Measurement of the top-quark Yukawa coupling from $t\overline{t}$ production in the lepton+jets final state using $pp$ collisions 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 presents the first measurement of the top-quark Yukawa coupling via the $t\overline{t}$ invariant mass spectrum in the lepton+jets channel, finding results consistent with the Standard Model and setting a 95% confidence level upper limit of $Y_t < 2.1$.

The Gist

The Big Picture: Weighing the "King" of Particles

Imagine the universe is a giant construction site, and the Standard Model is the blueprint. In this blueprint, particles get their mass by interacting with an invisible field (the Higgs field), kind of like how a celebrity walking through a crowded room gets slowed down by fans wanting autographs. The stronger the interaction, the heavier the particle.

The Top Quark is the "celebrity" of this world. It is the heaviest known elementary particle. Because it is so heavy, its interaction with the Higgs field (called the Yukawa coupling) is incredibly strong. In fact, it's so strong that we can't just watch a Higgs boson decay into top quarks to measure it (because the Higgs isn't heavy enough to break apart into two top quarks).

This paper is the first time the ATLAS experiment at CERN has tried to measure this "strength of interaction" by watching how top quarks behave when they are created in pairs, rather than by watching them decay.

The Experiment: A High-Speed Collision

The scientists used the Large Hadron Collider (LHC), which is essentially a massive, circular racetrack for protons. They smashed protons together at nearly the speed of light (13 TeV of energy) and collected data equivalent to 140 "femtobarns" (a unit of data volume, think of it as a massive library of collision events).

They were looking for a specific event: a Top-Antitop pair ($t\bar{t}$) being created.

• The Setup: They focused on events where one of the top quarks decayed into an electron or a muon (a heavy cousin of an electron) and the other decayed into jets of particles.
• The Filter: They built a digital sieve to catch only the "good" events: exactly one isolated electron or muon, at least four jets of particles, and at least two of those jets must be tagged as coming from a bottom quark (a "b-jet"). This ensured they were looking at the right kind of collision.

The Secret Sauce: The "Threshold" and the Ghostly Echo

Here is the clever part of the physics.

When two top quarks are created, they usually fly apart very fast. But sometimes, they are created with very little energy, just barely enough to exist. This is called the production threshold.

Think of two heavy dancers (the top quarks) trying to spin together. If they spin too fast, they fly apart. But if they spin just at the right slow speed, they might briefly hold hands or feel a strong pull before letting go.

In this "slow dance" region (near the threshold), the laws of physics say that virtual Higgs bosons (ghostly, fleeting versions of the Higgs particle that pop in and out of existence) can be exchanged between the two top quarks.

• The Analogy: Imagine the two dancers are connected by a rubber band (the Higgs exchange). The tighter the rubber band (the stronger the Yukawa coupling), the more it affects how they move.
• The Measurement: The scientists didn't measure the rubber band directly. Instead, they measured the invariant mass (the combined weight/energy) of the two dancers. They looked at the shape of the distribution of these masses. If the rubber band (the coupling) were stronger or weaker than the Standard Model predicts, the shape of this mass distribution would change, especially right near the "slow dance" threshold.

The Result: A Perfect Match

The team took their massive dataset, reconstructed the mass of the top-quark pairs, and compared it to computer simulations. They ran a statistical "fit" to see which strength of the rubber band (Yukawa coupling) matched the data best.

• The Finding: The data matched the Standard Model prediction almost perfectly.
• The Limit: They couldn't pin down the exact number with extreme precision yet, but they set a strict upper limit. They are 95% confident that the top quark's interaction strength is less than 2.1 times what the Standard Model predicts.
• The Conclusion: The top quark is behaving exactly as the "blueprint" says it should. There is no evidence of "new physics" (like a rubber band that is suddenly twice as tight or loose) in this specific measurement.

Why This Matters (According to the Paper)

This is the first time ATLAS has done this specific measurement. Previously, the CMS experiment (a different detector at CERN) had done similar work.

The paper emphasizes that this method is a complementary way to check the Standard Model.

• Direct Method: Measuring top quarks produced alongside a Higgs boson ($t\bar{t}H$).
• Indirect Method (This Paper): Measuring the subtle "echo" of the Higgs boson in the way top quarks are created ($t\bar{t}$).

By using two different methods to measure the same thing, scientists can be more sure that the Standard Model is correct. If the two methods gave different answers, it would be a huge clue that new, unknown physics is hiding in the shadows. For now, the shadows remain empty, and the Standard Model stands firm.

Summary in One Sentence

The ATLAS collaboration smashed protons together to watch heavy top quarks dance, found that their "dance steps" (mass distribution) near the slowest speeds perfectly match the Standard Model's prediction, and confirmed that the top quark's connection to the Higgs field is exactly as strong as we thought it was.

Technical Summary

Technical Summary: Measurement of the top-quark Yukawa coupling from $t\bar{t}$ production in the lepton+jets final state

Problem and Motivation
In the Standard Model (SM), fermion masses arise from the Englert-Brout-Higgs mechanism via Yukawa couplings. While the top-quark Yukawa coupling ($g_t$) is the largest, its direct measurement is complicated because the top quark is heavier than half the Higgs boson mass, preventing direct extraction from Higgs decays. Current direct measurements rely on the associated production process $t\bar{t}H$, which depends on the total Higgs width. Indirect constraints exist from loop-induced processes (e.g., $gg \to H$) and four-top production.

This paper addresses the extraction of the top-quark Yukawa coupling strength ($Y_t = g_t/g_t^{\text{SM}}$) using a complementary approach: the virtual electroweak (EW) corrections to $t\bar{t}$ production. Specifically, the analysis focuses on the region near the $t\bar{t}$ production threshold. In this kinematic regime, the $t\bar{t}$ invariant mass spectrum is sensitive to virtual Higgs boson exchange between top-quark lines. These corrections depend quadratically on $Y_t$ and interfere with the Born-level amplitudes. This method provides a model-independent probe that is distinct from direct $t\bar{t}H$ measurements, offering sensitivity to potential new physics (such as top-philic scalars) that might mimic deviations in $Y_t$.

Methodology
The analysis utilizes proton-proton collision data at $\sqrt{s} = 13$ TeV collected by the ATLAS detector during 2015–2018, corresponding to an integrated luminosity of 140 fb$^{-1}$.

• Event Selection: The study focuses on the single-lepton final state ($e$ or $\mu$ + jets). Events are required to have exactly one isolated lepton ($p_T > 27$ GeV), at least four jets ($p_T > 25$ GeV), and at least two $b$-tagged jets. To suppress backgrounds, specific kinematic cuts are applied: $E_T^{\text{miss}} > 30$ GeV and reconstructed $W$ boson transverse mass ($m_T^W$) requirements. The analysis is split into electron and muon signal regions (SRs) to handle systematic uncertainties separately.
• Reconstruction: A dedicated algorithm reconstructs the $t\bar{t}$ invariant mass ($m_{t\bar{t}}$). The hadronic top is reconstructed by combining a $b$-jet with a $W$ boson candidate (formed from two light jets). The leptonic top is reconstructed using the lepton, the remaining $b$-jet, and missing transverse energy, solving for the neutrino $z$-momentum using the $W$ mass constraint. Events are selected within $m_{t\bar{t}} < 1050$ GeV, with finer binning near the production threshold to maximize sensitivity.
• Signal and Background Modelling:
  • Signal: The nominal $t\bar{t}$ sample is generated using Powheg Box-v2 (NLO QCD) interfaced with Pythia 8. To extract $Y_t$, the samples are reweighted using electroweak corrections calculated with HATHOR 2.1-b3. These corrections are implemented as a function of the generator-level $m_{t\bar{t}}$, $\cos \theta^*$, and initial-state parton flavor. The corrections are applied multiplicatively to the NLO QCD predictions.
  • Backgrounds: Major backgrounds include single-top quarks, $W/Z$+jets, dibosons, and fake/non-prompt leptons. Backgrounds are modelled using various generators (Sherpa, MadGraph, Powheg) and normalised to NNLO or N3LO QCD predictions where available. Fake leptons are estimated using a data-driven matrix method.
• Fit Strategy: A profile likelihood fit is performed on the reconstructed $m_{t\bar{t}}$ distribution. The parameter of interest (POI) is $Y_t^2$, as the EW corrections depend quadratically on $Y_t$. Templates for various $Y_t^2$ values are generated via morphing. Systematic uncertainties (experimental, signal modelling, background modelling) are treated as nuisance parameters with Gaussian constraints.

Key Contributions

• First ATLAS Measurement: This work presents the first measurement of the top-quark Yukawa coupling by ATLAS exploiting the sensitivity of the $t\bar{t}$ production threshold to virtual electroweak corrections.
• Threshold Sensitivity: The analysis specifically targets the kinematic region near the $t\bar{t}$ production threshold where the sensitivity to $Y_t$ is maximized due to the small relative velocity of the top quarks.
• Complementary Approach: It provides an indirect constraint on $Y_t$ that is independent of the Higgs total width, complementing direct $t\bar{t}H$ measurements and other loop-induced constraints.
• Systematic Handling: The study rigorously addresses the ambiguity between multiplicative and additive approaches for combining EW and QCD corrections, adopting the multiplicative approach as the nominal method based on theoretical arguments regarding the scale separation of QCD and EW radiation in $t\bar{t}$ production.

Results
The measured value of the squared Yukawa coupling strength is $Y_t^2 = 1.3 \pm 1.7$. This result is consistent with the Standard Model prediction of $Y_t^2 = 1$.

Based on this measurement, a 95% confidence level (CL) upper limit on the coupling strength is established:

• Observed Limit: $Y_t < 2.1$
• Expected Limit: $Y_t < 2.1$

The result is consistent with previous measurements by the CMS Collaboration in both the single-lepton and dilepton channels. The uncertainty is dominated by systematic effects, primarily from $t\bar{t}$ modelling (specifically the renormalisation scale variation and jet energy scale) and background modelling (notably the fake-lepton estimate).

Significance
The paper claims that this measurement provides a valuable, complementary constraint on the top-quark Yukawa coupling. While the sensitivity to $Y_t$ from virtual corrections is not expected to match that of direct $t\bar{t}H$ measurements, the approach is highly valuable for testing the consistency of the SM. It offers a distinct probe for new physics scenarios, such as top-philic scalars, which could modify virtual corrections differently than direct production processes. The result confirms the SM prediction within the current experimental precision and sets a competitive upper limit on potential deviations in the top-quark Yukawa coupling strength.