Some of the most intriguing developments in physics begin not with a discovery, but with an anomaly, subtle, persistent, and difficult to ignore. In 2019, CMS reported a mild excess of around three standard deviations in a search for heavy pseudoscalar (A) or scalar (H) bosons decaying to top quark-antiquark pairs [1]. The excess resembled the signature of a pseudoscalar particle with a mass around 400 GeV and was interpreted in the context of extended Higgs sector models.

The analysis has now been repeated using the full Run 2 dataset recorded between 2016 and 2018 [2]. With improved methods and increased sensitivity, the excess not only persists, it surpasses five standard deviations, with the most pronounced deviation occurring at the top quark-antiquark production threshold. While this may still be interpreted in terms of heavy resonance models, the excess has also prompted renewed interest in a long-predicted but rarely discussed standard model phenomenon: the possible formation of toponium.

Toponium refers to a bound state of a top quark and its antiquark, similar to quarkonia like charmonium or bottomonium. While such states are predicted by quantum chromodynamics (QCD), they have long been considered unobservable at the LHC. The top quark’s exceptionally short lifetime of 5×10⁻²⁵ seconds causes it to almost always decay before hadronisation can occur, precluding the formation of a stable bound state. As a result, any residual structure from threshold dynamics would be extremely subtle and easily masked by experimental limitations.

The invariant mass spectrum of the top quark-antiquark pairs, m_tt̄, is a key observable in searches for heavy resonances decaying to top quarks. However, its precise modelling and measurement present significant challenges. This is especially true near the production threshold, where small shifts in modelling assumptions can have a large impact on the predicted spectrum.

On the theoretical side, the shape of the m_tt̄ distribution is highly sensitive to effects such as off-shell top quark production, electroweak corrections, parton shower modelling, and the value of the top quark mass itself. These factors introduce sizeable uncertainties in the predicted shape. And even more crucially, they can contribute to a localised excess at the threshold, which means they must be thoroughly controlled.

From an experimental perspective, the situation is further complicated by the limited resolution in reconstructing the top quark decay products. In the dileptonic final state, which was used in this analysis, each top quark decays into a bottom quark and a W boson, with the W subsequently decaying leptonically. The resulting two neutrinos escape detection, and only the total missing transverse energy is measured. Reconstructing the full event kinematics relies on applying mass constraints from the W and top decays, as well as the measured missing transverse energy. These constraints are sufficient to solve for the neutrino momenta. Yet the reconstruction remains sensitive to detector resolution effects, particularly in the jet measurements, which impact the precision of the inferred m_tt̄ value.

To address both modelling and reconstruction challenges, the analysis also employs two spin correlation observables​. These observables probe the angular correlation between the decay products of the top quark and antiquark, offering a second, largely independent handle.

While spin observables are not entirely immune to theoretical uncertainties, they are sensitive to different aspects than the mass spectrum. Importantly, they test the nature of the tt̄ production itself. A pseudoscalar resonance, for example, leads to a distinct spin correlation signature compared to standard model or scalar production. Therefore, explaining both the excess in the m_tt̄ spectrum and the observed spin correlation pattern would require a systematic effect that specifically enhances pseudoscalar-like spin correlations at the tt̄ threshold.

Invariant mass distribution of the top quark–antiquark pair in data and simulation after the fit, shown for an event category defined by the observables c_hel and c_han, which are sensitive to the spin and CP structure of the tt system. The selected category is dominated by events with pseudoscalar-like spin correlations. The lower panel displays the ratio to the fixed-order perturbative QCD prediction. The contribution from the toponium-inspired model is shown as a red line and describes the data well.

This prompted a central question: could the observed signal still be the result of an overlooked or underestimated effect?

To address this, a series of stress tests were conducted, going well beyond the nominal systematics model. A variety of Monte Carlo generators and theoretical predictions were explored. We also examined whether correlations between nuisance parameters across the m_tt̄ spectrum could inadvertently distort the shape in the threshold region. On the reconstruction side, alternative observables were tested, such as replacing the full kinematic reconstruction with the invariant mass of the leptons and leading b-jets. Similarly, key experimental systematics, such as the jet energy scale, were exaggerated far beyond their expected ranges. These examples, among others, were not designed to refine the signal but to break it: an attempt to disprove the result by probing every plausible loophole. Yet in all variations explored, the excess persisted.

This persistence naturally raises the question of whether similar effects have appeared elsewhere at the LHC. Indeed, the observed excess in the CMS search is closely connected to other measurements that explore this phase space through different approaches. Entanglement studies [3,4] in dileptonic tt events, which rely on spin correlation observables, as well as differential measurements of the m_tt spectrum [5,6], have shown mild but consistent deviations near the threshold region. While none of these independently constitutes evidence for new phenomena, together they suggest that the dynamics in this region may not be fully understood. To further test the excess of top quark–antiquark events observed in a pseudoscalar configuration at the threshold, it would be exciting to see a corresponding result from ATLAS, ideally probing the same robust and powerful observables. If confirmed, such an excess would represent a significant and unexpected breakthrough at the LHC. Hints of a bound state involving top quarks, long considered experimentally out of reach, could open a new chapter in our understanding of QCD in the top quark sector.

The next steps are clear: refine the analysis with upcoming Run 3 data, deepen our treatment of systematic uncertainties, and explore novel observables that can help confirm or exclude the toponium hypothesis. Additional theoretical input will be crucial in interpreting the signal and guiding future searches.
 

Further Reading

[1] CMS Collaboration, Search for heavy Higgs bosons decaying to a top quark pair in proton–proton collisions at √s = 13 TeV, J. High Energy Phys. 04 (2020) 171. https://doi.org/10.1007/JHEP04(2020)171

[2] CMS Collaboration, Observation of a pseudoscalar excess at the top quark pair production threshold, arXiv:2503.22382 [hep-ex]. https://arxiv.org/abs/2503.22382

[3] ATLAS Collaboration, Observation of quantum entanglement in top–antitop quark pairs, Nature 633 (2024) 8030. https://www.nature.com/articles/s41586-024-07824-z

[4] CMS Collaboration, Quantum information and entanglement in top quark pair production, Rep. Prog. Phys. 87 (2024) 117801. https://iopscience.iop.org/article/10.1088/1361-6633/ad7e4d

[5] ATLAS Collaboration, Measurement of differential cross sections of top-quark pair production in the lepton+jets channel in pp collisions at √s = 13 TeV using the ATLAS detector, J. High Energy Phys. 07 (2023) 141. https://link.springer.com/article/10.1007/JHEP07(2023)141

[6] CMS Collaboration, Measurement of differential cross sections for top quark pair production using the lepton+jets final state in proton–proton collisions at √s = 13 TeV, Eur. Phys. J. C 80 (2020) 7. https://link.springer.com/article/10.1140/epjc/s10052-020-7917-7