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arxiv: 2509.03596 · v2 · submitted 2025-09-03 · ✦ hep-ph · hep-ex

Prospects for toponium formation at the LHC in the single-lepton mode

Benjamin Fuks , Kaoru Hagiwara , Kai Ma , L\'eandre Munoz-Aillaud , Ya-Juan Zheng This is my paper

Pith reviewed 2026-05-18 18:54 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords toponiumLHCsingle-leptonnon-relativistic QCDtop quarkbound stateRun 2
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0 comments X

The pith

Toponium formation at the LHC can yield a statistically significant excess in single-lepton events using Run 2 data.

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

The paper examines how a bound state of top and antitop quarks, known as toponium, might be detected in events where one top decays to a lepton at the Large Hadron Collider. It employs a framework that includes non-perturbative QCD effects by using the Green's function from the non-relativistic QCD Hamiltonian and re-weighting hard-scattering events in Monte Carlo simulations. This setup shows that such an excess could already show up as statistically significant in the data collected during Run 2. The work also points to specific observables that can help distinguish the signal and positions the single-lepton mode as a viable alternative or complement to other search strategies for toponium.

Core claim

By incorporating the Green's function of the non-relativistic QCD Hamiltonian and re-weighting the hard-scattering matrix elements, we demonstrate that a statistically significant excess from toponium formation could already be accessible in Run 2 data in the single-leptonic final state at the LHC. Our results also highlight observables that provide handles for signal characterisation and establish the single-leptonic channel as a competitive and complementary avenue for the ongoing exploration of toponium signatures at colliders.

What carries the argument

The Green's function of the non-relativistic QCD Hamiltonian combined with a re-weighting procedure for hard-scattering matrix elements, which incorporates non-perturbative effects into Monte Carlo simulations of toponium formation.

If this is right

  • A statistically significant excess from toponium formation could already be accessible in Run 2 data.
  • Observables exist that provide handles for signal characterisation.
  • The single-leptonic channel serves as a competitive and complementary probe for toponium signatures at colliders.

Where Pith is reading between the lines

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

  • The single-lepton results could be combined with searches in other final states to strengthen the overall case for toponium.
  • Confirmation of the excess would test the non-relativistic treatment of top-quark pairs near production threshold in a new channel.
  • The framework offers a template for applying similar non-perturbative modeling to near-threshold phenomena in other heavy-particle processes.

Load-bearing premise

The Green's function of the non-relativistic QCD Hamiltonian together with the re-weighting procedure correctly captures the non-perturbative formation dynamics in the single-lepton final state.

What would settle it

A search in the LHC Run 2 single-lepton dataset that finds no excess in the invariant mass or other kinematic distributions predicted by the non-relativistic framework would show the accessibility claim does not hold.

Figures

Figures reproduced from arXiv: 2509.03596 by Benjamin Fuks, Kai Ma, Kaoru Hagiwara, L\'eandre Munoz-Aillaud, Ya-Juan Zheng.

Figure 1
Figure 1. Figure 1: Differential cross section for toponium (teal) and conventional top-antitop (orange) production in proton-proton collisions at √ 𝑠 = 13 TeV in the single-leptonic channel, shown as a function of the minimum angular separation between the lepton and the two leading light jets. The predictions include a fiducial selection requiring exactly one lepton, two light jets, two 𝑏-jets and 𝐸 miss 𝑇 > 30 GeV. In addi… view at source ↗
read the original abstract

We investigate the formation of toponium in the single-leptonic final state at the LHC. Our study builds on our recently proposed framework that incorporates the associated non-perturbative effects into Monte Carlo simulations through the Green's function of the non-relativistic QCD Hamiltonian and the re-weighting of hard-scattering matrix elements. This allows us to perform a phenomenological analysis that demonstrates that a statistically significant excess from toponium formation could already be accessible in Run~2 data. Moreover, our results highlight observables that provide handles for signal characterisation and establish the single-leptonic channel as a competitive and complementary avenue for the ongoing exploration of toponium signatures at colliders.

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 / 2 minor

Summary. The manuscript presents a Monte Carlo phenomenological study of toponium formation in the single-leptonic final state at the LHC. It builds on a recently proposed framework that incorporates non-perturbative effects through the Green's function of the non-relativistic QCD Hamiltonian combined with re-weighting of hard-scattering matrix elements. The central claim is that this approach reveals a statistically significant excess over Standard Model backgrounds that could already be accessible in existing Run 2 data, while also identifying observables useful for signal characterization and positioning the single-lepton channel as competitive and complementary for toponium searches.

Significance. If the modeling holds, the result would be significant because it suggests toponium signatures may be detectable in a previously under-explored final state using existing data, thereby broadening experimental strategies beyond dilepton or other channels. The integration of NRQCD Green's functions with re-weighting to capture non-perturbative formation dynamics represents a methodological advance for such studies, provided the procedure's robustness is established.

major comments (2)
  1. [Abstract and framework description] Abstract and framework description: The headline claim that a statistically significant excess is accessible in Run 2 data depends on the re-weighting procedure correctly incorporating non-perturbative formation dynamics into single-lepton kinematics (lepton pT, MET, b-jet distributions) without inflating the excess relative to SM ttbar backgrounds; however, no quantitative validation, error budget, or sensitivity study to variations in the non-perturbative modeling is presented.
  2. [Phenomenological analysis section] Phenomenological analysis section: The predicted excess relies on the framework introduced in prior work by the same collaboration, yet no independent cross-checks against data, alternative non-perturbative models, or explicit treatment of interference with continuum ttbar under the applied lepton cuts are shown, leaving the size of the excess tied to choices in that earlier work.
minor comments (2)
  1. The manuscript would benefit from explicit statements of the assumed color-singlet dominance and any neglected interference terms in the re-weighting step.
  2. Figure captions and legends should more clearly distinguish the toponium signal contribution from the SM background after all selection cuts.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We respond point by point to the major comments below, indicating where we will revise the text to strengthen the presentation of our results and the robustness of the framework.

read point-by-point responses

  1. Referee: [Abstract and framework description] Abstract and framework description: The headline claim that a statistically significant excess is accessible in Run 2 data depends on the re-weighting procedure correctly incorporating non-perturbative formation dynamics into single-lepton kinematics (lepton pT, MET, b-jet distributions) without inflating the excess relative to SM ttbar backgrounds; however, no quantitative validation, error budget, or sensitivity study to variations in the non-perturbative modeling is presented.

    Authors: We agree that an explicit sensitivity study and error budget for the single-lepton channel would improve the manuscript. The re-weighting procedure and its validation against perturbative limits were presented in our prior work that introduced the framework. In the revised version we will add a dedicated paragraph (or short appendix) showing the effect of varying the NRQCD parameters on the predicted excess significance and on the lepton pT, MET and b-jet distributions, together with a simple uncertainty estimate derived from those variations. revision: yes

  2. Referee: [Phenomenological analysis section] Phenomenological analysis section: The predicted excess relies on the framework introduced in prior work by the same collaboration, yet no independent cross-checks against data, alternative non-perturbative models, or explicit treatment of interference with continuum ttbar under the applied lepton cuts are shown, leaving the size of the excess tied to choices in that earlier work.

    Authors: Direct cross-checks against data are not possible because toponium has not yet been observed. The framework was validated in the preceding publication through comparisons with fixed-order perturbative calculations. We will revise the phenomenological analysis section to include an explicit discussion of interference between the resonant toponium contribution and the continuum ttbar background under the applied lepton and jet cuts. We will also add a short comparison to an alternative threshold-enhancement model to illustrate the dependence on non-perturbative modeling assumptions. revision: partial

Circularity Check

1 steps flagged

Central non-perturbative framework for excess prediction rests on self-citation to authors' prior work without independent benchmarks shown here

specific steps
  1. self citation load bearing [Abstract]
    "Our study builds on our recently proposed framework that incorporates the associated non-perturbative effects into Monte Carlo simulations through the Green's function of the non-relativistic QCD Hamiltonian and the re-weighting of hard-scattering matrix elements. This allows us to perform a phenomenological analysis that demonstrates that a statistically significant excess from toponium formation could already be accessible in Run~2 data."

    The statistically significant excess is generated by feeding the NRQCD Green's function and re-weighting procedure into the single-lepton analysis. Because the procedure is taken from the authors' own recent prior work and no independent external benchmark, parameter-free derivation, or alternative non-perturbative modeling is supplied in the present paper, the size of the predicted excess is fixed by the modeling decisions made in that self-citation.

full rationale

The paper's headline claim of a statistically significant toponium excess in single-lepton Run 2 data is obtained by applying the Green's function of the NRQCD Hamiltonian plus re-weighting of hard matrix elements to Monte Carlo simulations. This framework is explicitly introduced as 'our recently proposed framework' in the abstract, with no parameter-free derivation, external cross-check, or alternative modeling presented in the current manuscript. The re-weighting step directly controls the size and shape of the predicted excess above SM backgrounds after lepton, MET and b-jet selections; because the procedure originates in the authors' own prior work and is imported without new validation against data or independent non-perturbative calculations, the excess prediction reduces to the modeling choices made in that earlier paper. This matches the self-citation load-bearing pattern and raises the circularity score to 6 while leaving room for the underlying perturbative matrix elements to retain independent content.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the NRQCD non-relativistic approximation and the reweighting procedure introduced in the authors' prior work; no explicit free parameters or new entities are named in the abstract.

axioms (1)
  • domain assumption Non-relativistic QCD Hamiltonian Green's function accurately encodes toponium formation dynamics near threshold
    Invoked to justify the re-weighting of hard-scattering matrix elements (abstract description of framework)

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discussion (0)

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Forward citations

Cited by 5 Pith papers

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  1. Observation of a cross-section enhancement near the $t\bar{t}$ production threshold in $\sqrt{s}=13$ TeV $pp$ collisions with the ATLAS detector

    hep-ex 2026-01 unverdicted novelty 8.0

    ATLAS reports an 8+ sigma excess in ttbar production near threshold, consistent with NRQCD quasi-bound states and measuring 9.3 pb.

  2. Observation of a cross-section enhancement near the $t\bar{t}$ production threshold in $\sqrt{s}=13$ TeV $pp$ collisions with the ATLAS detector

    hep-ex 2026-01 conditional novelty 7.0

    ATLAS observes an excess over 8 sigma in ttbar production near threshold, consistent with NRQCD color-singlet S-wave quasi-bound states, with measured cross-section 9.3^{+1.4}_{-1.3} pb.

  3. Phenomenology of Hypothetical Single-Top Hadronic States

    hep-ph 2026-05 unverdicted novelty 5.0

    QCD sum rule calculations produce ground-state masses for single-top baryons like Lambda_t and mesons like T_t b-bar, with several central values slightly below constituent quark mass sums suggesting possible weak bin...

  4. Masses of Purely Top-Quark Bound States: Toponium and the Triply-Top Baryon

    hep-ph 2025-11 unverdicted novelty 5.0

    QCD sum-rule calculations give negative binding energies for toponium states consistent with near-threshold experimental signals and a central mass for the triply-top baryon slightly above three times the top-quark mass.

  5. Top Pair Threshold Revisited

    hep-ph 2026-05 unverdicted novelty 4.0

    Updated non-relativistic Green's function formalism for ttbar threshold production gives a below-threshold cross section of order 6.5 pb matching recent LHC excess observations.

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