Observation of $W^{+}W^{-}\gamma$ production in $pp$ collisions at $\sqrt{s}$ = 13 TeV with the ATLAS detector and constraints on anomalous quartic gauge-boson couplings

Using 140 fb$^{-1}$ of 13 TeV proton-proton collision data, the ATLAS experiment reports the first observation of $W^{+}W^{-}\gamma$ triboson production with a significance of 5.9 standard deviations and derives constraints on anomalous quartic gauge-boson couplings within the effective field theory framework.

The Gist

The Big Picture: Catching a Rare Cosmic "Triple Play"

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle smasher. It fires two beams of protons (tiny subatomic particles) at each other at nearly the speed of light. When they crash, it's like smashing two watches together at high speed; the gears, springs, and glass fly everywhere, creating a chaotic mess of new particles.

Usually, these collisions produce predictable debris. But sometimes, nature throws a "rare triple play." This paper reports that the ATLAS detector (a giant, high-tech camera surrounding the collision point) has finally caught a clear picture of a specific, rare event: the creation of two W bosons and one photon all at the same time.

• The W Bosons: Think of these as the "muscle" particles. They are heavy, short-lived carriers of the weak nuclear force (the force responsible for things like radioactive decay).
• The Photon: This is a particle of light.

Seeing these three specific particles appear together is like finding a specific, rare combination of cards in a shuffled deck. It's so rare that you need to look at 140 trillion collisions (140 inverse femtobarns of data) just to find about 250 of them.

The Detective Work: Finding a Needle in a Haystack

The scientists didn't just look for the particles; they had to prove they were real and not just a trick of the light or a common background noise.

The Analogy: The "Ghost" in the Room
When the W bosons decay (break apart), they turn into an electron and a muon (two types of heavy electrons) and some invisible particles called neutrinos. Neutrinos are like ghosts; they pass right through the detector without leaving a trace.

Because these "ghosts" escape, the detector sees an imbalance. It's like a bank vault where money is stolen, but the thief leaves no footprints. The only clue is that the total weight of the room has suddenly decreased. The scientists measured this "missing money" (called Missing Transverse Momentum) to confirm the neutrinos were there.

The Filter:
To find their rare event, the scientists set up a very strict filter:

1. The Opposite Charge: They looked for one positive electron and one negative muon (like a magnet pair).
2. The Flash: They looked for a high-energy photon (a bright flash of light).
3. The Ghost: They looked for the missing energy from the neutrinos.

They used a super-smart computer program (a "Boosted Decision Tree") trained to act like a seasoned detective. This program learned to distinguish between the "rare triple play" signal and the millions of boring, common collisions happening in the background.

The Result: A New Discovery

The team found 5.9 "sigma" worth of evidence.

• What does that mean? In the world of particle physics, "sigma" is a measure of certainty. A 5-sigma result is the "gold standard." It means there is less than a 1-in-3.5-million chance that this result was just a random fluke. It is a definitive Observation.

They measured how often this happens (the cross-section) and found it matches the Standard Model (our current best theory of physics) almost perfectly. It's like predicting exactly how many times a specific rare coin flip will land on heads after a million tries, and the result matches the prediction.

The Twist: Testing the Rules of the Universe

While the results matched the Standard Model, the scientists weren't just there to confirm what they already knew. They were also looking for glitches.

The Analogy: The "Speed Limit" of Physics
Imagine the Standard Model is a strict set of traffic laws. The scientists are driving a car (the experiment) and checking if anyone is speeding or breaking the rules.

They used a framework called Effective Field Theory (EFT) to ask: "What if there are hidden rules we don't know about yet?" They looked for signs of "Anomalous Quartic Gauge-Boson Couplings" (aQGC).

• Translation: They were checking if the W bosons and photons interact with each other in a way that is slightly stronger or stranger than the Standard Model predicts.

They set up a "trap" by looking specifically at collisions where the photon had extremely high energy (like a car speeding way past the limit). If new physics existed, it would show up here.

The Verdict:
No glitches were found. The "traffic laws" held up perfectly. However, this is actually good news! By not finding new physics, they have set tighter constraints (stricter speed limits) on where new physics could be hiding. They have effectively told future physicists: "If you are looking for new particles, don't look here; look somewhere else."

Why Does This Matter?

1. It's a Victory Lap: Observing this process is a technical triumph. It proves our detectors and computers are good enough to see the universe's most subtle tricks.
2. It Tests the Foundation: The Standard Model is our best map of reality. Every time we confirm a prediction like this, the map gets more reliable.
3. It Narrows the Search: By ruling out certain "weird interactions," they help guide the search for the next big discovery (like Dark Matter or a Theory of Everything) to the places where it's actually likely to be found.

In short: The ATLAS team took a massive pile of data, filtered out the noise, found a rare cosmic event that happens only once in a blue moon, confirmed it matches our best theories, and used that confirmation to draw a tighter fence around where the unknown mysteries of the universe might be hiding.

Technical Summary

1. Problem and Motivation

The Standard Model (SM) of particle physics is based on the non-Abelian $SU(2)_L \times U(1)_Y$ gauge group, which predicts specific interactions (couplings) between electroweak gauge bosons ($W$, $Z$, and $\gamma$). These interactions occur via triple gauge-boson couplings (TGC) and quartic gauge-boson couplings (QGC).

While TGCs have been extensively tested, QGCs are less constrained. Deviations from SM predictions in these couplings could signal "New Physics" (Beyond the Standard Model, or BSM). The production of three gauge bosons (triboson production), specifically $W^+W^-\gamma$, provides a unique laboratory to probe these QGCs. Previous studies by ATLAS and CMS at $\sqrt{s}=8$ TeV and 13 TeV had observed $WW\gamma$ processes, but a definitive observation with high significance and precise constraints on anomalous QGCs using the full Run-2 dataset (140 fb$^{-1}$) was required to test the SM at higher precision and constrain Effective Field Theory (EFT) parameters.

2. Methodology

Data and Detector:

• Dataset: Proton-proton collision data collected by the ATLAS detector at the LHC between 2015 and 2018.
• Energy: Center-of-mass energy $\sqrt{s} = 13$ TeV.
• Integrated Luminosity: 140 fb$^{-1}$.

Event Selection (Signal Region):
The analysis targets the $W^+W^-\gamma \to e^\pm \mu^\mp \nu \bar{\nu} \gamma$ final state. Key selection criteria include:

• Leptons: Exactly one electron and one muon with opposite electric charges.
  • Leading lepton $p_T > 27$ GeV, subleading $p_T > 20$ GeV.
  • Strict identification and isolation criteria (TightLH for electrons, Medium for muons).
• Photon: Exactly one isolated photon with $p_T > 20$ GeV and $|\eta| < 2.37$ (excluding the transition region).
• Missing Transverse Momentum ($E_T^{miss}$): $> 20$ GeV to account for neutrinos from $W$ decays.
• Vetos:
  • Z-boson veto: $|m(e\gamma) - m_Z| > 5$ GeV to suppress $WZ$ backgrounds where an electron is misidentified as a photon.
  • b-jet veto: To suppress top-quark backgrounds ($t\bar{t}\gamma$, $tW\gamma$).

Background Estimation:
Backgrounds were estimated using a combination of Monte Carlo (MC) simulation and data-driven methods:

• Prompt Backgrounds: $t\bar{t}\gamma$, $Z\gamma$, and $VZ\gamma$ ($V=W,Z$) were modeled using MC (Sherpa, MadGraph5_aMC@NLO) and normalized using dedicated Control Regions (CRs).
• Fake/Non-prompt Backgrounds:
  • Jet-to-photon ($j \to \gamma$): Estimated using a sideband technique and scale factors derived from data in regions with inverted isolation criteria.
  • Electron-to-photon ($e \to \gamma$): Estimated using a data-driven reweighting method based on $Z \to e^+e^-$ events.
• Control Regions: Defined to constrain normalizations of major backgrounds (e.g., $t\bar{t}\gamma$ CR requires 1 b-jet; $Z\gamma$ CRs require same-flavor lepton pairs).

Multivariate Analysis (MVA):

• A Boosted Decision Tree (BDT) using the XGBoost algorithm was trained to separate signal from background.
• Input Variables: 12 variables were used, with the top 10 selected based on feature importance. Key discriminators included transverse mass of the leading lepton ($m_T(\ell_1, E_T^{miss})$), di-jet separation ($\Delta R(jj)$), dilepton invariant mass ($m(\ell\ell)$), and subleading jet $p_T$.
• Training: Performed on MC samples with 5-fold cross-validation to ensure stability.

Statistical Analysis:

• A simultaneous binned maximum-likelihood fit was performed on the BDT output distributions across the Signal Region (SR) and all Control Regions.
• Nuisance parameters were included to account for systematic uncertainties (luminosity, detector calibration, theoretical modeling).

EFT Interpretation:

• To constrain BSM physics, the analysis utilized an Effective Field Theory (EFT) framework focusing on dimension-8 operators (anomalous quartic gauge couplings).
• The analysis was split into a low-$p_T(\gamma)$ region (used for SM measurement) and a high-$p_T(\gamma)$ region ($p_T(\gamma) > 500$ GeV) to enhance sensitivity to BSM effects, which typically manifest at high energies.
• Wilson coefficients for 13 specific operators ($f_{M0} \dots f_{T7}$) were constrained.

3. Key Contributions

1. First Observation of $WW\gamma$ by ATLAS: This paper reports the first observation of $W^+W^-\gamma$ production by the ATLAS collaboration with a significance exceeding the $5\sigma$ discovery threshold.
2. Precision Cross-Section Measurement: Provides a precise measurement of the fiducial cross-section for the $e^\pm \mu^\mp \nu \bar{\nu} \gamma$ final state.
3. EFT Constraints: Sets the first limits on 13 dimension-8 Wilson coefficients specifically derived from the $WW\gamma$ channel, probing anomalous quartic gauge couplings (aQGC) at high photon transverse momentum.
4. Methodological Rigor: Demonstrates a robust background estimation strategy combining MC normalization via CRs with data-driven techniques for fake-photon backgrounds, validated by a multivariate analysis.

4. Results

Observation and Significance:

• Observed Significance: $5.9\sigma$ (Expected: $6.0\sigma$).
• Signal Yield: The post-fit signal yield is $250 \pm 40$ events.
• Background Composition: The dominant backgrounds in the SR are $t\bar{t}\gamma$ (45%), $Z\gamma$ (13%), and $VZ\gamma$ (3%). Non-prompt photon backgrounds ($j \to \gamma$ and $e \to \gamma$) contribute approximately 13% combined.

Cross-Section Measurement:

• Measured Fiducial Cross-Section: $\sigma_{fid} = 6.2 \pm 0.8 \text{ (stat.)} \pm 0.6 \text{ (sys.)} \text{ fb} = 6.2 \pm 1.0 \text{ fb}$.
• Total Uncertainty: 16%.
• Comparison with SM: The result is in excellent agreement with the SM prediction of $6.1^{+1.0}_{-0.7}$ fb (calculated at NLO in QCD for 0-jet and LO for 1-2 jet events).
• Signal Strength: The measured signal strength relative to the SM is $\mu = 1.03^{+0.22}_{-0.21}$.

EFT Limits:

• 95% Confidence Intervals (CI) were derived for 13 dimension-8 Wilson coefficients.
• Example Limits (Observed):
  • $f_{M0}/\Lambda^4$: $[-6, 6] \text{ TeV}^{-4}$
  • $f_{T0}/\Lambda^4$: $[-1.1, 1.1] \text{ TeV}^{-4}$
• Unitarity: Limits were also evaluated using a "clipping" technique to enforce unitarity bounds. For instance, the coefficient $f_{M3}/\Lambda^4$ is constrained to $[-9.5, 9.5] \text{ TeV}^{-4}$ at a cutoff scale of $\sqrt{\hat{s}} = 1.9$ TeV.

5. Significance

• Validation of SM: The observation confirms the existence of the $W^+W^-\gamma$ triboson production process and validates the SM prediction for quartic gauge boson interactions at the 13 TeV scale.
• BSM Sensitivity: By setting constraints on dimension-8 operators, this analysis probes energy scales and interaction types that are complementary to existing diboson measurements. It specifically targets the quartic vertices which are less constrained than triple vertices.
• Future Physics: These results provide critical input for global EFT fits, helping to narrow the parameter space for potential new physics models that might manifest at higher energy scales (e.g., future colliders). The high-precision measurement of the cross-section also serves as a benchmark for theoretical calculations at higher orders.