Measurements of electroweak production of a photon in association with two jets in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb$^{-1}$ of proton-proton collision data at 13 TeV collected by the CMS experiment, this paper presents the first observation of electroweak production of a photon in association with two forward jets, measuring a cross section of 202 fb with over five standard deviations of significance and setting constraints on effective field theory operators.

The Gist

The Big Picture: Catching a Rare Ghost in a Storm

Imagine the Large Hadron Collider (LHC) at CERN as a massive, high-speed car race. Two beams of protons (tiny particles) are zooming toward each other at nearly the speed of light and smashing together. Usually, when these cars crash, they create a chaotic explosion of debris—thousands of particles flying everywhere. This is the "background noise."

The scientists in this paper (the CMS Collaboration) were looking for something very specific and very rare in that chaos: a single photon (a particle of light) appearing alongside two specific "tagging" jets (sprays of particles), created by a specific, delicate mechanism called "Vector Boson Fusion" (VBF).

Think of it like this:

• The Normal Crash (QCD): Most of the time, when protons collide, they act like two billiard balls hitting each other and shattering. This creates a huge mess of debris. This is the "QCD" background. It happens constantly and is very loud.
• The Rare Event (Electroweak VBF): Sometimes, two protons don't crash head-on. Instead, they graze past each other. As they pass, they each throw out a "messenger" particle (a vector boson). These two messengers meet in the middle, fuse together, and create a new particle (a photon). The original protons keep going but get nudged slightly to the side, creating two jets far apart from the center.

The Challenge: The "messy crash" (background) happens about 30 times more often than the "grazing fuse" (signal). Finding the signal is like trying to hear a single violin playing a specific note while standing in the middle of a roaring stadium crowd.

What Did They Do?

1. The Data: They looked at data collected between 2016 and 2018. That's a massive amount of information, equivalent to 138 "inverse femtobarns" (a unit of collision data).
2. The Filter: They set up strict rules to catch the "grazing fuse" events:
   • They needed a very energetic photon (high energy).
   • They needed two jets (sprays of particles) that were far apart from each other (like two people standing at opposite ends of a football field).
   • They looked for a "quiet zone" between those two jets. In the rare "grazing" events, there shouldn't be much debris between the jets. In the "messy crash" events, the space between the jets is usually full of garbage.
3. The Detective Work (AI): To separate the signal from the noise, they used a sophisticated computer program called a Boosted Decision Tree (BDT). Think of this as a super-smart detective that looks at all the clues (how far apart the jets are, how much energy the photon has, the shape of the event) and gives the event a "score."
   • High score = Likely the rare signal.
   • Low score = Likely just background noise.

The Results: A "Five-Star" Discovery

After running the numbers, the scientists found something exciting:

• They saw the signal. They didn't just guess; they actually observed the electroweak production of a photon with two jets.
• The Confidence: They calculated the odds that this was just a random fluke. The result was more than five standard deviations away from zero. In the world of particle physics, "five sigma" is the gold standard for claiming a discovery. It's like flipping a coin 10 times and getting heads every single time; the odds are so low you can be sure the coin is weighted.
• The Numbers: They measured how often this happens (the cross-section) and found it to be 202 fb (femtobarns). This matches very closely with what the Standard Model (our current best theory of physics) predicted: 177 fb. The fact that the measurement and the prediction agree is a huge win for our understanding of the universe.

Checking the Rules: The "Effective Field Theory" Test

The scientists also used this data to test if there are any "secret rules" of physics we haven't discovered yet. They used a framework called Effective Field Theory (EFT), which is like checking if the laws of physics have any tiny cracks or hidden levers we can pull.

• They looked for specific "Wilson coefficients" (mathematical knobs that would change how particles interact).
• The Verdict: The knobs are set exactly where the Standard Model says they should be. They didn't find any evidence of "new physics" or hidden forces. The universe, at least in this specific interaction, is behaving exactly as our current textbooks say it should.

Summary in Plain English

The CMS team successfully caught a very rare type of particle interaction where a photon is created by two protons "fusing" their energy without crashing head-on. They had to filter out a massive amount of background noise to find it.

• Did they find it? Yes.
• Is it real? Yes, with a confidence level that is the highest possible in science (5 sigma).
• Does it match our theories? Yes, perfectly.
• Did they find new physics? No, but proving that the old physics works in this difficult scenario is a major achievement.

This paper confirms that our current understanding of how light and matter interact at the subatomic level is robust, even in the most chaotic environments the universe can create.

Technical Summary

Technical Summary: Measurements of Electroweak Production of a Photon in Association with Two Jets

Problem and Motivation
Vector boson fusion (VBF) is a fundamental process in proton-proton collisions where two vector bosons radiated from incoming quarks fuse to produce a third boson. This mechanism provides direct sensitivity to triboson interactions and serves as a critical tool for validating parton shower models due to the characteristic "rapidity gap" (low hadronic activity) between the two forward tagging jets. While the VBF production of $Z$ and $W$ bosons has been extensively measured at the LHC, the electroweak (EW) production of a photon in association with two jets ($\text{EW } \gamma jj$) remains unmeasured. This process is challenging to isolate because it is overwhelmed by irreducible Quantum Chromodynamics (QCD) backgrounds, specifically dijet production with a hard final-state radiation (FSR) photon, which has a cross-section approximately 30 times larger than the signal. Furthermore, signal interference with QCD-induced processes complicates the theoretical modeling. This paper presents the first dedicated measurement of purely EW $\gamma jj$ production at the LHC.

Methodology
The analysis utilizes proton-proton collision data recorded by the CMS experiment at a center-of-mass energy of $\sqrt{s} = 13$ TeV during the 2016–2018 run, corresponding to an integrated luminosity of $138 \text{ fb}^{-1}$.

• Event Selection: Events are selected requiring a central photon ($|\eta| < 1.44$) with transverse momentum $p_T^\gamma > 200$ GeV and at least two jets. The leading and subleading jets (tagging jets) must satisfy $|\Delta\eta_{jj}| > 2.5$ and an invariant mass $m_{jj} > 500$ GeV to enrich the VBF topology.
• Simulation and Backgrounds: Signal samples ($\text{EW } \gamma jj$) and QCD-induced backgrounds ($\text{QCD } \gamma jj$) are generated using MADGRAPH5_aMC@NLO at next-to-leading-order (NLO) accuracy. The interference between EW and QCD processes is modeled at leading order. Other backgrounds, including $W\gamma$, $Z\gamma$, $\gamma\gamma$, and $t\bar{t}\gamma$, are also simulated.
• Background Estimation: Prompt photon backgrounds are estimated using simulation normalized to theoretical cross-sections. Non-prompt photons (from hadron decays or instrumental origins) are estimated using an ABCD method, utilizing orthogonal regions defined by relaxed photon identification criteria and modified $m_{jj}$ requirements.
• Signal Discrimination: To separate the signal from the dominant QCD $\gamma jj$ background, a Boosted Decision Tree (BDT) with gradient boosting is trained on kinematic variables including jet pseudorapidities, $\Delta\eta_{jj}$, $m_{jj}$, photon $p_T$, event centrality ($C_\gamma$), and the Zeppenfeld variable.
• Statistical Analysis: A binned maximum likelihood fit is performed on the BDT output distribution to extract the inclusive and differential cross-sections. Systematic uncertainties, including jet energy scale/resolution, photon identification, and theoretical scale variations, are treated as nuisance parameters.
• EFT Interpretation: To probe new physics in the $WW\gamma$ interaction, the results are interpreted within the Standard Model Effective Field Theory (SMEFT) framework. A Deep Neural Network (DNN) is trained to discriminate between the Standard Model and dimension-6 operators (specifically Wilson coefficients $c_W$ and $c_{HWB}$) to constrain anomalous couplings.

Key Contributions and Results

• First Observation: The paper reports the first observation of electroweak production of a photon in association with two forward jets. The signal is observed with a significance exceeding five standard deviations relative to the null hypothesis.
• Cross-Section Measurement: The measured fiducial cross-section is $\sigma_{\text{EW } \gamma jj} = 202^{+36}_{-32} \text{ fb}$. This result is in agreement with the Standard Model prediction of $177^{+13}_{-12} \text{ fb}$. The dominant systematic uncertainty arises from the jet energy scale and resolution.
• Differential Measurements: Normalized differential cross-sections are measured as functions of the tagging jets' pseudorapidities ($\eta_{j1}, \eta_{j2}$), the dijet invariant mass ($m_{jj}$), the photon transverse momentum ($p_T^\gamma$), event centrality ($C_\gamma$), and the Zeppenfeld variable. These measurements are unfolded to the particle level. While most observables agree with NLO QCD predictions, a slight tension (approx. two standard deviations) is noted in the pseudorapidity distribution of the softer tagging jet ($\eta_{j2}$), potentially due to mismodeling of the second jet in the QCD background.
• Rapidity Gap Validation: The hadronic activity within the pseudorapidity gap between tagging jets is studied. The measured rapidity gap fraction agrees with simulation, supporting the accuracy of parton shower modeling (PYTHIA 8.240) for VBF-like processes.
• EFT Constraints: Limits are set on the dimension-6 Wilson coefficients $c_W$ and $c_{HWB}$. The observed 95% confidence intervals are $[-0.11, 0.16]$ for $c_W$ and $[-1.6, 1.5]$ for $c_{HWB}$. These constraints are consistent with the Standard Model expectation.

Significance
The primary significance of this work is the establishment of the first measurement of purely electroweak $\gamma jj$ production at the LHC. By successfully isolating this rare process from overwhelming QCD backgrounds using advanced multivariate techniques and rigorous background estimation methods, the analysis validates the theoretical modeling of VBF processes involving photons. The agreement between the measured cross-section and Standard Model predictions reinforces the current understanding of electroweak triboson interactions. Furthermore, the derived constraints on SMEFT operators provide new limits on potential anomalous $WW\gamma$ couplings, complementing existing searches in $Zjj$ and $Wjj$ channels. The differential measurements and rapidity gap studies offer valuable inputs for refining parton shower models and improving the precision of future electroweak measurements.