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Measurements of differential cross-sections of $WbWb$ production in the dilepton channel in $pp$ collisions at $\sqrt{s}$ = 13 TeV using the ATLAS detector

Using 140 fb $^{-1}$ of 13 TeV proton-proton collision data collected by the ATLAS detector, this paper presents the first measurement of differential cross-sections for $WbWb$ production in the dilepton channel at the particle level, providing crucial constraints on the modeling of top-quark processes and their interference effects.

Original authors: ATLAS Collaboration

Published 2026-07-14

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CC BY 4.0

Original authors: ATLAS Collaboration

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Large Hadron Collider (LHC) as the world's most powerful, high-speed particle racetrack. In this race, protons smash into each other at nearly the speed of light, creating a chaotic explosion of new particles. Among the debris, physicists are hunting for a very specific, rare combination: two heavy "top" quarks (the heaviest known particles) that decay into a final state containing two $b$ -quarks (bottom quarks), two $W$ bosons, and finally, two charged leptons (an electron and a muon).

Think of this final state, called $WbWb$, as a complex puzzle. Usually, when scientists see this puzzle, they assume it was built by a pair of top quarks ( $t\bar{t}$ ) splitting apart. But there's a twist: sometimes, a single top quark can team up with a $W$ boson and a $b$ -quark ($tW$) to create the exact same final picture.

Here is the tricky part: in the quantum world, these two different ways of building the puzzle can happen at the same time and "interfere" with each other, like two sound waves crashing together to create silence or a louder noise. This interference is a subtle, invisible force that makes it hard to know exactly how the puzzle was put together.

The Big Hunt
The ATLAS collaboration, a team of thousands of scientists using a giant detector called ATLAS, decided to investigate this interference. They looked at a massive pile of data—140 fb $^{-1}$ of proton-proton collisions recorded between 2015 and 2018 at a collision energy of 13 TeV. That's like watching 140 trillion collisions to find just the right ones.

They focused on events where they found exactly one electron and one muon (with opposite electric charges) and at least two jets of particles containing $b$ -quarks. By measuring how often these events happened and how the particles moved, they mapped out the "differential cross-sections." In plain English, this means they measured the probability of finding these particles moving at specific speeds and angles.

The "Minimax" Clue
To catch the interference in the act, the scientists invented a special variable called $m_{bl}^{\text{minimax}}$ . Imagine you have two $b$ -jets and two leptons. You try to pair them up in two different ways and calculate the mass of each pair. You pick the pairing that gives the largest mass, and then you look at the smallest of those largest masses.

If the event came from two top quarks (the "double resonance"), this number is usually kept below the mass of a top quark. But if the event involves the interference from the single-top process, this number can shoot up higher. It's like a speed trap that only catches the cars that are breaking the quantum rules.

What They Found (and What They Didn't)
The team compared their real-world measurements against various computer simulations (Monte Carlo generators) that try to predict how these particles should behave.

The Best Guess: The simulation that used a method called "Diagram Removal" (DR) to handle the interference matched the data the best. However, even this "best" guess failed to perfectly describe the very high-energy tail of the $m_{bl}^{\text{minimax}}$ distribution. It's like having a map that gets you to the city, but the details of the downtown streets are still a bit fuzzy.
The "Full State" Simulation: There was a more advanced simulation that tried to model the entire $WbWb$ process at once (including all interference effects naturally). While this was expected to be the most accurate, it actually underestimated the number of events in the high-energy tail. The paper notes that this simulation is still being reviewed and doesn't have a full set of error bars yet, so we can't say for sure if it's "wrong," but it doesn't fit the current data perfectly.
The "No-Go" Zone: The paper explicitly argues against the idea that a single, simple prediction can describe all the different measurements at once. Whether they looked at the speed of the jets, the mass of the particle groups, or the number of jets, no single computer model got every single variable right simultaneously. Some models got the jet speeds right but missed the lepton speeds; others got the masses right but missed the jet counts.

The Numbers
The scientists measured the total "fiducial cross-section" (a measure of how often this specific event happens within their detector's view).

In the region with exactly two $b$ -jets, the rate was 5.77 ± 0.01 (stat) +0.27 -0.29 (syst) ± 0.05 (lumi) pb.
In the region with two or more $b$ -jets, the rate was 5.97 ± 0.01 (stat) +0.27 -0.30 (syst) ± 0.05 (lumi) pb.

These numbers are precise, but the paper is careful to say the biggest uncertainty comes from not knowing exactly how the computer models should behave (signal modelling) and how well they can tag the $b$ -quarks (flavour tagging).

The Takeaway
This study is a massive upgrade from previous work, cutting the total uncertainty in half thanks to more data and better tools. The results show that while our current computer models are "reasonable," they aren't perfect. They struggle to capture the full complexity of the quantum interference between single-top and top-pair production.

The paper concludes that we need better computer simulations to untangle these effects. Until then, the "perfect" model that explains every angle, speed, and mass of these particle collisions remains a work in progress. The measurements provide a strict set of rules that future theories must follow, acting as a guide for the next generation of particle physics models.

Technical Summary: Measurements of Differential Cross-Sections of $WbWb$ Production in the Dilepton Channel

Problem and Motivation
At the Large Hadron Collider (LHC), the final state consisting of two $b$ -quarks and two $W$ bosons ($WbWb$) is a critical region for studying top-quark physics. This state is dominated by top-quark pair ( $t\bar{t}$ ) production but includes significant contributions from single-top processes ($tWb$). A fundamental challenge in modeling this process is the quantum mechanical interference between diagrams with one time-like top-quark propagator (singly resonant, $tW$) and those with two (doubly resonant, $t\bar{t}$ ). Standard theoretical approaches often rely on the narrow-width approximation, which separates these processes and neglects interference. However, fixed-order calculations at next-to-leading order (NLO) and beyond have demonstrated that this interference is non-negligible and introduces significant uncertainties in Standard Model (SM) measurements and Beyond the Standard Model (BSM) searches. Previous measurements by ATLAS using 36.1 fb $^{-1}$ of data provided initial insights, but a more precise characterization using the full Run 2 dataset is required to constrain theoretical models and improve the modeling of these interference effects.

Methodology
This analysis utilizes 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 fb $^{-1}$ recorded between 2015 and 2018. The study focuses on the dilepton decay channel ( $e\mu$ ), which offers a clean signature with reduced background from $Z$ +jets processes compared to same-flavor channels.

Event Selection: Events are selected requiring exactly one electron and one muon of opposite charge with transverse momentum $p_T > 28$ $p_{T} > 28$ GeV. The analysis defines two fiducial regions:
1. $2b$ -inclusive: Events with at least two $b$ -tagged jets ( $N_{b\text{-tags}} \ge 2$ ).
2. $2b$ -exclusive: Events with exactly two $b$ -tagged jets ( $N_{b\text{-tags}} = 2$ ), specifically optimized to measure the variable $m_{bl}^{\text{minimax}}$ , which is most sensitive to $t\bar{t}/tW$ interference.
Signal and Background Modeling: Signal samples ( $t\bar{t}$ and $tW$) are generated using Powheg Box v2 interfaced with Pythia 8. To handle the interference, the Diagram Removal (DR) scheme is used as the nominal approach, with Diagram Subtraction (DS) and full $bb4\ell$ (four-lepton) off-shell calculations used for comparison and uncertainty estimation. Backgrounds ( $Z$ +jets, dibosons, $t\bar{t}X$ , and fake/non-prompt leptons) are estimated using Monte Carlo (MC) simulations.
Unfolding: Measured distributions at the detector level are corrected for detector effects (efficiency, acceptance, and resolution) using an iterative Bayesian unfolding procedure. This yields differential cross-sections at the particle level within the defined fiducial phase spaces.
Systematic Uncertainties: A comprehensive set of uncertainties is evaluated, including object reconstruction (leptons, jets, $E_T^{\text{miss}}$ ), flavor tagging, pile-up modeling, and extensive signal modeling variations (parton shower, matrix-element matching, renormalization/factorization scales, and top-quark mass).

Key Contributions

First Combined Measurements: This work presents the first measurements of differential cross-sections for the combined $t\bar{t}$ and $tW$ signal process in the $WbWb$ final state, covering 11 kinematic observables.
Interference Sensitivity: The analysis specifically targets the $m_{bl}^{\text{minimax}}$ variable in the $2b$ -exclusive region to probe the interference between singly and doubly resonant top production.
High-Precision Dataset: By leveraging the full 140 fb $^{-1}$ Run 2 dataset, the analysis achieves a significant reduction in total measurement uncertainty compared to previous results, reducing the uncertainty in the interference-sensitive region from above 20% to approximately 10%.
Model Comparison: The results provide a rigorous benchmark for various NLO+PS (Next-to-Leading Order + Parton Shower) generators, including different interference schemes (DR vs. DS), alternative parton showers (Herwig 7), and higher-order corrections (NNLO reweighting and MiNNLOPS).

Results

Differential Cross-Sections: The differential cross-sections are measured as a function of lepton $p_T$ , jet $p_T$ , jet multiplicity ( $N_{\text{jets}}$ ), and various system masses and transverse momenta ( $m_{bbll}$ , $p_T^{bb}$ , $p_T^{bb4\ell}$ , etc.).
Interference Modeling: In the $2b$ -exclusive region, the DR scheme shows the best agreement with data for the $m_{bl}^{\text{minimax}}$ distribution, though it fails to accurately describe the tail of the distribution ( $>180$ GeV). The DS scheme and the full $bb4\ell$ calculation show poorer agreement in this high-mass region.
Global Agreement: No single NLO+PS prediction is capable of simultaneously describing all measured observables.
- The nominal Powheg+Pythia 8 (DR) model generally provides reasonable agreement but struggles with specific tails.
- The inclusion of NNLO corrections for the $t\bar{t}$ component (via NNLO reweighting or MiNNLOPS) significantly improves the description of most observables. Notably, the NNLO-reweighted sample is the only prediction that describes all variables simultaneously within uncertainties.
- Models with alternative $h_{\text{damp}}$ or $p_{T,\text{hard}}$ parameters are compatible with only a single observable each.
Integrated Cross-Sections: The integrated fiducial cross-sections are measured as:
- $2b$ -exclusive: $5.77 \pm 0.01 \text{ (stat.)} ^{+0.27}_{-0.29} \text{ (syst.)} \pm 0.05 \text{ (lumi.)}$ pb.
- $2b$ -inclusive: $5.97 \pm 0.01 \text{ (stat.)} ^{+0.27}_{-0.30} \text{ (syst.)} \pm 0.05 \text{ (lumi.)}$ pb.
  These measurements are consistent with theoretical predictions when normalized to NNLO+NNLL ( $t\bar{t}$ ) and NLO+NNLL ($tW$) cross-sections.

Significance
The paper claims that these measurements provide valuable constraints on the modeling of $WbWb$ production, particularly regarding the interference between $t\bar{t}$ and $tW$ processes. The results highlight that while current NLO+PS generators offer reasonable descriptions, they are insufficient for a simultaneous description of all kinematic distributions. The data serves as a critical input for refining future generator versions, particularly for the $bb4\ell$ off-shell calculation and the treatment of interference. The reduction in uncertainty achieved in this analysis allows for better discrimination between theoretical models, paving the way for more precise Standard Model tests and BSM searches in top-quark sectors. The authors emphasize that the current limitations are primarily driven by uncertainties in signal modeling (specifically interference and parton showering) and statistical uncertainties in the distribution tails, suggesting that future improvements will rely on both increased data (Run 3) and optimized MC simulations.

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