Measurement of high-mass $t\bar{t}\ell^{+}\ell^{-}$ production and lepton flavour universality-inspired effective field theory interpretations at $\sqrt{s}=13$ TeV with the ATLAS detector

Using 140 fb⁻¹ of 13 TeV proton-proton collision data collected by the ATLAS detector, this study measures high-mass $t\bar{t}\ell^{+}\ell^{-}$ production and interprets the results within an effective field theory framework to constrain anomalous four-fermion interactions and test lepton flavor universality, finding no significant deviations from Standard Model predictions.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle smasher. Inside its circular tunnel, scientists crash protons together at nearly the speed of light to see what happens when the universe's building blocks collide. Usually, these collisions create a chaotic mess of particles, but sometimes, they create something rare and special: a pair of top quarks (the heaviest known particles) accompanied by a pair of electrons or muons (lighter cousins of electrons).

This paper is a report from the ATLAS experiment, one of the giant detectors at the LHC, describing a specific hunt for these rare events. Here is the story of their search, explained simply.

The Mission: Hunting the "Ghost" in the High-Energy Zone

The scientists were looking for a specific event: a top quark and an anti-top quark appearing alongside two leptons (electrons or muons). In the "Standard Model" (our current best rulebook for physics), this happens when a top quark pair is created along with a Z boson (a carrier particle of the weak force), and that Z boson decays into the two leptons.

However, the team wasn't just looking for the standard version. They were specifically interested in the "high-mass" version of this event.

• The Analogy: Imagine a piano. Most of the time, when you play a note, it sounds normal. But if you hit the keys hard enough, you might hear a strange, high-pitched squeak that shouldn't be there. The scientists focused on the "squeak"—events where the two leptons have a huge amount of energy (high mass).
• Why? If there are new, unknown forces or particles in the universe, they might only reveal themselves at these extreme energy levels, like a hidden gear that only turns when the machine spins fast enough.

The Strategy: Filtering the Noise

The LHC produces billions of collisions, but most are boring or messy. Finding the specific "three-lepton" signal (two from the Z boson, plus a third one that often appears in these complex decays) is like trying to find three specific grains of sand in a massive beach storm.

1. The Net: The team set up a digital "net" to catch events with exactly three isolated particles (electrons or muons) and some specific jets (sprays of particles from quarks).
2. The Background Noise: The biggest problem is "fake" signals. Sometimes, particles from other common processes (like top quarks interacting with W bosons) mimic the signal. It's like hearing a knock on the door and thinking it's a delivery, but it's actually just the wind.
3. The Control Rooms: To fix this, the scientists created "Control Regions." These are like practice areas where they know exactly what the "wind" (background noise) looks like. They measured the wind there, calculated how much it would blow into their "Signal Room," and subtracted it out.

The Search for "New Physics" (EFT)

The team wanted to know if the data matched the Standard Model perfectly or if there were tiny deviations suggesting "New Physics." To do this, they used a framework called Effective Field Theory (EFT).

• The Analogy: Imagine the Standard Model is a map of a city. EFT is a way of checking if there are hidden shortcuts or secret tunnels that the map doesn't show. If the cars (particles) start driving faster or taking weird turns at high speeds, it suggests a secret tunnel exists.
• The Test: They checked if the top quarks were interacting with electrons and muons in a way that the standard map predicted. They also checked for Lepton Flavor Universality (LFU). This is the idea that electrons and muons should behave exactly the same way (just with different weights). If electrons acted differently than muons, it would be a huge clue that the Standard Model is incomplete.

The Results: The Map Holds Up

After analyzing 140 units of data (a massive amount of collision history from 2015–2018), the team found:

1. No New Shortcuts: The number of rare, high-energy events they found matched the Standard Model predictions almost perfectly. There were no "ghosts" in the machine.
2. Electrons and Muons are Twins: The behavior of electrons and muons was identical. There was no evidence that the universe treats them differently in these interactions.
3. Setting Limits: While they didn't find new physics, they set very strict "fences" around where it could be hiding. They told future physicists: "If there is new physics here, it must be weaker than this limit."

The Conclusion

The paper concludes that the Standard Model remains the champion. The "high-mass" region of top quark production is still behaving exactly as the old rulebook says it should. While they didn't find the new physics they were hoping for, they successfully mapped out the territory with high precision, proving that if new physics exists, it is very well hidden or requires even more powerful tools to find.

In short: The ATLAS team looked for a rare, high-energy particle dance to see if the universe's rulebook had any hidden pages. They found the dance was perfect, the rulebook was correct, and the electrons and muons were dancing in perfect sync. No new secrets were revealed this time, but the map of the known universe is now even more detailed.

Technical Summary

1. Problem and Motivation

The Standard Model (SM) predicts the production of a top-antitop quark pair in association with a $Z$ boson ($t\bar{t}Z$), where the $Z$ decays leptonically ($t\bar{t}\ell^+\ell^-$). While on-shell $t\bar{t}Z$ production (where the dilepton invariant mass $m_{\ell\ell} \approx m_Z$) has been measured, the off-shell region, where the lepton pair originates from a virtual $Z/\gamma^*$ decay with high invariant mass, remains largely unexplored by ATLAS.

This high-mass region is critical for two reasons:

1. Sensitivity to New Physics: Effective Field Theory (EFT) operators describing four-fermion interactions ($t\bar{t}\ell^+\ell^-$) exhibit energy growth. Their impact on cross-sections increases significantly at high energies, making the high-mass tail a sensitive probe for Beyond the Standard Model (BSM) physics.
2. Lepton Flavour Universality (LFU): Anomalies observed in $B$-hadron decays suggest potential violations of LFU. Since the couplings of top quarks and $B$-mesons are linked in many BSM models, probing LFU in the top sector is essential. This analysis aims to test for LFU violation by comparing electron and muon couplings to the top quark.

2. Methodology

Data and Simulation:

• Dataset: Proton-proton collision data at $\sqrt{s}=13$ TeV collected by the ATLAS detector from 2015–2018, corresponding to an integrated luminosity of 140 fb$^{-1}$.
• Signal: $t\bar{t}\ell^+\ell^-$ events where the dilepton invariant mass is high ($m_{\ell\ell} > m_Z + 10$ GeV).
• Backgrounds: Dominated by $t\bar{t}W$, $t\bar{t}H$, diboson ($WZ, ZZ$), and fake/non-prompt leptons from $t\bar{t}$ events.
• EFT Framework: The analysis interprets results using dimension-6 SMEFT operators (Table 1 in the paper) involving top-lepton interactions. The effects are parameterized by Wilson Coefficients ($c_i$) assuming a new physics scale $\Lambda = 1$ TeV.

Event Selection and Categorization:

• Final State: Events are required to have exactly three isolated leptons (electrons or muons) with $p_T > 27, 20, 15$ GeV.
• Kinematic Requirements:
  • At least one opposite-sign same-flavour (OSSF) lepton pair with $m_{\ell\ell} > 10$ GeV.
  • The OSSF pair closest to the $Z$ mass must satisfy $m_{\ell\ell} > 101.2$ GeV to target the high-mass region.
  • At least three jets, with at least one $b$-tagged jet (85% efficiency working point).
• Signal Regions (SRs): Split into two channels based on lepton flavour: $t\bar{t}e^+e^-$ and $t\bar{t}\mu^+\mu^-$.
• Control Regions (CRs): Thirteen dedicated CRs are defined to constrain backgrounds:
  • 2LSS CRs: Two same-sign leptons to constrain $t\bar{t}W$ and charge-flip backgrounds.
  • On-shell CRs: $m_{\ell\ell}$ within the $Z$ peak to constrain $t\bar{t}Z$ and $WZ$.
  • Fake/Non-prompt CRs: Regions enriched in heavy-flavour (HF) and light-flavour (LF) fakes, and photon conversions.

Statistical Analysis:

• A profile likelihood fit is performed simultaneously across all SRs and CRs.
• The fit extracts signal strengths ($\mu$) and constrains nuisance parameters for systematic uncertainties.
• EFT Interpretation: Fits are performed for:
  • Flavour-inclusive: Assuming identical couplings for electrons and muons.
  • Flavour-separated: Independent Wilson coefficients for $e$ and $\mu$.
  • LFU-violation sensitive: Directly fitting the difference $\Delta c = c_{\mu\mu} - c_{ee}$.
• Coverage Adjustment: Due to the quadratic dependence of EFT contributions ($O(\Lambda^{-4})$), the standard asymptotic approximation (Wilks' theorem) may fail. The analysis uses toy pseudodata to calculate coverage-adjusted confidence intervals.

3. Key Contributions

1. First High-Mass Measurement: This is the first ATLAS measurement of the $t\bar{t}\ell^+\ell^-$ process specifically in the high-dilepton invariant mass region ($m_{\ell\ell} > 101.2$ GeV), extending sensitivity to off-shell $Z/\gamma^*$ contributions.
2. Comprehensive EFT Interpretation: The paper provides constraints on seven specific dimension-6 SMEFT operators ($O_{te}, O_{Qe}, O_{tl}, O_{Ql}^{1,3}, O_{leQt}^{1,3}$) in both flavour-inclusive and flavour-separated scenarios.
3. LFU Violation Search: It presents the first LHC search for LFU violation in top-quark EFT interactions by directly measuring the difference between electron and muon Wilson coefficients.
4. Methodological Rigor: The analysis addresses the non-Gaussian nature of EFT likelihoods by implementing coverage corrections via pseudodata, ensuring robust statistical limits.

4. Results

Standard Model Measurements:

• The measured signal strength for $t\bar{t}\ell^+\ell^-$ ($m_{\ell\ell} > m_Z + 10$ GeV) is $\mu = 1.0^{+0.4}_{-0.4}$, consistent with the SM prediction.
• The significance of the signal observation is 2.9$\sigma$.
• Upper limits on the visible cross-section for BSM contributions in the very high mass region ($m_{\ell\ell} > 550$ GeV) are set at the 95% Confidence Level (CL), reaching $\approx 30$ ab.

EFT Constraints:

• Single Operator Fits: All fitted Wilson Coefficients are compatible with zero (the SM expectation).
  • The most constrained operator is $O_{leQt}^3$ (tensor structure), with a 95% CL interval of $[-0.38, 0.38]$ TeV$^{-2}$.
  • Other operators (e.g., $O_{tl}, O_{Qe}$) have 95% CL intervals roughly within $[-1.7, 1.9]$ TeV$^{-2}$.
• Flavour-Separated Fits: Constraints are slightly weaker than flavour-inclusive due to reduced statistics per channel but remain consistent with the SM.
• LFU Violation: The difference in Wilson coefficients ($\Delta c$) is consistent with zero. For example, for $O_{tl}$, $\Delta c = 0.79$ with a 95% CL interval of $[-3.44, 3.45]$ TeV$^{-2}$.
• Multi-Operator Fits: The analysis concludes that simultaneous fitting of multiple operators is currently not feasible due to strong correlations and limited sensitivity in the high-mass bins, particularly when signal injection is considered.

Systematics:

• The dominant uncertainties are statistical (limited data size) and modelling uncertainties for $t\bar{t}\ell^+\ell^-$ and $t\bar{t}W$ processes.
• Systematic uncertainties related to detector performance (jet energy scale, lepton ID) are sub-dominant.

5. Significance

• New Physics Reach: The results provide the most stringent constraints to date on specific four-fermion top-lepton EFT operators, improving upon previous limits (e.g., from CMS).
• LFU Testing: By demonstrating the feasibility of measuring flavour-dependent Wilson coefficients and their differences, this analysis sets the stage for future high-luminosity LHC runs (HL-LHC) where increased statistics will significantly improve the precision of LFU tests in the top sector.
• Validation of EFT Formalism: The successful application of coverage-adjusted confidence intervals for EFT fits serves as a methodological template for future searches where quadratic EFT terms dominate.
• No Deviations Observed: The data remains fully consistent with the Standard Model, placing tight bounds on the scale of potential new physics interacting with top quarks and leptons.