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

Using 140 fb⁻¹ of 13 TeV proton-proton collision data, the ATLAS detector observed a statistically significant excess of top-antitop production events near the kinematic threshold, providing strong evidence for the formation of color-singlet, spin-singlet quasi-bound $t\bar{t}$ states as predicted by non-relativistic QCD.

Original authors: ATLAS Collaboration

Published 2026-10-30

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CC BY 4.0

Original authors: ATLAS Collaboration

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the vast, high-energy collisions of the Large Hadron Collider, scientists often look for the heaviest known particle, the top quark. These particles are so massive and short-lived that they usually vanish almost instantly after being created, decaying into other particles before they can form any lasting structures. For decades, physicists have understood that when two top quarks are created together, they can become entangled, a strange quantum connection where the state of one instantly influences the other. However, there is a specific, fleeting moment just as these pairs are born, when they move very slowly relative to each other, where a different kind of interaction might occur. In this slow-motion zone, the strong force that binds the universe's fundamental particles together could act like a temporary glue, pulling the two top quarks into a brief, quasi-bound state before they fall apart. This phenomenon, predicted by the theory of quantum chromodynamics, has long been a target for observation, but the fleeting nature of the top quark makes it incredibly difficult to catch.

A recent study by the ATLAS collaboration at CERN has finally provided strong evidence that this temporary binding does happen. By analyzing a massive dataset of proton-proton collisions, the researchers focused on a narrow range of energy where top quark pairs are produced with very low speed. They compared the actual data against two different computer models: one that relied on standard calculations of particle interactions, and another that included the specific physics of these quasi-bound states. The results showed a clear and significant excess of events in the data that the standard model could not explain. This excess matched the predictions of the model that included the formation of these short-lived, bound states. The finding confirms that even though top quarks decay too quickly to form stable atoms like those made of lighter particles, they do briefly clump together in a specific quantum configuration, validating a decades-old prediction about how the strong force behaves at the edge of stability.

The researchers examined 140 units of collision data collected over several years, looking specifically for events where the top quark pairs decayed into two charged particles, either electrons or muons, along with several jets of other particles. To make sense of this complex debris, they reconstructed the original mass of the top quark pair and measured the angles at which the decay products flew apart. These angles are crucial because they reveal the spin relationship between the two top quarks; certain angles indicate that the pair was in a "spin-singlet" state, which is the specific configuration required for the quasi-bound state to form. The team divided their data into nine different categories based on these angles and the total mass of the pair, creating a detailed map of where events were occurring.

When they plotted the number of observed events against the predicted number from standard physics, a distinct pattern emerged. In the regions where the top quark pairs were moving the slowest, the data showed a significant surplus of events compared to the standard prediction. This surplus was not a random fluctuation; the statistical significance was so high that the chance of it being a fluke is less than one in a billion. The observed excess corresponded to a cross-section, a measure of the probability of this interaction occurring, of approximately 9.3 units. This value was notably higher than the theoretical prediction for the quasi-bound state alone, suggesting that the phenomenon is robust and perhaps even more prevalent than the simplest models anticipated.

The study explicitly ruled out the possibility that this excess was caused by errors in the standard calculations or by background noise from other known processes. The researchers tested their findings against alternative models and found that the standard model, which ignores the formation of these bound states, failed to describe the data. In contrast, the model that included the non-relativistic quantum effects of the bound states aligned perfectly with the observations. The agreement was so strong that the fit between the data and the extended model improved dramatically, while the fit with the standard model alone became statistically impossible. This confirms that the extra events are indeed due to the formation of these color-singlet, spin-singlet quasi-bound states, a state of matter that exists only for a fraction of a second before the top quarks decay.

While the result is a major confirmation of quantum chromodynamics in a non-relativistic regime, the paper notes that further work is needed to fully understand the details. The measured rate of these events is higher than the theoretical prediction, which could indicate that the current models need refinement or that there are additional subtle effects at play. The researchers plan to continue investigating this region of the energy spectrum, as it offers a unique laboratory for testing the fundamental forces of nature. By observing how these heavy particles interact when they are nearly at rest, scientists gain a clearer picture of the strong force, the invisible glue that holds the atomic nucleus together. This discovery does not just add a new entry to the particle physics ledger; it demonstrates that even the most unstable particles can exhibit the delicate, structured behavior of bound states, bridging the gap between the chaotic world of high-energy collisions and the orderly world of quantum mechanics.

Technical Summary: Observation of a Cross-Section Enhancement near the $t\bar{t}$ Production Threshold

Problem and Motivation
This paper addresses the kinematic regime of top-quark pair ( $t\bar{t}$ ) production near the threshold, where the invariant mass of the system ( $m_{t\bar{t}}$ ) is close to $2m_t \approx 345$ GeV. In this non-relativistic regime, a significant fraction of $t\bar{t}$ pairs are produced in a colour-singlet state. While the large mass and short lifetime of the top quark typically prevent the formation of narrow bound states (unlike charmonia or bottomonia), theoretical predictions in non-relativistic QCD (NRQCD) suggest the formation of "quasi-bound-states" (sometimes referred to as "toponia"). These states are predicted to manifest not as sharp resonances but as a local enhancement in the production cross-section just below the threshold.

Previous measurements by ATLAS and CMS have observed tensions between data and standard perturbative QCD (pQCD) Monte Carlo (MC) models in this region. While simplified models treating the quasi-bound-state as a narrow pseudo-scalar resonance ( $\eta_t$ ) have alleviated some tensions, a more complete description using NRQCD Green's function reweighting ( $t\bar{t}$ GFRW) has recently been developed. This analysis aims to quantify the agreement between data and two competing models: a baseline pQCD model and an extended model incorporating these advanced NRQCD quasi-bound-state effects.

Methodology
The measurement utilizes 140 fb $^{-1}$ of proton-proton collision data collected at $\sqrt{s} = 13$ TeV by the ATLAS detector during LHC Run 2 (2015–2018). The analysis focuses on the dileptonic decay channel ( $t\bar{t} \to \ell^+\nu b \ell^-\bar{\nu}\bar{b}$ , where $\ell = e, \mu$ ).

Event Selection and Categorization: Events are selected requiring exactly two oppositely charged leptons and at least two jets (one $b$ -tagged). To enhance sensitivity to the spin state of the $t\bar{t}$ system, events are categorized into nine Signal Regions (SRs) based on two angular observables, $c_{hel}$ and $c_{han}$ , calculated in the $t\bar{t}$ centre-of-mass frame. These observables are sensitive to spin correlations; specifically, the spin-singlet state (dominant in quasi-bound-state formation) yields a distinct distribution in $c_{hel}$ compared to the standard pQCD background.
Reconstruction: The $t\bar{t}$ invariant mass ( $m_{t\bar{t}}$ ) is reconstructed using the "Ellipse Method," which analytically solves for neutrino momenta using kinematic constraints (top and $W$ boson masses).
Theoretical Models:
- Baseline Model: Uses the Powheg v2 hvq generator at NLO accuracy, reweighted to approximate NNLO-QCD+NLO-EW accuracy.
- Extended Model: Includes the baseline plus a simulation of $t\bar{t}$ quasi-bound-state formation using the Green's Function Reweighted ( $t\bar{t}$ GFRW) approach, which accounts for the full spectrum of $S$ -wave colour-singlet states near the threshold.
Statistical Analysis: A binned profile-likelihood fit is performed on the reconstructed $m_{t\bar{t}}$ distributions across the nine SRs (300–500 GeV) and control regions. The fit extracts a signal strength parameter ( $\mu$ ) for the $t\bar{t}$ GFRW component, treating the normalisation of the quasi-bound-state contribution as a free-floating parameter.

Key Contributions

Observation of Threshold Enhancement: The analysis provides an observation of a significant cross-section enhancement near the $t\bar{t}$ threshold that is consistent with the formation of colour-singlet, spin-singlet $S$ -wave quasi-bound states. This builds upon previous work where the first observation of quantum entanglement at the LHC was made in this kinematic regime.
Spin-Sensitive Analysis: By utilizing the $c_{hel}$ and $c_{han}$ angular observables, the analysis significantly enhances sensitivity to the spin-singlet component compared to previous searches that did not fully reconstruct the $t\bar{t}$ system or used different angular variables.
Comprehensive Modeling Comparison: The paper rigorously compares data against both a standard pQCD baseline and a state-of-the-art NRQCD model, quantifying the necessity of including quasi-bound-state effects to describe the data.

Results

Significance: The baseline pQCD model (without quasi-bound-state contributions) is rejected with an observed significance of over 8 standard deviations ( $8\sigma$ ). The expected significance under the background-only hypothesis is $6\sigma$ .
Cross-Section Measurement: The extended model, including the $t\bar{t}$ GFRW component, provides a good description of the data. The measured cross-section for the quasi-bound-state contribution is:
$\sigma(t\bar{t}\text{GFRW}) = 9.3^{+1.4}_{-1.3} \text{ pb}$
This corresponds to a signal strength of $\mu(t\bar{t}\text{GFRW}) = 1.45^{+0.21}_{-0.20}$ relative to the theoretical prediction of 6.43 pb.
Systematic Uncertainties: The measurement precision is limited primarily by statistical uncertainties, followed by modelling uncertainties related to final-state radiation (FSR) in the $t\bar{t}$ GFRW sample and scale choices in the NNLO QCD reweighting for the pQCD sample.
Alternative Models:
- An alternative fit using the bb4 $\ell$ generator for the pQCD baseline yields a compatible result ( $\sigma = 8.5^{+1.2}_{-1.1}$ pb) with a significance of $>8\sigma$ .
- A fit using a simplified pseudo-scalar resonance model ( $\eta_t$ ) yields a larger cross-section ( $\sigma = 13.1^{+1.9}_{-1.7}$ pb) but also rejects the baseline with $>8\sigma$ significance. The paper notes that differences in the $m_{t\bar{t}}$ shape between the simplified and full NRQCD models lead to variations in the extracted cross-section.

Significance and Claims
The paper claims that the observed excess of events over the baseline perturbative QCD prediction is consistent with the formation of colour-singlet and spin-singlet $S$ -wave quasi-bound $t\bar{t}$ states, as predicted by non-relativistic QCD. This constitutes a stringent probe of QCD in the non-relativistic regime.

The author emphasizes that while the data strongly favors the inclusion of quasi-bound-state effects, further investigations are required to fully characterize the excess. Specifically, they note the need for improved matching between NRQCD and pQCD predictions, the inclusion of higher-order corrections (such as $P$ -wave and colour-octet contributions), and a better quantification of off-shell top-quark decay effects to reconcile the results obtained with different theoretical models (e.g., the full $t\bar{t}$ GFRW vs. the simplified $\eta_t$ model). The paper concludes that these improved models are essential not only for understanding this specific kinematic region but also for searching for physics beyond the Standard Model in this regime.

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