Measurements of inclusive and differential cross-sections of $t\bar{t}γ$ production in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

Using 140 fb$^{-1}$ of 13 TeV proton-proton collision data collected by the ATLAS detector, this study presents measurements of inclusive and differential cross-sections for top quark pair production with an associated photon, utilizing the photon transverse momentum distribution to constrain effective field theory operators related to the top quark's electroweak dipole moments.

The Gist

Imagine the Large Hadron Collider (LHC) as a massive, high-speed racetrack where tiny particles called protons are smashed together at nearly the speed of light. When they collide, they sometimes create a "family" of heavy particles called top quarks. Usually, these top quarks come in pairs (a top and an anti-top), and they immediately break apart into other particles.

This paper is like a detailed report card from the ATLAS detector, a giant camera watching this racetrack. The scientists looked at a huge amount of data (140 "inverse femtobarns," which is a fancy way of saying they watched about 140 trillion collisions) to study a very specific, rare event: When a top-quark pair is created, and at the same time, a flash of light (a photon) is shot out.

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

1. The Goal: Catching a Specific "Flash"

Most of the time, when top quarks are made, they just break apart. But sometimes, one of the particles involved in the crash shoots out a photon (a particle of light) right at the moment of creation.

• The Analogy: Imagine two cars crashing. Usually, they just crumple. But in this rare case, a spark flies off the engine exactly as they hit. The scientists wanted to count how often this happens and measure exactly how fast that spark is flying.
• Why it matters: This "spark" tells us about the invisible rules (forces) that govern how top quarks interact with light. It's like checking if the spark behaves exactly as the rulebook of physics (the Standard Model) predicts, or if it's doing something weird that hints at new, unknown physics.

2. The Hunt: Finding the Needle in the Haystack

The ATLAS detector sees billions of collisions, but most are just "noise" or common events. Finding these specific top-quark-plus-photon events is like finding a specific type of needle in a haystack.

• The Strategy: The scientists built a "filter" (using computer programs called Neural Networks) to sort the data. They looked for specific clues:
  • The Single-Lepton Channel: They looked for events with one photon, one "lepton" (a cousin of the electron, like a muon), and a bunch of other debris (jets), with at least one piece being a "b-jet" (a specific type of heavy debris).
  • The Dilepton Channel: They also looked for events with two photons and two leptons.
• The Background Noise: Sometimes, the detector gets tricked. A regular particle might look like a photon, or a jet might mimic a spark. The team used clever math and "control rooms" (areas of data they knew were safe) to figure out how much of what they saw was real and how much was just a trick of the light.

3. The Results: The Numbers Match the Theory

After sorting through the data, they counted the events and measured their properties.

• The Count: They found that this specific event happens about 319 times for every trillion collisions (measured in femtobarns).
• The Comparison: They compared their count to the "rulebook" prediction (a computer simulation called MadGraph). The prediction was 296.
• The Verdict: The difference between 319 and 296 is small enough to be explained by normal measurement errors. The data matches the current theory perfectly. There is no evidence of "new physics" breaking the rules here.

4. The Deep Dive: Checking the "Dipole Moments"

The scientists didn't just count; they measured how the photon was moving. They looked at the photon's speed (transverse momentum) and how far it was from the other particles.

• The Analogy: Imagine the top quark has a tiny magnetic "compass" inside it (called a dipole moment). If this compass is slightly off-center or weirdly shaped, the spark (photon) would fly out at a different angle or speed than expected.
• The Test: They used a mathematical framework called Effective Field Theory (EFT) to test if these "compasses" were behaving normally. They checked if the data fit the standard shape or if it was stretched or squashed.
• The Outcome: The data fit the standard shape perfectly. They also combined this with data from a similar process involving a Z boson (another heavy particle) to get an even tighter grip on the rules. Everything still matched the Standard Model.

Summary

In short, the ATLAS team took a massive snapshot of the universe's most energetic collisions to watch for a rare event where a top-quark pair shoots out a photon. They counted them, measured their speed, and checked if they followed the known laws of physics. Everything they found was exactly what the current laws of physics predicted. While they didn't find a "new" force of nature, confirming that the current rules work perfectly at these high energies is a crucial victory for our understanding of the universe.

Technical Summary

Technical Summary: Measurements of Inclusive and Differential Cross-Sections of $t\bar{t}\gamma$ Production

Problem and Motivation
The associated production of a top quark pair and a photon ($t\bar{t}\gamma$) serves as a critical probe for the electroweak coupling between the top quark and the photon ($t-\gamma$). This process is particularly sensitive to potential anomalous dipole moments of the top quark, which can be interpreted within the framework of Effective Field Theories (EFT). While photon radiation in $t\bar{t}$ events can originate from initial-state quarks, the top quarks themselves, or charged decay products, this analysis specifically targets the production stage where the photon is radiated. This topology offers the highest sensitivity to the $t-\gamma$ coupling. The primary objective is to measure inclusive and differential cross-sections to constrain EFT operators related to the electroweak dipole moments of the top quark.

Methodology
The analysis utilizes proton–proton collision data collected by the ATLAS detector at the Large Hadron Collider (LHC) during Run 2, corresponding to an integrated luminosity of $140 \text{ fb}^{-1}$ at a center-of-mass energy of $\sqrt{s} = 13 \text{ TeV}$. The study considers both single-lepton and dilepton decay channels of the $t\bar{t}$ system.

• Event Selection:

  • Single-lepton channel: Events are selected containing exactly one photon and one isolated lepton (electron or muon), at least four reconstructed jets, and at least one $b$-tagged jet.
  • Dilepton channel: Events require exactly two oppositely-charged, isolated leptons ($ee$, $e\mu$, or $\mu\mu$), at least two jets, and at least one $b$-tagged jet.
  • Kinematic Cuts: Additional kinematic requirements are applied to suppress backgrounds. Specifically, the angular distance $\Delta R = \sqrt{(\Delta\phi)^2 + (\Delta\eta)^2}$ between the photon and leptons, and between jets and the photon/leptons, must exceed 0.4.

• Background Estimation:
  Backgrounds are categorized based on whether the photon is prompt or a mis-reconstructed object.

  • Prompt photons: Estimated using Monte Carlo (MC) simulations for processes including $t\bar{t}\gamma$, $W/Z$, single-top, diboson, and $t\bar{t}$ associated with $W/Z$ bosons.
  • Fake/misidentified photons: Estimated using data-driven methods. Mis-reconstructed electrons are estimated using control regions enriched in $Z \to e\gamma$ and $Z \to ee$ events. Mis-reconstructed jets or hadronic-origin photons are estimated using the ABCD method.

• Signal Extraction:
  Neural networks (NNs) are employed to enhance the separation between signal and background.

  • In the single-lepton channel, a four-class NN defines a signal region enriched in $t\bar{t}\gamma$ production and three control regions enriched in $t\bar{t}\gamma$ decay, photon fakes, and other $t\bar{t}\gamma$ events.
  • In the dilepton channel, a binary classifier separates $t\bar{t}\gamma$ production events from all backgrounds.
  • Inclusive cross-sections are derived from a simultaneous profile-likelihood fit across the signal and control regions.

Key Contributions and Results
The paper presents measurements of cross-sections at the stable particle level within a fiducial phase space defined by high transverse momentum ($p_T$) photons and specific jet/lepton multiplicities.

• Inclusive Cross-Section: The combined inclusive cross-section for $t\bar{t}\gamma$ production is measured to be:
  $$\sigma_{t\bar{t}\gamma \text{ production}} = 319 \pm 15 \text{ fb} = 319 \pm 4 \text{ (stat)} +15_{-14} \text{ (syst) fb}.$$
  The uncertainty is dominated by the modeling of the $t\bar{t}\gamma$ processes. This result is compatible with the next-to-leading order (NLO) prediction from MadGraph5_aMC@NLO+Pythia 8, which is $296^{+29}_{-30} \text{ (scale)} +6_{-4} \text{ (PDF) fb}$.

• Differential Cross-Sections: Differential cross-sections are measured as functions of photon kinematic variables and angular separations between the photon, leptons, and jets. The distributions are compared against MC predictions (MG5_aMC+P8 and MG5_aMC+H7).

• EFT Interpretation: The results are interpreted in the context of the Standard Model Effective Field Theory (SMEFT). The analysis tests the sensitivity of the $t\bar{t}\gamma$ process to dipole operators $C_{tB}$ and $C_{tW}$, which couple to weak hypercharge and isospin gauge bosons, respectively.

  • Limits on Wilson coefficients are derived from the differential cross-section measurement of the photon $p_T$.
  • A simultaneous fit is performed using the photon $p_T$ spectrum from $t\bar{t}\gamma$ and the $Z$ boson $p_T$ spectrum from $t\bar{t}Z$ measurements, leveraging the fact that the same operators modify both processes.
  • Results are also presented in the rotated $(C_{tZ}, C_{t\gamma})$ basis to gauge the relevance of individual measurements.

Significance and Claims
The paper claims that the measured cross-sections and differential distributions are consistent with Standard Model predictions within uncertainties. The primary significance lies in the use of these measurements to set constraints on EFT parameters related to the electroweak dipole moments of the top quark. By combining $t\bar{t}\gamma$ and $t\bar{t}Z$ data, the analysis provides complementary constraining power on the Wilson coefficients. All derived limits on the real and imaginary parts of the coefficients are found to be compatible with the Standard Model predictions, with no evidence of anomalous dipole moments observed in the current dataset.