Measurements of ttW differential cross sections and the leptonic charge asymmetry at $\sqrt{s}$ = 13 TeV

Using 138 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}$ = 13 TeV collected by the CMS experiment, this paper presents measurements of differential cross sections and the leptonic charge asymmetry for top quark-antiquark pair production in association with a W boson, finding that normalized distributions agree with Standard Model predictions while absolute cross sections are slightly higher, consistent with previous inclusive results.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful, high-speed particle racetrack. Inside this ring, scientists smash protons together at nearly the speed of light, creating a chaotic explosion of energy that briefly recreates the conditions of the universe just after the Big Bang.

This paper is a report from the CMS Collaboration, one of the teams watching these crashes, specifically focusing on a very rare and tricky event: the production of a Top Quark pair accompanied by a W Boson.

Here is the story of what they found, explained without the heavy physics jargon.

The Cast of Characters

To understand the experiment, let's meet the players:

• The Top Quark: The "heavyweight champion" of the particle world. It's so massive and short-lived that it dies almost instantly, breaking apart into other particles.
• The W Boson: A messenger particle that carries the "weak force" (one of the four fundamental forces of nature). It's like a delivery truck that drops off a package and vanishes.
• The Signal (ttW): Usually, when Top Quarks are made, they come in pairs. Sometimes, they also bring a W Boson along for the ride. This is the ttW event. It's like finding a pair of twins (the Top Quarks) who are also holding hands with a specific delivery truck (the W Boson).
• The Background Noise: The racetrack is incredibly crowded. For every one of these rare "ttW" events, there are millions of boring, common crashes (like just two Top Quarks, or just a W Boson). The scientists' job is to find the needle in the haystack.

The Detective Work: How They Found It

The team looked at 138 "femtobarns" of data. To put that in perspective, that's like recording every single crash at the LHC for several years.

They were looking for specific "fingerprints" left behind by the decay of these particles. Since Top Quarks and W Bosons decay into other things, the scientists looked for events with:

1. Leptons: These are particles like electrons and muons (think of them as the "ghosts" that escape the crash).
2. Jets: Clumps of debris from the heavy quarks.

They focused on two specific scenarios:

• The "Same-Sign" Duo: Finding two leptons that have the same electric charge (both positive or both negative). This is rare in normal physics, so if they see it, it's a strong hint that a ttW event happened.
• The "Three-Lepton" Trio: Finding three leptons in a single crash.

The Two Strategies: The "Sniper" and the "Sweeper"

Because the data is so messy, the team used two different methods to separate the signal from the noise:

1. The "Sweeper" (Counting Method): This method is strict. It only looks at events that perfectly match the rules (very clean data). It's like a sniper who only shoots when the target is perfectly aligned. It's very safe and accurate but misses some events that are slightly messy. They used this for the "Three-Lepton" events.
2. The "Sweeper" (MVA Method): This method is more flexible. It uses a super-smart computer algorithm (a "Multivariate Analysis" or MVA) that looks at everything about the crash—the angles, the energy, the timing—and gives it a score. It's like a seasoned detective who can tell if a suspect is guilty even if they don't fit the perfect profile, because they know the "vibe" of the crime. They used this for the "Two-Lepton" events.

The Big Findings

1. The "Heavier" Than Expected Result
When the scientists counted how many of these ttW events happened, they found more than the Standard Model (our current best theory of physics) predicted.

• The Analogy: Imagine you have a recipe for a cake that says it should weigh 1 pound. You bake 100 cakes, and they all weigh 1.2 pounds. You know your scale is working, and your ingredients are correct, but the cake is just... heavier.
• The Result: The measured rate was about 17–29% higher than expected. This isn't a huge explosion of new physics, but it's a persistent "tension" that has been seen before. It suggests our theoretical recipe might be missing a tiny ingredient, or perhaps there's a subtle effect we haven't fully calculated yet.

2. The "Charge Asymmetry" (Who Goes Where?)
The team also measured a "leptonic charge asymmetry." In simple terms, they asked: "Do the positive leptons fly off in a different direction than the negative ones?"

• The Analogy: Imagine a spinning top. If you throw it, does the red side fly left and the blue side fly right? The Standard Model predicts a specific spin pattern.
• The Result: They measured a value of -0.19. The theory predicted -0.085. While the numbers aren't identical, the difference is small enough that it fits within the "margin of error" (uncertainty) of the experiment. So, the universe is behaving exactly as the Standard Model predicted regarding this specific spin.

Why Does This Matter?

You might ask, "Why do we care about a slightly heavier cake?"

• Testing the Limits: The Standard Model is our best map of the universe, but we know it's incomplete (it doesn't explain gravity or dark matter). Finding small discrepancies, like the higher-than-expected rate, is like finding a crack in the map. It tells us where to look for "New Physics" (like Supersymmetry or extra dimensions).
• The Background Problem: The ttW process is a major "background" for other exciting searches. For example, if you are looking for the production of four Top Quarks (a super-rare event), the ttW events look very similar and can hide the signal. By measuring ttW so precisely, the CMS team is cleaning up the noise so other scientists can see the rare signals more clearly.

The Bottom Line

The CMS team successfully mapped out the behavior of these rare Top Quark + W Boson crashes with incredible precision.

• Did they find new particles? No.
• Did they break physics? No.
• Did they confirm the Standard Model? Mostly yes, but with a lingering hint that the "production rate" might be slightly higher than our current math predicts.

It's a bit like checking the weather forecast. The forecast said "sunny," and it was sunny, but it was slightly warmer than the model predicted. It's not a disaster, but it makes the meteorologists (physicists) want to tweak their models to get a perfect prediction next time.

Technical Summary

1. Problem and Motivation

The production of a top quark-antiquark pair in association with a W boson ($t\bar{t}W$) is a critical process for testing the Standard Model (SM) and probing physics beyond the Standard Model (BSM).

• Theoretical Sensitivity: The process is sensitive to top quark interactions with electroweak bosons. It receives contributions from quark-antiquark annihilation at Leading Order (LO) and gluon-quark channels at Next-to-Leading Order (NLO). It is also sensitive to electroweak corrections and potential four-quark contact interactions.
• Existing Tensions: Previous inclusive cross-section measurements by both ATLAS and CMS have consistently reported values 17–29% higher than SM predictions (calculated at NNLO), creating a significant tension.
• Charge Asymmetry: The $t\bar{t}W$ process exhibits a leptonic charge asymmetry ($A_c^\ell$) due to interference effects and the polarizing nature of the W boson. Measuring this asymmetry provides a robust probe for BSM physics that could modify these asymmetries.
• Background Role: $t\bar{t}W$ is the leading irreducible background for rare processes like four-top quark production ($t\bar{t}t\bar{t}$) and $t\bar{t}H$ production, particularly in final states with same-sign (SS) dileptons.

2. Methodology

The analysis utilizes proton-proton collision data collected by the CMS experiment at $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$ (2016–2018).

Event Selection

Events are selected based on the presence of leptons (electrons or muons) and jets:

• Two-Lepton Region (2$\ell$SS): Events with exactly two same-sign leptons ($p_T > 25, 15$ GeV), at least 3 jets (with $\ge 2$ b-tagged), and missing transverse momentum ($p_T^{miss} > 30$ GeV).
• Three-Lepton Region (3$\ell$): Events with exactly three leptons ($p_T > 25, 15, 15$ GeV), at least 2 jets (with $\ge 2$ b-tagged), and at least one opposite-charge same-flavor (OSSF) pair.

Background Estimation

Backgrounds are categorized into four groups:

1. Non-prompt leptons: Estimated using a "tight-to-loose" ratio method in data sidebands.
2. Charge-misidentified leptons: Dominated by electrons; estimated using simulation corrected by data-driven scale factors derived from Z-boson mass regions.
3. Photon conversions: Estimated via simulation.
4. Irreducible backgrounds: Processes like $t\bar{t}Z$, $t\bar{t}H$, $WZ$, and $ZZ$ estimated using Monte Carlo (MC) simulations normalized to data or theoretical cross-sections.

Analysis Strategies

Two complementary methods are employed to extract differential cross-sections:

1. MVA-based Method (2$\ell$SS region): Uses a Gradient Boosted Decision Tree (BDT) trained on 37 kinematic variables (lepton/jet $p_T$, $\eta$, isolation, b-tag scores, etc.) to discriminate signal from background. This allows for a looser lepton selection, increasing signal efficiency.
2. Counting Method (3$\ell$ region and 2$\ell$SS cross-check): Relies on stricter lepton identification (tight working points) to achieve high signal purity without complex multivariate discrimination.

Statistical Framework

• Unfolding: A likelihood-based unfolding strategy is used to correct for detector effects and reconstruct particle-level distributions. The fit includes the Signal Region (SR) and multiple Control Regions (CRs) to constrain background normalizations.
• Systematics: Uncertainties include experimental factors (luminosity, jet energy scale/resolution, b-tagging, lepton ID) and theoretical factors (PDFs, renormalization/factorization scales, ISR/FSR).

3. Key Contributions

• Differential Cross-Sections: First measurements of $t\bar{t}W$ differential cross-sections as a function of 14 kinematic variables, including jet multiplicity, scalar sum of jet $p_T$ ($H_T$), leading/subleading jet and lepton $p_T$ and $\eta$, lepton separation ($\Delta R, \Delta \eta$), and invariant mass of the lepton system.
• Dual-Method Approach: The paper provides a robust comparison between an MVA-driven approach (optimized for sensitivity in the 2$\ell$SS channel) and a counting method (optimized for purity in the 3$\ell$ channel), validating the robustness of the results against modeling assumptions.
• Charge Asymmetry Measurement: A precise measurement of the leptonic charge asymmetry ($A_c^\ell$) in the 3$\ell$ channel, utilizing a neural network to correctly pair leptons with their parent top quarks.
• BSM Robustness Checks: Stress tests were performed using pseudodata reweighted by Effective Field Theory (EFT) operators (dim6top model) to ensure the measurement methods are resilient to large deviations from SM predictions.

4. Results

Differential Cross-Sections

• Normalized Distributions: The shapes of the normalized differential cross-sections are generally consistent with Standard Model expectations (specifically NLO QCD+EW predictions from aMC@NLO with FxFx matching).
• Absolute Cross-Sections: The measured absolute cross-sections are consistently higher than the SM predictions by approximately one standard deviation.
  • Observed inclusive cross-section: $\sigma_{obs} = 938 \pm 45 \text{ (stat)} \pm 52 \text{ (syst)}$ fb.
  • SM Prediction (NNLO): $745 \pm 52$ fb.
  • This confirms the tension observed in previous inclusive measurements.

Leptonic Charge Asymmetry

• The measured value is $A_c^\ell = -0.19^{+0.16}_{-0.18}$.
• This is consistent with the NLO SM prediction of $-0.085 \pm 0.006$.
• The result improves upon the sensitivity of previous ATLAS measurements.

Uncertainties

• Statistical uncertainties dominate the measurement (10–25% per bin).
• Systematic uncertainties are sub-dominant but significant, primarily driven by background estimation (non-prompt leptons) and theoretical modeling of $t\bar{t}H$ and $t\bar{t}Z$.

5. Significance

• Validation of SM Modeling: The agreement in normalized distributions suggests that the kinematic modeling of $t\bar{t}W$ production in current MC generators is largely correct, despite the normalization discrepancy.
• Background Constraints: These measurements provide crucial constraints on the $t\bar{t}W$ background, which is essential for future searches for rare processes like $t\bar{t}t\bar{t}$ and $t\bar{t}H$ in multilepton channels.
• BSM Sensitivity: The charge asymmetry measurement and the differential distributions serve as sensitive probes for BSM physics, particularly in the context of Effective Field Theories (EFT) that modify top-quark couplings.
• Resolution of Tension: While the paper does not resolve the normalization tension (the measured cross-section remains high), it provides the most detailed differential breakdown to date, helping theorists understand if the discrepancy lies in specific kinematic regimes or is a global normalization issue.

In summary, this work represents a high-precision characterization of the $t\bar{t}W$ process, confirming the persistent excess in the total cross-section while validating the kinematic modeling of the Standard Model, and setting a new benchmark for charge asymmetry measurements in top quark physics.