The CMS collaboration has reported a statistically strong excess near the energy threshold for producing top-quark pairs in proton-proton collision data with one electron or muon plus jets. In its test of the background-only hypothesis, the excess reached 6.1 standard deviations; the expected significance was 7.3 standard deviations. The analysis searches for a contribution consistent with quasi-bound top-quark–antiquark states, often described here as toponium.
The result is an arXiv version 1 preprint dated 20 August 2026, and the manuscript is identified as submitted to Reports on Progress in Physics. Its interpretation remains tied to the signal models used in the fit: the authors say those models are approximate and that further theory is needed.
A search in one decay channel
The study uses CMS proton-proton collision data at 13 TeV with an integrated luminosity of 138 fb−1, collected from 2016 through 2018. It focuses on the e/µ+jets channel: one W boson decays leptonically and the other hadronically, while top-originating tau-lepton decays are excluded.
At the event-selection stage, CMS required exactly one electron or muon, no additional isolated electron or muon above 15 GeV in transverse momentum, and at least four jets. Those criteria define the single-lepton-plus-jets sample from which the threshold comparison is built.
The central question is whether the threshold region contains an excess consistent with a quasi-bound top-quark–antiquark state. In the fit, that question is tested by comparing a signal contribution with the background-only hypothesis, rather than by treating every event in the region as evidence for toponium.
The fit was built around motion as well as mass
One of the analysis’s main choices was to use β∗t, the relative velocity of the top quarks, instead of m(tt), the reconstructed top-pair mass, alongside angular observables sensitive to spin correlations and parity. The strategy uses both how the pair moves and how its decay products are distributed when separating a possible signal from background.
CMS combined the selection categories across the data-taking periods in a binned profile maximum-likelihood fit. In plain language, the fit compared how well the selected data matched different signal strengths against a background-only option.
For the principal interpretation, the ηt signal model was a color-singlet pseudoscalar with a mass of 343 GeV and a width of 2.8 GeV. The model used an assumed total production cross section of 6.43 pb. The fitted result therefore describes how strongly this specified signal model is favored, rather than measuring an unconstrained new state.
The signal stood out against background
Against the background-only hypothesis, assigned signal strength µ = 0, the observed significance was 6.1 standard deviations. The expected significance, calculated for the analysis’s expected sensitivity, was 7.3 standard deviations. The observed figure was lower than expected, but it still represented the strong excess reported by CMS under the stated test.
The best-fit ηt signal strength was 0.80, with an uncertainty of +0.14 and −0.13. Expressed as a total production cross section for that model, the result was 5.1 ± 0.9 pb. This is a fitted description of the excess in the chosen ηt framework, not a model-free count of toponium production.
A separate saturated-model goodness-of-fit test returned p = 0.59, which the paper describes as consistent with the data. That test addresses whether the fitted description is compatible with the observed distributions; it does not remove the need to decide which physical model best represents the threshold region.
The answer changes with the model
The choice of observable made a substantial difference in the study’s model-based sensitivity comparison. The expected significance was 2.1 standard deviations when the fit used m(tt), compared with 6.3 standard deviations when it used β∗t alone. Those are expected values from the comparison, not a replacement for the 6.1-standard-deviation observed result.
CMS also fitted an alternative description called the tt GFRW model. That fit produced an observed significance of 5.9 standard deviations and an expected significance of 13 standard deviations. Its best-fit signal strength was 0.44, with +0.08 and −0.07 uncertainty, corresponding to a cross section of 2.8 ± 0.5 pb.
Taken together, the two fits point to the same broad feature in the threshold region, but they assign it different fitted cross sections: 5.1 ± 0.9 pb for ηt and 2.8 ± 0.5 pb for tt GFRW. The authors report that both models give a roughly 3 pb enhancement below 350 GeV, while also saying the descriptions are approximate.
Evidence, but not a bound-state verdict
CMS interprets the single-lepton result as an independent confirmation of an excess previously reported in the dilepton channel and as compatible with the simplified ηt model. That is the collaboration’s interpretation of the preprint; it is not a claim that the analysis has established a model-independent toponium bound state.
The caution matters because the reported cross sections come from specified descriptions of the threshold region. The authors explicitly describe both ηt and tt GFRW as approximate models and say further theoretical work is needed before the interpretation can be made more precise.
The result is also limited to the selected e/µ+jets final state. It does not by itself establish that the same excess appears across every top-quark decay channel, and it does not settle how the measured enhancement should be mapped onto physical toponium production.
For now, the preprint’s clearest conclusion is narrower: in 13 TeV CMS data, the single-lepton-plus-jets threshold region contains a statistically significant, model-dependent excess. The fit gives a 6.1-standard-deviation observed exclusion of background-only, while the size assigned to the feature changes with the model used.
Paper data and sources
Original title: Observation of an excess at the top quark pair production threshold in the single-lepton channel
Authors: CMS Collaboration
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text