Differential top quark cross section results from the ATLAS and CMS experiments

This report summarizes recent differential top quark cross-section measurements from the ATLAS and CMS experiments, highlighting that while no single theoretical model fully describes the data across all bins, higher-order perturbative QCD predictions offer an improved description.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful, high-speed particle smasher. Inside its giant ring, scientists crash protons together at nearly the speed of light to see what happens. The "star" of this show is the top quark. It's the heaviest known particle in the universe—think of it as the "elephant in the room" of the particle world. Because it's so heavy, it interacts strongly with the Higgs boson (the particle that gives everything mass), making it a perfect test subject to see if our current rules of physics (the Standard Model) hold up or if there are cracks in the foundation.

This paper is a report card from two giant teams of scientists, ATLAS and CMS, who are like two different detective agencies working at the same crime scene. They analyzed a massive amount of data (from 2015 to 2018) to measure exactly how often these top quarks are made and how they behave.

Here is a breakdown of their findings using simple analogies:

1. The Main Event: Top Quark Pairs ($t\bar{t}$)

When protons smash, they usually create top quarks in pairs (a top and an anti-top). It's like a dance floor where partners are almost always created together.

• The Decay: These top quarks are unstable and die instantly. They break apart into a "W boson" and a "bottom quark."
• The Channels: The W boson can decay in different ways, creating different "channels" for the scientists to watch:
  • All-Hadronic (46%): Everything turns into jets of particles (like a chaotic mosh pit).
  • Single-Lepton (45%): One W turns into a clean electron or muon (a "clean" signal), while the other makes a mess.
  • Dilepton (9%): Both Ws turn into clean electrons or muons. This is the "VIP section"—rare, but very clean and easy to track.

2. The New Tricks: Boosted Tops and Substructure

In the past, scientists mostly looked at "resolved" tops, where the decay products are spread out enough to see individually. But with more energy, tops can be "boosted" (moving so fast that their decay products get squashed together into a single giant blob).

• The Analogy: Imagine trying to identify a car by looking at its wheels. If the car is parked, you see the wheels clearly (resolved). If the car is zooming by at 200 mph, the wheels blur into a single shape (boosted).
• The Breakthrough: The teams developed new techniques to look inside these "blurred blobs" (jet substructure). They used "neural networks" (AI) to figure out if a giant blob was actually a top quark.
• The Result: They found that while current computer simulations (Monte Carlo generators) are good at predicting the general shape of the "blob," they struggle to predict the fine details of how the particles are arranged inside it.

3. The "Interference" Mystery ($WbWb$)

Sometimes, a top quark pair is created, and sometimes a single top quark is created alongside a W boson. These two processes can happen at the same time and interfere with each other, like two sets of waves crashing into one another.

• The Challenge: It's hard to tell if you are seeing a "double top" event or a "single top" event because they look identical in the detector.
• The Discovery: The ATLAS team measured this "interference" directly. They found that while the simulations get the low-energy part right, they fail miserably at the high-energy "tails" (the extreme ends of the data). It's like a weather forecast that predicts rain perfectly for a light drizzle but completely misses the hurricane.

4. The "Solo" Act: Single Top Quarks

Sometimes, a top quark is created alone, not in a pair. This happens via a specific exchange of a virtual W boson.

• The Asymmetry: Because protons are made of "up" quarks and "down" quarks, and there are twice as many "up" quarks, it's easier to create a top quark than an anti-top quark.
• The Result: The teams measured this ratio precisely. The data matches the theory well, which helps scientists refine their understanding of the proton's internal structure (Parton Distribution Functions).

5. The Big Picture: Theory vs. Reality

The most important takeaway from this report is a mix of success and frustration:

• Success: The new data is incredibly precise. The uncertainties (the "margin of error") have been cut in half compared to previous years.
• The Problem: No single computer model can explain all the data perfectly.
  • Some models work great for low energies but fail at high energies.
  • Some models get the "average" right but miss the "extremes."
  • Moving to higher levels of mathematical complexity (NNLO QCD) helps, but it's not a magic bullet yet.

The Bottom Line

Think of the Standard Model as a map of the world. These experiments have filled in a lot of new details on the map, making it much more accurate. However, they also found some "terra incognita" (unknown territory) where the map doesn't match the terrain.

The scientists are saying: "We have the best data ever, and our current maps are getting better, but they still don't explain the extreme corners of the universe perfectly. We need to update our maps (theories) to match the new terrain."

With the next run of the LHC (Run 3) bringing even more data, the hope is that these discrepancies will either be resolved by better math or point us toward entirely new physics beyond what we currently know.

Technical Summary

1. Problem Statement

The top quark, being the heaviest particle in the Standard Model (SM), offers a unique laboratory for precision tests of the SM and probing the limits of perturbative Quantum Chromodynamics (QCD) at Next-to-Next-to-Leading Order (NNLO). While inclusive cross-section measurements are well-established, there is a critical need for differential cross-section measurements to:

• Constrain Monte Carlo (MC) generator parameters regarding top quark decay, parton showering (PS), and hadronization.
• Test the accuracy of state-of-the-art theoretical predictions (NLO and NNLO) across the full kinematic phase space.
• Investigate complex interference effects between top-quark pair production ($t\bar{t}$) and single-top production ($tW$).
• Extract Parton Distribution Functions (PDFs) and the top quark mass with higher precision.

Despite previous progress, existing theoretical models often fail to describe data uniformly across all kinematic bins, particularly in extreme regions (high momentum/mass) and high-dimensional distributions.

2. Methodology

The report summarizes results from the ATLAS and CMS collaborations using the full Run 2 dataset ($\sqrt{s} = 13$ TeV) with integrated luminosities of 140 fb$^{-1}$ (ATLAS) and 138 fb$^{-1}$ (CMS). The analysis employs several advanced techniques:

• Event Selection & Reconstruction:

  • Single-Lepton Channel: Uses resolved topologies ($p_T < 500$ GeV) and boosted topologies (overlapping decay products). Jet assignment maximizes likelihood functions with constraints on $W$-boson and top masses. Neural Networks (NNs) distinguish signal from background in boosted regimes.
  • Dilepton Channel: Utilizes kinematic fits to reconstruct neutrino 4-vectors. An alternative "looser" selection preserves sensitivity for future top mass extractions.
  • Jet Substructure: Large-radius jets ($R=1.0$) are reconstructed using the anti-$k_t$ algorithm for boosted $t\bar{t}$ events.
  • $WbWb$ Inclusive: Defines the final state directly as $WbWb$ to include both $t\bar{t}$ and $tW$ processes, studying their interference.

• Unfolding & Statistical Analysis:

  • Data is unfolded from detector level to particle level (post-decay) and parton level (pre-decay) to allow direct comparison with theory.
  • Iterative Bayesian Unfolding (IBU) and TUnfold (regularized matrix inversion) are used to correct for acceptance, resolution, and efficiency.
  • Systematic uncertainties are dominated by jet energy scale (JES), integrated luminosity, and signal modeling (PDFs, PS).

• Theoretical Comparison:

  • Results are compared against various MC generators (Powheg+Pythia, MG5_aMC@NLO, Herwig) and fixed-order calculations (NLO, NNLO QCD).
  • Specific attention is paid to interference modeling schemes: Diagram Removal (DR) vs. Diagram Subtraction (DS).

3. Key Contributions

The paper presents a comprehensive suite of differential measurements that push the boundaries of current top quark physics:

1. First Combined Resolved/Boosted Analysis (CMS): The first analysis to combine resolved and boosted topologies to determine the full differential cross-section spectrum in the single-lepton channel, extending the measurement range to several TeV.
2. Triple-Differential $t\bar{t}$ Measurements (CMS): First measurements of triple-differential cross-sections as a function of the full $t\bar{t}$ kinematics ($p_T$, invariant mass, rapidity), providing crucial input for future PDF extractions.
3. Jet Substructure in Boosted Regime (ATLAS): Detailed study of eight substructure variables (e.g., Les Houches angularities, N-jettiness) in boosted $t\bar{t}$ events, testing the modeling of parton showering and hadronization.
4. Inclusive $WbWb$ Interference Study (ATLAS): A direct measurement of the $WbWb$ final state (combining $t\bar{t}$ and $tW$) to probe interference effects, utilizing the $m_{bl}^{minimax}$ observable to maximize sensitivity.
5. Single Top $t$-Channel Asymmetry (ATLAS): Differential measurements of top vs. anti-top production in the $t$-channel, including the cross-section ratio $tq/\bar{t}q$, which is sensitive to the valence quark density of the proton.
6. Lepton Differential Distributions (ATLAS): Precise measurements of inclusive $e\mu b\bar{b}$ production and differential lepton distributions, comparing traditional models against state-of-the-art generators like Powheg MiNNLO and Powheg bb4$\ell$.

4. Results

• Agreement with Theory:

  • NNLO QCD: Calculations at NNLO provide a significantly improved description of parton-level cross-sections with reduced theoretical uncertainties compared to NLO.
  • MC Generators: Generators like Powheg interfaced with Pythia/Herwig generally describe particle-level data well in standard kinematic regions.
  • Improved Models: The Powheg MiNNLO and Powheg bb4$\ell$ models show improved descriptions of lepton distributions compared to the traditional Powheg hvq model.

• Discrepancies and Tensions:

  • High-Energy Tails: No single theory model describes the data across all bins. Significant discrepancies appear in extreme kinematic regions (high $p_T$, high invariant mass).
  • Jet Substructure: While observables sensitive to jet broadness agree with NLO QCD simulations, models fail to describe observables probing the three-prong structure (e.g., N-jettiness).
  • $WbWb$ Interference:
    • The Diagram Removal (DR) scheme best describes the data but overestimates the cross-section at the highest masses.
    • The Diagram Subtraction (DS) scheme underestimates the cross-section in the high-mass tail.
    • The bb4$\ell$ model (generating $l^+\nu l^-\bar{\nu}b\bar{b}$ directly) performs better but still underestimates the high-mass tail.
  • Single Top: Measured cross-section ratios ($tq/\bar{t}q$) are consistent with predictions but highlight the need for precise PDF constraints.

5. Significance

• Precision Physics: The reduction of uncertainties by factors of up to two (compared to previous analyses) allows for stringent tests of the SM and perturbative QCD.
• Model Validation: The results expose specific limitations in current MC generators, particularly regarding the modeling of interference effects ($t\bar{t}$ vs. $tW$) and the three-prong structure of boosted tops. This drives the development of higher-order calculations and improved parton shower algorithms.
• Future Inputs: The triple-differential measurements and precise lepton distributions provide essential constraints for future extractions of the top quark mass and Parton Distribution Functions (PDFs).
• Roadmap for Run 3: The paper establishes a baseline for the upcoming LHC Run 3, where increased luminosity and refined techniques are expected to further resolve the observed tensions in the extreme phase-space regions.

In conclusion, while higher-order QCD predictions have significantly improved the description of top quark data, the persistent discrepancies in extreme kinematic regimes and interference modeling indicate that the theoretical understanding of top quark production and decay is not yet complete.