a fiducial dilepton phase space and relative to ATLAS's own SM reference, which is not shown to be identical to this LO computation and plausibly includes higher-order QCD corrections and possibly partial toponium content. If the ATLAS baseline differs, the target Δσ is misidentified and every contour in Fig. 3 shifts. The sentence claiming the approach is 'agnostic to phase-space-dependent implementation details' does not address this mismatch. A comparison at the fiducial level using public ATLAS data, or an explicit demonstration that the two baselines are equivalent, is required.
  2. [Eq. (3)] The pseudoscalar form factor A^A_{1/2}(M_a^2/4m_t^2) develops an imaginary part for M_a > 2m_t, which is precisely the mass region where the claimed reshaping occurs. The paper treats κ_t, and hence \tilde κ_g, as real throughout, including in Eq. (2) and the width-fixing procedure. No justification is given for neglecting this imaginary part; it affects the interference phase and the width-to-mass condition, and can therefore change the contours in Fig. 3. The authors should either include the imaginary part or quantify its numerical impact in the presented parameter range.
  3. [§3, Eq. (14)] The high-mass constraint σ_BSM < 1.05 σ_pQCD for m_ttbar > 400 GeV uses the same LO no-toponium baseline. Since the measured high-mass ttbar cross section exceeds LO QCD by a factor well above 1.05, this inequality does not correspond to any actual experimental limit and can spuriously exclude otherwise valid parameter points. The constraint should be reformulated against the real high-mass measurements or against a baseline that reproduces them.
minor comments (4)
  1. [Notation] The generator is referred to as 'MG5_AMC'; the standard name in Ref. [51] is 'MG5_aMC'. Please correct for consistency.
  2. [Fig. 2 (right)] The dashed grey line labeled '6.43 pb' is introduced without an error bar or an explicit definition. State whether this is σ_QCD − σ_pQCD in the m_ttbar < 400 GeV bin and whether it includes any scale/PDF uncertainty.
  3. [Eq. (9)] The colour-matrix replacement is hard to follow. A short explanation of the entries (why the SM block is [16,-2; -2,16] and why the singlet projection replaces it by [2,2; 2,2]) would improve reproducibility.
  4. [Eqs. (5) and (8)] σ_NRQCD is used as an additive term in Eq. (5) and as a functional of the amplitude in Eq. (8). Unify the notation to avoid confusion.

Circularity Check

0 steps flagged

No significant circularity: the allowed-region calculation is an independent simulation confronted with an external ATLAS excess; the baseline-matching assumption is a validity risk, not a definitional reduction.

full rationale

The paper's derivation chain is self-contained in the sense that no parameter is fitted to the 9.0 pb excess. The scanned parameters (M_a, c_t) are free inputs; kappa_g is fixed by a width benchmark (Gamma_a/M_a = 1% or 5%), not by the ATLAS data point. The cross sections sigma_pQCD, sigma_pBSM, sigma_QCD and sigma_BSM are computed from the authors' own MG5_aMC simulations using the Lagrangian of Eq. (1), with the NRQCD Green's function supplied by a public lookup table (refs [5,55,56]) and the reweighting method of refs [16,20,27]. The self-citations are methodological rather than load-bearing: even if the reweighting papers were disregarded, the Green's function is externally provided and the short-distance amplitudes are tree-level Feynman-diagram output. Equation (11) does impose Delta_sigma = sigma_BSM - sigma_pQCD in (9.0 +/- 1.3k) pb, which assumes that the ATLAS excess is defined relative to the authors' LO sigma_pQCD ('Since this quantity effectively corresponds to the difference between the data and the SM perturbative QCD prediction sigma_pQCD'). That is an assumption about the experimental reference prediction, potentially incorrect, but it is not a circular construction: sigma_BSM is not defined in terms of the data, and no fitted value is renamed as a prediction. Any mismatch with the ATLAS baseline would shift the contours in Fig. 3, but that is an external-validity/correctness concern, which the instructions exclude from circularity scoring. The 6.43 pb SM toponium benchmark is likewise a computed output of the public Green's-function machinery, not an adjustable input. Hence no circular step can be exhibited; the only minor caveat is the reliance on the authors' own previous reweighting implementation, which is not load-bearing because it is publicly available and independently checkable.

Axiom & Free-Parameter Ledger

4 free parameters · 6 axioms · 1 invented entities

The quantitative output rests on four scanned/fixed model parameters (M_a, c_t, κ_g set by the width benchmark, Γ_a/M_a = 1% or 5%), the inherited NRQCD reweighting machinery, and the identification of the ATLAS excess with a leading-order-normalized difference. No entity beyond the pseudoscalar is invented; the pseudoscalar is constrained by data rather than fitted to it. The main paper-specific assumptions are the LO-baseline equivalence with the ATLAS excess and treating the top-loop coupling as real above threshold.

free parameters (4)
  • c_t (pseudoscalar–top Yukawa coupling) = scanned over ≈0–1 (log scale in Figure 3)
    Scanned model parameter; the whole analysis maps which values are compatible with the excess.
  • M_a (pseudoscalar mass) = scanned ≈320–400 GeV in Figure 3
    Scanned model parameter, placed near 2m_t in the toponium window; the mass-dependence of the contours is the central output, not a fitted constant.
  • κ_g (short-distance agg coupling) = fixed by Γ_a/M_a = 1% or 5%; positive root chosen
    Determined by hand through the width benchmark, up to a sign; the positive-sign convention sets the SM–BSM interference sign and is not motivated by data.
  • Γ_a/M_a (relative width benchmark) = 1% and 5%
    Chosen benchmark values defining the two scenarios; the 1% case is where the reshaping is most visible.
axioms (6)
  • domain assumption The NRQCD Green's-function ratio G/G0 applied to the full singlet-projected amplitude (Eqs. 4, 7) correctly captures non-perturbative toponium effects for both SM and BSM amplitudes.
    Section 2; inherited reweighting method of refs [16,20,27] now applied to the coherent SM+BSM amplitude. Its validity for the BSM piece is assumed, not derived.
  • domain assumption The pseudoscalar-exchange potential between top quarks is negligible relative to the QCD Coulomb potential.
    Section 2: 'its range is however exponentially suppressed by exp(−M_a r), so the resulting potential is subdominant'. Reasonable for M_a ~ 340–400 GeV but an assumption.
  • domain assumption LO QCD with NNPDF23 LO PDFs is an adequate baseline; higher-order corrections cancel in Δσ.
    Sections 2–3: σ_pQCD is LO. The difference σ_BSM − σ_pQCD cancels the SM LO piece, but NLO/NNLO corrections to the BSM and interference terms are not assessed.
  • ad hoc to paper The ATLAS excess of 9.0 ± 1.3 pb equals the difference between data and a purely perturbative SM prediction (the paper's σ_pQCD).
    Section 3, Eq. (10)–(11): the operational constraint. Paper-specific normalization assuming the ATLAS baseline is perturbative-only; if wrong, double counting shifts all contours.
  • domain assumption The NRQCD validity window m_ttbar ≲ 350 GeV, p* ≲ 50 GeV.
    Section 2: reweighting applied only where NRQCD is expected to hold; the boundary is a smooth cut taken from the literature.
  • ad hoc to paper κ_t is treated as a real effective coupling (Eq. 3).
    Section 2, Eq. (3): the top-loop pseudoscalar form factor is complex for M_a > 2m_t; the paper does not state whether the absorptive part is implemented.
invented entities (1)
  • Gauge-singlet pseudoscalar a (top-philic, mass near 2m_t) independent evidence
    purpose: Candidate BSM explanation for the ttbar threshold excess; couples via a G G̃ and a t iγ5 t (Eq. 1).
    Although a is a model input, the analysis gives it a falsifiable handle: the allowed (M_a, c_t) band in Figure 3 predicts specific contributions to the ttbar threshold spectrum and to the high-mass tail (Eq. 14), testable by LHC run 3 and HL-LHC data. It is constrained by, not fitted to, the 9.0 pb excess.

pith-pipeline@v1.3.0-alltime-deepseek · 11430 in / 25939 out tokens · 223795 ms · 2026-08-03T18:51:11.254497+00:00 · methodology

0 comments
read the original abstract

ATLAS and CMS have recently reported enhancements in the top-antitop production rate near threshold, a region where non-perturbative QCD dynamics associated with toponium formation become relevant. We investigate how this behaviour is modified in the presence of a neutral pseudoscalar that couples to gluons and top quarks, using an effective description that consistently incorporates perturbative Standard Model and new physics contributions, their interference and non-perturbative threshold effects. We show that the combined effect of those ingredients markedly shapes the viable region of the pseudoscalar parameter space, particularly for narrow resonances with masses close to twice the top mass. While Standard Model threshold effects could explain a sizeable part of the measured enhancements, the current data remain compatible with additional contributions from pseudoscalar interactions.

Figures

Figures reproduced from arXiv: 2512.03220 by Benjamin Fuks, Dongchan Kim, Jinheung Kim, L\'eandre Munoz-Aillaud, Seung J. Lee, Thomas Flacke.

Figure 1
Figure 1. Figure 1: Feynman diagram representing the contribution of a pseudoscalar resonance 𝑎 to 𝑡𝑡̄ production in the gluon fusion channel. This amplitude interferes with the SM one and affects both the total rate and the spin-correlation structure. incorporate toponium effects. Section 3 presents the com￾bined impact of BSM and toponium contributions on 𝑡𝑡̄ production near threshold as well as its implications for the exp… view at source ↗
Figure 2
Figure 2. Figure 2: Invariant mass 𝑚𝑡𝑡̄ distribution (left) and total cross-section shifts (right) induced by the presence of the pseudoscalar state in the theory. Left – Predictions for a scenario with 𝑐𝑡 = 0.01 and 𝑀𝑎 = 340 GeV. We show perturbative SM (dashed black) and perturbative BSM (dashed blue) results, together with predictions including toponium effects through NRQCD matrix-element re-weighting (solid black and sol… view at source ↗
Figure 3
Figure 3. Figure 3: Exclusion contours in the (𝑀𝑎 , 𝑐𝑡 ) plane for Γ∕𝑀𝑎 = 1% (left) and 5% (right). The three rows correspond to different theoretical assumptions: the full perturbative SM and BSM contributions supplemented by the non-perturbative corrections (top row), predictions in which the non-perturbative corrections are applied only to the SM part (middle row), and predictions with only perturbative contributions (bott… view at source ↗

discussion (0)

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Forward citations

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