Precise measurement of the $t\bar{t}$ production cross-section and lepton differential distributions in $eμ$ dilepton events

Using 140 fb$^{-1}$ of ATLAS data from 13 TeV proton-proton collisions, this paper presents precise measurements of inclusive and differential $t\bar{t}$ cross-sections in $e\mu$ dilepton events, which are utilized to determine the top-quark pole mass and provide complementary $e\mu b\bar{b}$ production results.

The Gist

Imagine the Large Hadron Collider (LHC) as a massive, high-speed billiard table where tiny particles are smashed together at nearly the speed of light. In this specific experiment, the ATLAS team at CERN acted like super-precise statisticians trying to count a very specific type of "collision event" to understand the rules of the universe.

Here is a breakdown of what they did and found, using everyday analogies:

The Goal: Counting the "Heavyweights"

The scientists were looking for top quarks, which are the heaviest known elementary particles. Think of them as the "sumo wrestlers" of the particle world. When two protons collide, they sometimes create a pair of these sumo wrestlers (a top quark and an anti-top quark, or $t\bar{t}$).

The team wanted to answer two main questions:

1. How often do these pairs appear? (This is the "cross-section," or simply the frequency of the event).
2. How do they move? (This is the "differential distribution," or the speed and direction of the particles they produce).

The Detective Work: Finding the "eµ" Signature

Top quarks are unstable; they decay (fall apart) almost instantly. The team focused on a specific "fingerprint" left behind:

• The top quarks turn into W bosons and b-quarks.
• The W bosons then turn into an electron and a muon (two different types of light, fast particles) plus some invisible neutrinos.
• The b-quarks turn into jets of particles that can be "tagged" (identified) by the detector.

So, the team looked for a very specific scene in the data: a collision that produced one electron, one muon, and two tagged b-jets. It's like looking for a crime scene with exactly two specific types of footprints and two specific types of tire tracks to confirm a suspect was there.

The Method: The "Double-Tag" Trick

To count these events accurately without getting confused by background noise (other collisions that look similar), the team used a clever counting strategy called double-tagging.

Imagine you are trying to count how many people in a room are wearing red hats.

• Method A: Count everyone wearing exactly one red hat.
• Method B: Count everyone wearing exactly two red hats.

By comparing the numbers from Method A and Method B, and knowing how good your "hat detector" is, you can mathematically solve for the total number of people wearing red hats, even if your detector misses some of them. The paper used this math to separate the true top-quark events from the "noise" of other particle collisions.

The Results: A New Mass Measurement

After analyzing a massive amount of data (140 "inverse femtobarns"—which is a fancy way of saying they looked at a huge number of collisions), they found:

1. The Frequency: They calculated exactly how often top-quark pairs are made. This number is incredibly precise, with uncertainties as small as 0.3% in some areas.
2. The Weight (Mass): Because the frequency of top-quark production depends heavily on how heavy the top quark is, the team used their new, precise count to "weigh" the particle.
   • They didn't weigh it on a scale; they weighed it by seeing how often it appears.
   • Their calculation suggests the top quark's mass is 172.8 GeV (with a small margin of error). This is like determining the weight of a car by counting how many times it fits in a parking lot, rather than putting it on a scale.

The Comparison: New vs. Old Maps

The team also checked if their computer simulations (the "maps" used to predict how these particles behave) were accurate.

• They found that older simulation tools were like an old, slightly blurry map.
• Newer tools (like POWHEG-BOX MiNNLO) acted like a high-definition GPS, matching the real-world data much better. This means physicists can now trust their computer models more when predicting how these heavy particles behave.

Why It Matters (According to the Paper)

This isn't about building new technology or curing diseases. Instead, it's about refining the "Standard Model"—the rulebook of particle physics. By measuring these numbers with extreme precision, the team is checking if the universe behaves exactly as our current theories predict. If the numbers had been different, it might have hinted at "new physics" (unknown forces or particles). Since the numbers match the new, improved computer models, it confirms that our current understanding of the "heavyweight" sumo wrestlers of the particle world is solid.

Technical Summary

Technical Summary: Precise Measurement of the $t\bar{t}$ Production Cross-Section and Lepton Differential Distributions in $e\mu$ Dilepton Events

Problem and Motivation
The study of top-quark pair ($t\bar{t}$) production serves as a critical probe of Quantum Chromodynamics (QCD) at the highest accessible energy scales. Given the top quark's large mass, which is close to the electroweak symmetry breaking scale, it occupies a unique position within the Standard Model (SM). Furthermore, $t\bar{t}$ production constitutes a significant background for searches involving physics beyond the SM. While previous measurements of the inclusive cross-section ($\sigma_{t\bar{t}}$) for the $t\bar{t} \to W^+bW^-\bar{b} \to e^+\mu^-\nu\bar{\nu}b\bar{b}$ decay channel have improved in precision, this analysis aims to further refine these measurements using the full Run 2 dataset collected by the ATLAS experiment at the Large Hadron Collider (LHC).

Methodology
The analysis utilizes 140 fb$^{-1}$ of proton–proton collision data at a center-of-mass energy of $\sqrt{s} = 13$ TeV. The event selection focuses on the $e\mu$ dilepton channel, requiring an opposite-charge electron-muon pair and $b$-tagged jets. Jets are reconstructed using the anti-$k_t$ algorithm with a radius parameter $R = 0.4$, and $b$-tagging is performed using a multivariate discriminant based on deep-learning techniques, incorporating track impact parameters and reconstructed secondary vertices.

To estimate backgrounds from misidentified leptons, same-charge $e\mu$ pairs are utilized. The core measurement employs a double-tagging technique, counting events with exactly one ($N_1$) and exactly two ($N_2$) $b$-tagged jets within the opposite-charge sample. These counts are governed by a system of tagging equations involving the integrated luminosity ($L$), the efficiency for $t\bar{t}$ events to pass the $e\mu$ selection ($\epsilon_{e\mu}$), the $b$-tagging efficiency ($\epsilon_b$), and a tagging correlation coefficient ($C_b$). By solving these equations, the inclusive cross-section $\sigma_{t\bar{t}}$ and the correlation coefficient are determined.

The analysis also derives the fiducial cross-section ($\sigma_{t\bar{t}}^{\text{fid}}$) for events with particle-level leptons satisfying $p_T > 20$ GeV and $|\eta| < 2.5$. Additionally, ten single-differential and three double-differential cross-sections are measured as functions of lepton and dilepton kinematic variables for both the $t\bar{t} \to e\mu$ process and the $e\mu b\bar{b}$ final state.

Key Contributions and Results
The primary result is a precise determination of the inclusive $t\bar{t}$ production cross-section:
$$\sigma_{t\bar{t}} = 829.3 \pm 1.3 \text{ (stat)} \pm 8.0 \text{ (syst)} \pm 7.3 \text{ (lumi)} \pm 1.9 \text{ (beam)} \text{ pb}$$
This result is reported for a top-quark mass of $m_t = 172.5$ GeV. The measurement relies on the full Run 2 dataset and benefits from precise calibration of lepton efficiencies and improved modeling of lepton kinematics using the POWHEG-BOX MiNNLO event generator.

A secondary significant outcome is the extraction of the top-quark pole mass ($m_t^{\text{pole}}$). Exploiting the strong dependence of the predicted cross-section on $m_t^{\text{pole}}$, a Bayesian likelihood formulation is used to maximize compatibility with the measured $\sigma_{t\bar{t}}$. This yields:
$$m_t^{\text{pole}} = 172.8^{+1.5}_{-1.7} \text{ GeV}$$
This extraction utilizes the NNPDF3.1_notop parton distribution function set, which excludes top-quark data as input, thereby providing an independent constraint.

Differential measurements reveal that uncertainties as low as 0.3% are achieved for normalized distributions in specific fiducial regions. Comparisons with event generators indicate that state-of-the-art generators, specifically Powheg MiNNLO and Powheg bb4l, model lepton kinematics more accurately than the traditional Powheg hvq process.

Significance
The paper claims that these measurements provide high-precision input for refining the modeling of top-quark production at hadron colliders. By demonstrating the superior performance of modern event generators (MiNNLO, bb4l) over traditional approaches in describing lepton kinematics, the results offer a benchmark for future theoretical developments. The precise determination of $\sigma_{t\bar{t}}$ and the subsequent extraction of $m_t^{\text{pole}}$ contribute to the rigorous testing of the Standard Model and the reduction of systematic uncertainties in $t\bar{t}$-related background estimations for new physics searches.