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

The ATLAS Collaboration reports a significant excess of top-antitop events near their production threshold in 13 TeV proton-proton collisions, a finding consistent with the long-hypothesized formation of top-antitop quasi-bound states.

The Gist

Imagine the Large Hadron Collider (LHC) as a giant, high-speed particle racetrack. Scientists smash protons together at nearly the speed of light to see what tiny pieces fly out. For decades, they've been looking for a specific "ghost" in the machine: a fleeting moment where a top quark and its anti-matter twin (an antitop) stick together just long enough to form a temporary couple before flying apart.

This paper is the story of how the ATLAS experiment at CERN finally caught a glimpse of this ghost.

The Star of the Show: The Top Quark

Think of the top quark as the "heavyweight champion" of the subatomic world. It's so massive that it's incredibly unstable. It lives for a blink of an eye—about 500 billionths of a billionth of a second.

Because it dies so fast, it usually doesn't have time to hold hands with other particles to form "atoms" (called hadrons) like its lighter cousins do. It's like a dancer who spins so fast they never get a chance to link arms with a partner.

The Mystery: The "Almost-Bound" Couple

However, physics has a rulebook called Quantum Mechanics. About 40 years ago, theorists predicted a weird exception: If you create a top quark and an antitop quark with just the right amount of energy (not too fast, not too slow), they might slow down enough to feel a magnetic-like pull. They would form a "quasi-bound state"—a couple that holds hands for a split second before the top quark dies.

Scientists called this hypothetical couple "Toponium."

For a long time, everyone thought this was impossible to see at the LHC. The signal was expected to be too faint, like trying to hear a whisper in a hurricane. Standard computer models used to predict what happens in the collider didn't even bother to include this "whisper" because they assumed it didn't exist.

The Discovery: Hearing the Whisper

The ATLAS team took a massive amount of data (140 "inverse femtobarns"—a fancy way of saying a huge pile of collision records) from 2015–2018. They looked specifically at the moment when the top and antitop were created with just enough energy to be near the "threshold" (the minimum speed needed to make them).

What they found:
Instead of a smooth curve of data matching the standard computer models, they saw a huge spike. It was like looking at a crowd of people walking through a door and suddenly seeing a massive, unexpected crowd jamming the entrance.

• The Result: There were significantly more top-antitop pairs than the standard models predicted.
• The Significance: The chance that this was a random fluke is less than 1 in a billion (over 8 sigma). It's a definitive discovery.
• The Explanation: The data matches the prediction for Toponium. The top quarks are briefly forming these short-lived, "almost-bound" states before decaying.

How They Did It (The Detective Work)

To find this needle in the haystack, the scientists had to be very clever:

1. The Filter: They looked for specific "fingerprints" left behind: two charged particles (leptons) and two jets of debris, with at least one jet coming from a bottom quark.
2. The Reconstruction: Since the top quarks decay instantly, they couldn't see them directly. They had to use math (the "Ellipse Method") to work backward from the debris to figure out the speed and mass of the original top pair.
3. The Spin Check: They used special angles to check if the tops were "spinning" in a way that only happens if they are in this special bound state. This helped them separate the signal from the background noise.

The "New" Computer Model

The standard computer models (the "Baseline") failed to predict this spike. So, the team created an "Extended Model" that included the new physics of Toponium.

When they compared the real data to this new model, the fit was perfect. They calculated that this new "Toponium" state is being produced at a rate of about 9.3 picobarns (a tiny unit of probability). Interestingly, this is about 45% higher than the theoretical prediction from 1987, suggesting our understanding of how these particles interact is still a bit incomplete.

Why This Matters

This isn't just about finding a new particle; it's about opening a new window into the universe.

• A New Tool: Because the top quark is so heavy and dies so fast, it's a perfect probe for studying the fundamental forces of nature.
• Testing the Rules: This discovery confirms that even the heaviest particles can form "atoms" under the right conditions, validating decades-old theories.
• Future Work: The scientists admit their current models are still a bit rough. They need to refine the math to understand exactly why the observed rate is higher than expected. This will be a major focus for the next round of experiments (Run 3) at the LHC.

In a nutshell: The ATLAS team found that top quarks, despite being the most impatient particles in the universe, can sometimes slow down just enough to hold hands and form a brief, exotic couple. This discovery confirms a 40-year-old prediction and opens up a new chapter in understanding how the universe works at its smallest scales.

Technical Summary

1. Problem and Scientific Context

The Standard Model (SM) predicts that the top quark has an extremely short lifetime ($\approx 5 \times 10^{-25}$ s), which is shorter than the timescale required for hadronization ($\approx 3 \times 10^{-24}$ s). Consequently, top quarks were traditionally assumed not to form hadronic bound states. However, theoretical work from 1987 hypothesized that if a top-antitop ($t\bar{t}$) pair is produced near the kinematic threshold ($2m_{top}$) with small relative velocities, they could form short-lived quasi-bound states known as "toponia" via the attractive Coulomb potential of Non-Relativistic QCD (NRQCD) in a color-singlet state.

These states were predicted to manifest as a narrow enhancement in the $t\bar{t}$ production cross-section just below the threshold, dominated by pseudo-scalar $1S_0$ states. Despite these predictions, standard Monte Carlo (MC) models used at the Large Hadron Collider (LHC) typically omitted these NRQCD effects, assuming them unobservable. The ATLAS Collaboration recently observed a significant excess of events in this region, prompting this study to characterize the phenomenon and quantify the cross-section.

2. Methodology

Data and Simulation

• Dataset: Proton-proton collision data collected by the ATLAS detector at a center-of-mass energy of $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of $140 \text{ fb}^{-1}$ (LHC Run 2).
• Baseline Model: Standard $t\bar{t}$ production modeled at Next-to-Leading Order (NLO) in perturbative QCD (pQCD) using PowhegBox (hvq model) interfaced with Pythia8.2. This model includes no specific NRQCD bound-state effects. Differential predictions were reweighted to NNLO-QCD+NLO-EW accuracy using MATRIX and HATHOR.
• Extended Model: Includes the baseline pQCD model plus an NRQCD component ($t\bar{t}_{GFRW}$). This component models the formation of color-singlet $1S_0$ states using the NRQCD Green's function in the Coulomb gauge. The reweighting is applied only to events with invariant mass $m_{t\bar{t}} < 350$ GeV and top momentum $p^* < 50$ GeV to minimize overlap with the pQCD sample.
• Off-shell Effects: An alternative pQCD sample (bb4l model) was used to estimate the impact of off-shell top decays and non-resonant contributions.

Event Selection and Reconstruction

• Final State: Events with two oppositely charged leptons (electrons/muons) and at least two jets.
• Kinematic Cuts:
  • Leptons: $p_T > 10$ GeV (at least one $> 28$ GeV).
  • Jets: $p_T > 25$ GeV, with at least one $b$-tagged.
  • Same-flavor leptons: Dilepton mass $> 15$ GeV and outside the $Z$-boson mass window ($81-101$ GeV).
  • Missing transverse energy ($E_T^{miss}$): $> 60$ GeV to suppress $Z$+jets background.
• Reconstruction: The $t\bar{t}$ invariant mass ($m_{t\bar{t}}$) is reconstructed using the "Ellipse Method," which applies kinematic constraints from $W$ boson and top quark masses to solve for neutrino momenta. The resolution is $\approx 22\%$ at the threshold.
• Signal Regions (SRs): Events with $m_{t\bar{t}} < 500$ GeV are categorized into nine SRs based on two angular observables ($c_{hel}$ and $c_{an}$) sensitive to $t\bar{t}$ spin correlations, allowing discrimination between spin-singlet states and standard pQCD events.

Statistical Analysis

A binned profile-likelihood fit is performed on the $m_{t\bar{t}}$ distributions across the nine SRs. The normalizations for both the pQCD background and the NRQCD signal are free-floating parameters in the fit.

3. Key Contributions

• First Quantitative Measurement: Provides the first experimental extraction of the cross-section for $t\bar{t}$ quasi-bound states at the LHC.
• Model Validation: Confirms the existence of the predicted threshold enhancement, validating the NRQCD framework in a regime previously thought inaccessible at hadron colliders.
• Methodological Framework: Establishes a robust analysis strategy using spin-correlation observables to isolate the quasi-bound state signal from the dominant pQCD background.

4. Results

• Significance: The baseline pQCD model (without quasi-bound states) is rejected with an observed significance of over $8\sigma$ (expected $6\sigma$).
• Cross-Section Measurement: The cross-section for the NRQCD component ($t\bar{t}_{GFRW}$) is measured as:
  $$\sigma(t\bar{t}_{GFRW}) = 9.3^{+1.4}_{-1.3} \text{ pb} = 9.3^{+1.1}_{-1.0} (\text{stat.}) \pm 0.8 (\text{syst.}) \text{ pb}$$
  This value is approximately 45% higher than the theoretical calculation of $6.43$ pb, though consistent within uncertainties.
• Robustness:
  • Using the bb4l model for the pQCD baseline yields a consistent result ($8.5^{+1.2}_{-1.1}$ pb).
  • A simplified model treating the effect as a pseudoscalar resonance ($\eta_t$) yields a higher cross-section ($13.1$ pb), attributed to differences in the $m_{t\bar{t}}$ distribution modeling (specifically the lack of parton-level upper bounds in the simplified model).
• Uncertainties: The dominant systematic uncertainties arise from modeling final- and initial-state radiation (for the NRQCD component) and the scale choice in NNLO QCD reweighting (for the pQCD component).

5. Significance and Outlook

This observation confirms a phenomenon hypothesized nearly 40 years ago, demonstrating that top quarks can form quasi-bound states before decaying. The results have profound implications for:

1. QCD Theory: They provide a unique testing ground for NRQCD and the interplay between perturbative and non-perturbative QCD.
2. Future Measurements: The discrepancy between the measured cross-section and the theoretical prediction (and between different models like $t\bar{t}_{GFRW}$ and $\eta_t$) highlights the need for improved theoretical models.
3. Next Steps: Future work must focus on:
   • Developing complete MC models that include P-wave states, color-octet contributions, and higher-order NRQCD terms.
   • Improving the matching between NRQCD and pQCD predictions.
   • Incorporating accurate treatments of off-shell top decays.
   • Utilizing LHC Run 3 data to further characterize the nature of this excess with higher precision.

In summary, the ATLAS Collaboration has successfully observed and quantified the formation of top-antitop quasi-bound states, marking a significant milestone in high-energy physics and opening new avenues for precision QCD studies.