ATLAS and CMS measurements of the $t\bar{t}$ cross section, including off-shell and near threshold

This paper reviews recent inclusive and differential $t\bar{t}$ cross-section measurements by the ATLAS and CMS collaborations, highlighting investigations into off-shell effects, Monte Carlo modeling, and the observation of quasi-bound states near the production threshold for indirect Yukawa coupling extraction.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful, high-speed particle smasher. During its "Run 2" phase (2015–2018), it was essentially a Top Quark Factory, churning out pairs of these heavy particles (a top quark and an anti-top quark, or $t\bar{t}$) at a rate of over 15 per second.

The ATLAS and CMS experiments are like two massive, ultra-precise cameras surrounding the collision point, taking billions of photos of these events. This paper is a report card on what these cameras have learned about the top quark, focusing on three main stories: counting the particles, understanding their messy behavior, and watching them dance before they disappear.

Here is the breakdown in simple terms:

1. The Great Count: Measuring the "Top Quark Factory" Output

The first job was to simply count how many top quark pairs are being made. It's like trying to count how many cars pass through a busy intersection, but the cars are subatomic particles.

• The "Quiet" Approach (CMS): One team (CMS) waited for a rare moment when the traffic was light. They used a special dataset where there were very few overlapping collisions (low "pileup"). It was like watching a single car drive through an empty intersection. They counted the cars (top pairs) and got a very clean number, though they didn't have many photos to work with.
• The "Busy" Approach (ATLAS): The other team (ATLAS) looked at the entire chaotic traffic jam from the last few years. They focused on a very specific, rare type of car crash (where the particles decay into an electron and a muon). Because they had so many photos (140 times more data than the first team), they could count with incredible precision.
• The Result: Both teams got numbers that match the theoretical predictions almost perfectly. It's like the factory's output meter matches the blueprint exactly.

2. The Messy Middle: When Things Don't Go as Planned

Usually, physicists look for the "perfect" crash where two top quarks are born and immediately die. But in reality, nature is messy. Sometimes, the particles don't behave like perfect, isolated top quarks. They are "off-shell," meaning they are in a fuzzy, transitional state, or they interfere with other processes (like a single top quark appearing alongside a W boson).

• The Analogy: Imagine trying to listen to a specific instrument in an orchestra. Usually, you listen to the violin solo. But sometimes, the violinist is playing a bit out of tune, or the cello is playing a note that sounds exactly like the violin.
• The Problem: The computer simulations (Monte Carlo generators) used to predict these events were getting the "music" slightly wrong. They were treating the particles as if they were perfect, solid objects, ignoring the fuzzy, quantum mechanical "glitch" where particles overlap and interfere.
• The Fix: The teams introduced new, smarter simulation tools (like Powheg bb4ℓ). These tools treat the particles more realistically, accounting for the fact that they are fuzzy and can interfere with each other. The new simulations fit the data much better, especially in the "tails" of the distribution (the rare, extreme events).

3. The Threshold Dance: Quasi-Bound States and the "Toponium"

This is the most exciting part. When two top quarks are created with just enough energy to barely make it, they move very slowly relative to each other.

• The Analogy: Imagine two heavy magnets thrown at each other. If they are moving slowly, they might stick together for a split second before flying apart. In physics, this is called a quasi-bound state. For top quarks, this temporary molecule is called "Toponium."
• Why it's special: Top quarks are so heavy and unstable that they usually decay (explode) before they can stick together. However, the experiments saw a tiny "bump" or excess of events right at the energy threshold where this sticking should happen.
• The Discovery: Both ATLAS and CMS saw this bump with high confidence (over 5 sigma, which is the gold standard for a discovery). It confirms that for a fleeting moment, the top quarks form a "ghostly" pair, exchanging soft gluons (the glue of the universe) and even virtual Higgs bosons.

4. The Secret Message: Measuring the Top Quark's "Weight"

Because these top quarks are moving so slowly near the threshold, they are sensitive to the Higgs field (the field that gives particles mass).

• The Analogy: Think of the top quark as a swimmer in a pool of molasses (the Higgs field). The "Yukawa coupling" is a measure of how sticky the molasses is for that specific swimmer.
• The Measurement: By looking at how the top quarks behave near the threshold, the scientists could indirectly measure this "stickiness" (the Yukawa coupling). While the measurement has a large margin of error (it's a bit like guessing the swimmer's weight by watching them splash), the result is consistent with the Standard Model. It's a new, clever way to weigh the heaviest known particle without needing to produce a Higgs boson directly.

Summary

This paper tells us that the LHC has become a precision instrument for studying the top quark.

1. We can count them with extreme accuracy.
2. We are learning to model their messy, quantum behavior better than ever before.
3. We have spotted them forming a fleeting "dance" (Toponium) just before they decay.
4. We are using this dance to measure their fundamental connection to the Higgs field.

It's a triumph of both experimental engineering (building better cameras) and theoretical physics (writing better software to understand the blurry, quantum world).

Technical Summary

1. Problem Statement

The Large Hadron Collider (LHC) has produced an unprecedented dataset of top-antitop ($t\bar{t}$) pairs (over 115 million pairs during Run 2, 2015–2018). While the Standard Model (SM) predicts $t\bar{t}$ production with high precision, several complex physical regimes challenge current experimental and theoretical capabilities:

• Precision Limits: Achieving percent-level precision in inclusive and differential cross-section measurements is hindered by systematic uncertainties related to background modeling, pileup, and parton-shower matching.
• Off-Shell Effects: Traditional analyses often rely on the "Narrow-Width Approximation" (NWA) and treat resonant ($t\bar{t}$) and non-resonant ($tW$, $WbWb$) processes separately. This ignores interference effects and off-shell contributions that become significant in specific kinematic regions (e.g., high transverse momentum or near the production threshold).
• Threshold Physics: Near the $t\bar{t}$ production threshold ($m_{t\bar{t}} \approx 2m_t$), non-relativistic QCD (NRQCD) effects, such as the formation of quasi-bound states ("toponium") and the exchange of virtual Higgs bosons, modify the cross-section and spin correlations. These effects are not naturally captured by standard perturbative QCD (pQCD) Monte Carlo (MC) generators.

2. Methodology

The paper reviews recent measurements from ATLAS and CMS employing distinct strategies to address these challenges:

A. Inclusive and Differential Cross-Section Measurements

• CMS Approach (Low-Pileup): Utilized a specialized 2017 dataset at $\sqrt{s}=5.02$ TeV with extremely low pileup ($\langle\mu\rangle=2$). The analysis targeted the semi-leptonic $t\bar{t}$ final state. Backgrounds ($W$+jets, $tW$, QCD) were suppressed using multivariate techniques and data-driven estimates. A maximum likelihood fit was performed in bins of jet and $b$-jet multiplicities.
• ATLAS Approach (Dileptonic): Used the full Run 2 dataset ($140 \text{ fb}^{-1}$) focusing on the clean $e\mu + b\bar{b}$ final state. This employed an in-situ $b$-jet counting technique for efficiency extraction and the Powheg MiNNLOps generator for NNLO-accurate modeling of lepton $p_T$. Differential cross-sections were unfolded to particle level.

B. Off-Shell Modeling (The $bb4\ell$ Framework)

• To address interference between $t\bar{t}$, $tW$, and non-resonant $WbWb$ processes, the authors discuss the Powheg $bb4\ell$ generator.
• Unlike traditional approaches using "Diagram Removal" (DR) or "Diagram Subtraction" (DS) schemes (which are non-gauge-invariant), $bb4\ell$ calculates the full $2 \to 6$ matrix element ($pp \to \ell^\pm \bar{\nu} b \ell'^\mp \nu \bar{b}$) at NLO QCD.
• This approach naturally includes off-shell effects, spin correlations, and interference without ad-hoc approximations.

C. Threshold and Bound State Analysis

• Toponium Search: Both collaborations searched for an excess of events near $m_{t\bar{t}} \approx 2m_t - 2$ GeV, indicative of quasi-bound states.
  • CMS: Modeled a pseudo-scalar resonance ($\eta_t$) using MadGraph, tuned to NRQCD predictions.
  • ATLAS: Used a "Green's function reweighted" ($t\bar{t}_{GFRW}$) approach, reweighting SM matrix elements based on the ratio of NRQCD Green's functions for bound vs. free states.
• Yukawa Coupling Extraction: ATLAS performed a fit to the $m_{t\bar{t}}$ distribution to extract the top quark Yukawa coupling modifier ($Y_t = g_t / g_t^{SM}$), parameterizing NLO electroweak effects as a function of $Y_t^2$.

3. Key Contributions

• High-Precision Cross Sections:
  • CMS reported $\sigma(t\bar{t}) = 62.5 \pm 1.6 \text{ (stat.)} +2.6_{-2.5} \text{ (syst.)} \pm 1.2 \text{ (lumi.)}$ pb at 5.02 TeV.
  • ATLAS reported $\sigma(t\bar{t}) = 829.3 \pm 1.3 \text{ (stat.)} \pm 8.0 \text{ (syst.)} \pm 7.3 \text{ (lumi.)} \pm 1.9 \text{ (beam)}$ pb at 13 TeV. Both are in excellent agreement with NNLO+NNLL QCD predictions.
• Validation of Advanced Generators:
  • Demonstrated that Powheg MiNNLOps provides the best description of differential observables compared to baseline NLO setups (like $hvq$).
  • Validated the Powheg $bb4\ell$ generator, showing it significantly improves the modeling of off-shell regions (e.g., $m_{min}^{b\ell}$ tails) and interference effects compared to DR/DS schemes.
• Discovery of Toponium:
  • Both experiments observed a significant excess ($>5\sigma$) near the production threshold, consistent with the formation of spin-singlet, color-singlet quasi-bound states (toponium).
  • Measured cross-sections for this excess were $\sigma(t\bar{t}_{GFRW}) = 9.3^{+1.1}_{-1.0}$ pb (ATLAS) and $\sigma(\eta_t) = 8.8 \pm 0.5$ pb (CMS).
• Indirect Yukawa Coupling:
  • Extracted $Y_t^2 = 1.3 \pm 1.7$, setting a 95% CL upper limit of $Y_t < 2.1$. This provides a complementary constraint to direct $t\bar{t}H$ measurements.

4. Results

• Differential Measurements: While overall agreement with theory is good, discrepancies remain in specific kinematic regions. Notably, the $\Delta\phi_{e\mu} \times m_{e\mu}$ distribution (sensitive to the threshold) shows data excesses over all tested MC generators, including MiNNLOps, suggesting missing higher-order or non-perturbative effects.
• Off-Shell Modeling: The $bb4\ell$ generator successfully models the $e\mu + b\bar{b}$ fiducial volume without requiring artificial "lineshape" uncertainties, though it introduces new sensitivities to parton shower matching and $\alpha_S$ variations.
• Threshold Excess: The observed excess is localized below the kinematic threshold and exhibits spin-singlet characteristics, strongly supporting the NRQCD prediction of toponium formation.
• Systematics: The dominant uncertainties in these precision measurements stem from modeling (parton shower matching, $b$-tagging efficiency) and, for the threshold analysis, the theoretical modeling of the pQCD background.

5. Significance

• Precision Physics: The results confirm the LHC's capability as a "precision machine," validating QCD predictions at NNLO+NNLL accuracy and refining the understanding of $t\bar{t}$ production dynamics.
• Theoretical Advancement: The successful application of the $bb4\ell$ generator marks a shift away from ad-hoc interference treatments toward full off-shell matrix element calculations, setting a new standard for future top quark analyses.
• New Physics Probes: The observation of toponium is a landmark achievement, providing the first experimental evidence of non-relativistic QCD bound states involving heavy quarks. This opens a new window for studying strong interactions in the non-perturbative regime.
• Fundamental Parameters: The indirect extraction of the top Yukawa coupling demonstrates the utility of threshold kinematics in constraining fundamental SM parameters, offering a cross-check against direct Higgs coupling measurements.

In conclusion, this work synthesizes the latest ATLAS and CMS results to demonstrate that while the Standard Model holds firm at high precision, the complex regimes of off-shell interference and near-threshold dynamics require advanced theoretical tools (NRQCD, full off-shell MC) to fully interpret the data. These findings pave the way for even more precise measurements in LHC Run 3.