Inclusive and differential measurements of the $\mathrm{t\bar{t}}\gamma$ cross section and the $\mathrm{t\bar{t}}\gamma$ / $\mathrm{t\bar{t}}$ cross section ratio in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}$ = 13 TeV collected by the CMS detector, this study presents inclusive and differential measurements of the $\mathrm{t\bar{t}}\gamma$ cross section and its ratio to the $\mathrm{t\bar{t}}$ cross section, all of which are found to be in agreement with Standard Model predictions.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful, high-speed particle racetrack. Inside, scientists smash protons together at nearly the speed of light to recreate the conditions of the universe just after the Big Bang.

This paper is a detailed report from the CMS Collaboration, one of the teams watching the race through a massive, 14,000-ton digital camera (the CMS detector). They are looking for a very specific, rare, and tricky event: Top Quark pairs shooting out a photon (a particle of light).

Here is the story of their findings, broken down with some everyday analogies.

1. The Main Event: The "Top Quark" and the "Flash"

In the subatomic world, the Top Quark is the heavyweight champion. It's the heaviest known particle, so heavy that it decays (falls apart) almost instantly. Usually, when two top quarks are created, they just vanish into other particles.

But sometimes, one of them gets excited and flashes a photon (a particle of light) before it disappears. This is the $t\bar{t}\gamma$ event.

• Why do they care? It's like watching a heavyweight boxer throw a punch, but instead of just hitting the opponent, the boxer also accidentally throws a glowing fireball. If the fireball behaves strangely, it might mean the boxer is using a new, unknown type of glove (New Physics) that the Standard Model (our current rulebook of physics) didn't predict.

2. The Challenge: Finding a Needle in a Haystack

The team analyzed data from 2016 to 2018, which corresponds to 138 "inverse femtobarns" of data.

• The Analogy: Imagine trying to find a specific, rare type of grain of sand on a beach that stretches from New York to London. To do this, they had to sift through trillions of collisions.
• The Strategy: They looked for events where two "leptons" (electrons or muons, which are like light, fast cousins of the top quark) and a photon appeared together. It's like looking for a specific trio of dancers in a crowded ballroom: two fast movers and one person holding a bright flashlight.

3. The "Production" vs. The "Decay"

One of the clever parts of this paper is how they separated the light source. The photon could come from two places:

1. The Production Stage (The "Spark"): The photon is emitted right when the top quarks are being created. This is the "pure" signal scientists want to study to test new physics.
2. The Decay Stage (The "Afterglow"): The photon is emitted as the top quark is falling apart. This is more like background noise.

The Result: They successfully separated these two.

• They measured the "Production" rate and found it matched the theory perfectly.
• They measured the total rate (Production + Decay) and it also matched the theory.
• The Verdict: The universe is behaving exactly as the Standard Model predicts. No new "magic gloves" were found... yet.

4. The "Ratio" Trick: Canceling the Noise

To get the most precise measurement, the scientists didn't just count the top quarks with light; they calculated a ratio.

• The Analogy: Imagine you are trying to measure the exact weight of a single apple, but your scale is a bit wobbly and the wind is blowing. Instead of weighing just the apple, you weigh the apple and a basket of oranges, then divide the apple's weight by the total weight. If the wind blows the whole scale up or down, the ratio stays the same.
• The Finding: They calculated the ratio of "Top Quarks with Light" to "Top Quarks without Light." The result was 0.0133. This tiny number means that for every 100 top quark pairs made, only about 1.3 of them flash a photon. This number matched the prediction perfectly.

5. The "Charge Asymmetry" Mystery

In physics, there's a subtle difference between matter and antimatter. Sometimes, particles prefer to fly in one direction more than the other.

• The Analogy: Imagine a crowd of people leaving a stadium. Usually, they exit evenly. But if there's a slight bias, maybe more people exit the left gate than the right.
• The Finding: The scientists looked to see if the Top Quarks (matter) and Anti-Top Quarks (antimatter) were exiting the collision at different angles. They found no significant difference. The crowd exited evenly. This is good news for the Standard Model, which predicts very little asymmetry here.

6. The "Fake" Light Problem

A major headache in this experiment was fake photons. Sometimes, a jet of particles (a spray of debris) looks like a photon to the detector, or a particle gets misidentified.

• The Analogy: It's like trying to spot a real firefly in a field, but there are also thousands of tiny LED lights on the grass that look exactly like fireflies.
• The Solution: The team used a clever statistical trick called the ABCD method. They divided their data into four zones based on how "clean" the light looked. By comparing the "dirty" zones to the "clean" zones, they could mathematically subtract the fake lights and count only the real fireflies.

Summary: What did they learn?

1. The Standard Model Wins: Every measurement they took—the total number of events, the energy of the particles, the angles they flew at—matched the theoretical predictions perfectly.
2. Precision is Key: They didn't just count the events; they measured them in tiny slices (differential measurements) to see if the physics changed at high energies. It didn't.
3. No New Physics (Yet): While they didn't find evidence of "New Physics" (like extra dimensions or new forces), this is actually a success. It tightens the net. If new physics does exist, it must be hiding in a very small, very specific corner that these measurements have now ruled out.

In short: The CMS team took a massive snapshot of the universe's most energetic collisions, filtered out the noise, and confirmed that the "Top Quark with a Flashlight" behaves exactly as our current best theories say it should. The universe is still playing by the rules, but the scientists are now watching the rules much more closely than before.

Technical Summary

1. Problem and Motivation

The production of a top quark-antiquark pair in association with a photon ($t\bar{t}\gamma$) is a critical process for testing the Standard Model (SM) of particle physics.

• Sensitivity to New Physics: Unlike other processes where new physics effects in the top quark's electromagnetic coupling appear only at higher orders in perturbation theory, $t\bar{t}\gamma$ production is sensitive to these effects at the Leading Order (LO). This makes it a powerful probe for anomalous top-photon couplings and New Physics (NP) in the context of the Standard Model Effective Field Theory (SMEFT).
• Charge Asymmetry: The interference between initial-state radiation (ISR) and radiation from top quarks induces a charge asymmetry in $t\bar{t}\gamma$ production. This asymmetry can be more pronounced than in standard $t\bar{t}$ production, offering a unique observable to test QCD predictions and potential CP-violating effects.
• Gap in Knowledge: While inclusive cross-sections and some differential distributions (lepton/photon observables) had been measured previously, this paper addresses the lack of differential measurements as a function of top quark kinematic properties and the first-ever measurement of the $t\bar{t}\gamma/t\bar{t}$ cross-section ratio ($R_\gamma$) in both inclusive and differential forms.

2. Methodology

Data and Simulation

• Dataset: Proton-proton collision data collected by the CMS detector at $\sqrt{s} = 13$ TeV during the 2016–2018 run, corresponding to an integrated luminosity of 138 fb$^{-1}$.
• Signal Selection: Events are selected requiring two oppositely charged leptons (electrons or muons) and one isolated photon. Events with $\tau$ leptons are included only if they decay to $e$ or $\mu$.
• Monte Carlo (MC) Simulation:
  • Signal ($t\bar{t}\gamma$): Modeled using MADGRAPH5_aMC@NLO at NLO accuracy in QCD. The process is split into two components:
    1. Production: Photon emitted from ISR or off-shell top quarks (sensitive to $t$-$\gamma$ coupling).
    2. Decay: Photon emitted from on-shell top quarks or decay products (FSR).
  • Backgrounds: Includes $Z\gamma$+jets, $tW\gamma$, Drell-Yan (DY)+jets, and diboson processes. Non-prompt photons (from hadron decays or misidentified jets) are estimated using data-driven methods.

Event Reconstruction and Selection

• Objects: Electrons/muons ($p_T > 25/15$ GeV), photons ($p_T > 20$ GeV, $|\eta| < 2.5$), and jets ($p_T > 30$ GeV, $|\eta| < 2.4$).
• Kinematic Reconstruction: A kinematic fit is used to reconstruct the top quark four-momenta by solving for neutrino momenta using constraints on $W$ boson and top quark masses.
• Background Estimation:
  • Prompt Photons: Estimated via MC, constrained by a control region (CR) selecting $Z \to \ell\ell\gamma$ events.
  • Non-Prompt Photons: Estimated using the ABCD method in data, utilizing photon isolation ($I_{ch}$) and shower shape ($\sigma_{i\eta i\eta}$) variables to separate prompt from non-prompt sources.

Statistical Analysis

• Fitting: A simultaneous maximum likelihood fit is performed on the Signal Region (SR) and Control Regions (CRs).
• Unfolding: Differential measurements are corrected for detector resolution and acceptance using a likelihood-based unfolding technique.
• Observables:
  • Inclusive: Total cross-sections and the ratio $R_\gamma = \sigma_{t\bar{t}\gamma} / \sigma_{t\bar{t}}$.
  • Differential: Measured as a function of photon $p_T$, lepton $p_T$, top quark $p_T$, invariant mass $m(t\bar{t})$, and angular variables ($\Delta R$, $\Delta \phi$).
  • Asymmetry: Top quark charge asymmetry ($A_C$) defined by the difference in absolute rapidity between top and anti-top quarks.

3. Key Contributions

1. First Differential Measurements of $t\bar{t}\gamma$ vs. Top Kinematics: This is the first measurement of the $t\bar{t}\gamma$ cross-section differential in observables related to the top quark system (e.g., $p_T(t_1)$, $m(t\bar{t})$), providing crucial constraints on the modeling of the production process.
2. First Measurement of $R_\gamma$: The paper reports the first inclusive and differential measurement of the ratio between the $t\bar{t}\gamma$ and $t\bar{t}$ cross-sections. This ratio cancels many systematic uncertainties, offering a precision test of theory.
3. Separation of Production and Decay Components: The analysis explicitly separates the cross-section into the "production" component (photon from ISR/off-shell) and the "decay" component (photon from FSR), allowing for targeted tests of the top-photon coupling.
4. Charge Asymmetry Measurement: A precise measurement of the charge asymmetry in $t\bar{t}\gamma$ events, testing SM predictions at NLO.

4. Results

Inclusive Cross Sections

• Fiducial Cross Section ($t\bar{t}\gamma$ total): Measured as $137 \pm 8$ fb (stat+syst).
  • Agreement with SM prediction: $126 \pm 19$ fb.
• Fiducial Cross Section (Production component only): Measured as $56 \pm 5$ fb.
  • Agreement with SM prediction: $57 \pm 5$ fb.
• Ratio ($R_\gamma$): The inclusive ratio is measured to be $0.0133 \pm 0.0005$.
  • Agreement with SM prediction: $0.0127 \pm 0.0008$.

Differential Measurements

• Differential cross-sections were measured for seven observables at both particle and parton levels.
• Model Comparison:
  • The nominal simulation (MADGRAPH5_aMC@NLO with LO matrix elements for photon emission) describes the data shapes well, particularly for angular observables.
  • The alternative model (POWHEG with photon emission from parton showers) systematically overpredicts the data, suggesting that modeling photon emission via parton showers is insufficient for this process.
  • Fixed-order NLO QCD calculations show excellent agreement with data, especially for angular variables.

Charge Asymmetry

• The top quark charge asymmetry is measured to be $A_C = -0.012 \pm 0.042$.
• This result is compatible with both the SM prediction ($-0.004 \pm 0.001$) and the hypothesis of zero asymmetry. The precision is currently limited by statistical uncertainties.

5. Significance

• Validation of Standard Model: All measurements are consistent with SM predictions, reinforcing the current understanding of top quark electromagnetic interactions.
• Constraints on New Physics: The differential measurements, particularly those sensitive to high-$p_T$ tails and angular correlations, provide stringent constraints on SMEFT operators describing anomalous top-photon couplings.
• Improved Modeling: The results highlight the necessity of using matrix-element calculations rather than parton-shower approximations for modeling photon emission in $t\bar{t}$ events, guiding future theoretical developments.
• Precision Benchmark: The measurement of the $t\bar{t}\gamma/t\bar{t}$ ratio serves as a robust benchmark for future LHC runs, as it minimizes experimental systematic uncertainties and isolates the specific dynamics of the photon emission.

In conclusion, this paper provides the most comprehensive study of $t\bar{t}\gamma$ production to date, combining inclusive and differential measurements with a novel ratio analysis to probe the top quark's electromagnetic properties with high precision.