Evidence of ZZ$\gamma$ production and observation of $4\ell\gamma$ in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb$^{-1}$ of proton-proton collision data at 13 TeV, the CMS experiment reports the first evidence for ZZ$\gamma$ production with a 3.7$\sigma$ significance and the first observation of inclusive 4$\ell\gamma$ production with a 5.0$\sigma$ significance, providing measured fiducial cross sections for both processes.

The Gist

The Big Picture: Catching a "Ghost" in the Machine

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful, high-speed particle cannon. It smashes protons together at nearly the speed of light. Most of the time, these collisions produce common debris, like a car crash where you see a lot of metal and glass flying everywhere.

But sometimes, very rarely, the crash produces something exotic and fragile, like a delicate glass sculpture that shatters instantly. This paper is about the CMS team finally catching a glimpse of one of these rare "glass sculptures": a collision that produces two Z bosons and a photon (a particle of light) all at once.

In the language of particle physics, this is called Triboson production (Tri = three, Boson = a type of force-carrying particle). It's like finding a specific, incredibly rare combination of three specific items in a pile of junk.

The Challenge: Finding a Needle in a Haystack

The scientists looked at data from 2016 to 2018, which corresponds to 138 "inverse femtobarns" of data. To put that in perspective, if you think of the data as a library, they read through billions of books to find just a handful of pages that mattered.

The process they were looking for ($pp \to ZZ\gamma$) happens so rarely that if you had a standard-sized football stadium filled with protons, you might only see this event happen once every few years. The predicted rate is about 47 "attobarns."

• Analogy: An attobarn is so small it's like trying to hit a specific grain of sand on a beach from a plane flying at 30,000 feet.

The Two "Detective Stories"

The paper actually reports on two different investigations, like a detective solving two related cases:

Case 1: The "Strict" Search (Evidence)

The Goal: Find the specific event where two Z bosons and a photon are born directly from the collision, without any extra "noise."

• The Rules: The scientists set very strict rules. The photon had to be energetic and far away from the other particles (like a guest at a party who isn't hugging anyone).
• The Result: They found 11 events where this happened. The computer predicted they should see about 10.8.
• The Verdict: This is Evidence. In science, "Evidence" is like seeing a footprint that strongly suggests a suspect was there, but you haven't caught them in the act yet. The statistical confidence is 3.7 standard deviations.
  • Analogy: If you flip a coin 100 times and get 60 heads, it's suspicious. If you get 90 heads, you are almost certain the coin is rigged. Here, the "rigging" is the new physics process. They are 99.9% sure it's not just a fluke, but they aren't 100% (which requires 5 standard deviations) just yet.

Case 2: The "Loose" Search (Observation)

The Goal: Find any event with four leptons (electrons or muons) and a photon, even if the photon was just a "side effect" (like a spark flying off a tire).

• The Rules: They relaxed the rules to include "Final State Radiation" (FSR). Imagine a car crash where a piece of the bumper flies off and hits a bystander. That's FSR. It's still a crash, just a slightly messier one.
• The Result: They found 24 events. The prediction was about 24.2.
• The Verdict: This is an Observation. This is the "gold standard" in particle physics. The statistical confidence is 5.0 standard deviations.
  • Analogy: This is like catching the suspect red-handed with the stolen goods. You can say with absolute certainty (99.9999% sure) that this process exists.

Why Does This Matter?

You might ask, "Why do we care about two Z bosons and a photon?"

1. Testing the Rules of the Universe: The Standard Model is the rulebook for how particles behave. This rulebook predicts exactly how often this rare event should happen. The CMS team measured the rate and found it matches the prediction almost perfectly.
   • Analogy: It's like checking if a new recipe works exactly as the chef wrote it. If the cake rises perfectly, the recipe is good. If it burns, the recipe (or our understanding of the ingredients) is wrong.
2. Looking for "New Physics": If the rate had been higher or lower than predicted, it would have been a huge discovery. It would mean there are hidden forces or particles we don't know about yet (like Dark Matter or extra dimensions) messing with the recipe.
   • The Good News: The recipe worked perfectly. The Standard Model is still holding strong.
   • The Exciting News: Because the measurement is so precise, we can now use it as a baseline. If we see future deviations, we will know exactly where to look.

The "Glass Ceiling" of Precision

The paper mentions that the measured cross-section (the probability of the event happening) is 60 attobarns for the strict case and 156 attobarns for the loose case.

• Analogy: If the entire LHC were a giant lottery machine, this result proves that the machine is working exactly as the engineers designed it. They have successfully measured the odds of winning the "Triple Z-Photon Jackpot," and the odds are exactly what the math said they would be.

Summary

• What they did: They smashed protons together and looked for a very rare combination of particles (2 Z bosons + 1 photon).
• What they found: They found it!
  • They have strong evidence for the "pure" version of the event.
  • They have definitive observation of the "messy" version (including side-sparks).
• What it means: The Standard Model of physics is passing another difficult test. The universe is behaving exactly as our best theories predict, even in these incredibly rare, high-energy scenarios.

It's a triumph of engineering and statistics, proving that we can hear the faintest whisper in a hurricane.

Technical Summary

1. Problem and Motivation

The paper addresses the measurement of rare electroweak (EW) processes involving the production of three vector bosons (triboson production) in proton-proton ($pp$) collisions. Specifically, it focuses on the process $pp \to ZZ\gamma$, where both $Z$ bosons decay leptonically ($Z \to \ell^+\ell^-$, where $\ell = e, \mu$), resulting in a final state of four leptons and a photon ($4\ell\gamma$).

• Scientific Context: Triboson processes are among the rarest accessible at the Large Hadron Collider (LHC), with cross-sections in the order of tens of attobarns (ab). They provide stringent tests of the Standard Model (SM), particularly regarding triple and quartic gauge couplings, and are sensitive to physics beyond the SM (BSM).
• Specific Challenge: The $ZZ\gamma$ channel is extremely rare. While ATLAS and CMS have previously observed $WZ\gamma$, $WW\gamma$, and $ZZ$ production, the $ZZ\gamma$ process had only recently been reported as "evidence" by ATLAS. This paper aims to provide the first evidence of $ZZ\gamma$ production in the CMS experiment and an observation of the more inclusive $4\ell\gamma$ process (which includes Final State Radiation contributions).

2. Methodology

Data and Simulation

• Dataset: Data collected by the CMS detector during Run 2 (2016–2018) at a center-of-mass energy of $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$.
• Signal Simulation:
  • The $pp \to 4\ell\gamma$ signal is simulated at Next-to-Leading Order (NLO) in QCD and Leading Order (LO) in EW interactions using MADGRAPH5_aMC@NLO.
  • The sample includes genuine triboson ($ZZ\gamma$) production and contributions from Final State Radiation (FSR) where a photon is emitted from a charged lepton.
  • Backgrounds ($ZZ$, $Z\gamma$, $t\bar{t}$, $VVV$, etc.) are simulated using various generators (POWHEG, MCFM, MADGRAPH) at NLO or LO, interfaced with PYTHIA 8 for parton showering and hadronization.
• Detector Simulation: GEANT4 is used to model particle interactions with the detector.

Event Selection and Reconstruction

• Lepton Selection: Events must contain four isolated leptons (electrons or muons) with $p_T > 7$ (5) GeV for electrons (muons) and $|\eta| < 2.5$ (2.4). Leptons must be isolated (scalar sum of $p_T$ in $\Delta R=0.3$ cone $< 35\%$ of lepton $p_T$).
• Photon Selection:
  • Signal photons must have $p_T^\gamma > 20$ GeV, $|\eta^\gamma| < 2.4$, and be separated from the barrel-endcap transition ($1.444 < |\eta| < 1.566$).
  • Recovery: Photons emitted at small angles ($\Delta R < 0.5$) from leptons are recovered and added to the lepton momentum to improve $Z$ mass resolution.
  • Separation: For the triboson search, a strict requirement $\Delta R(\ell, \gamma) > 0.5$ is applied to suppress FSR and enhance the genuine $ZZ\gamma$ component.
• Z Boson Reconstruction: Events must form two $Z$ candidates (oppositely charged, same-flavor pairs) with invariant masses between 60 and 120 GeV.
• Signal Regions (SR):
  1. Triboson SR ($ZZ\gamma$): Requires $m_{Z\gamma} > 100$ GeV for either lepton pair combined with the photon. This suppresses FSR and isolates the genuine triboson topology.
  2. Inclusive SR ($4\ell\gamma$): Removes the $m_{Z\gamma}$ requirement to include FSR contributions, studying the total $pp \to 4\ell\gamma$ cross-section.

Background Estimation

• Non-prompt Leptons: Estimated using a data-driven method based on "tight-to-loose" ratios in control regions (CRs) where one or both leptons fail tight isolation/ID criteria.
• Non-prompt Photons: Estimated using a data-driven "tight-to-loose" method in a $Z+\ell$ CR. The misidentification rate is measured and applied to the signal region.
• Rare Backgrounds: Processes like $t\bar{t}Z$, $t\bar{t}W$, and $WZ\gamma$ are estimated directly from simulation.

Statistical Analysis

• A maximum likelihood template fit is performed on the invariant mass distribution of the four-lepton and photon system ($m_{4\ell\gamma}$).
• The fit extracts the signal strength ($\mu$), defined as the ratio of the measured fiducial cross-section to the SM prediction.
• Systematic uncertainties (luminosity, efficiency, scale variations, PDFs, background modeling) are included as nuisance parameters.

3. Key Contributions

1. First CMS Evidence of $ZZ\gamma$: This paper reports the first observation of the $pp \to ZZ\gamma$ process in the CMS experiment.
2. Observation of Inclusive $4\ell\gamma$: It provides an observation of the inclusive $pp \to 4\ell\gamma$ process, which includes both the rare triboson component and the more common FSR component.
3. Fiducial Cross-Section Measurements: The paper provides precise measurements of the fiducial cross-sections for both the exclusive $ZZ\gamma$ and inclusive $4\ell\gamma$ channels.
4. Methodological Refinement: It demonstrates the use of distinct selection strategies (cutoff-based vs. multivariate) to optimize sensitivity for rare processes versus inclusive measurements.

4. Results

Triboson ($ZZ\gamma$) Measurement

• Significance: The observed significance is 3.7 standard deviations ($\sigma$), with an expected significance of 3.1 $\sigma$. This constitutes "evidence" for the process.
• Cross-Section: The measured fiducial cross-section is:
  $$\sigma_{\text{fid}}(pp \to ZZ\gamma \to 4\ell\gamma) = 60^{+27}_{-22} \text{ ab}$$
  The SM prediction is $47.56 \pm 0.04$ ab. The result is consistent with the SM.
• Uncertainties: Statistical uncertainty dominates (>98% of total uncertainty).

Inclusive ($4\ell\gamma$) Measurement

• Significance: The observed significance is 5.0 $\sigma$, with an expected significance of 4.2 $\sigma$. This constitutes an "observation" of the process.
• Cross-Section: The measured fiducial cross-section is:
  $$\sigma_{\text{fid}}(pp \to 4\ell\gamma) = 156^{+39}_{-35} \text{ ab}$$
  The SM prediction is $99.97 \pm 0.09$ ab. The result is consistent with the SM.
• Composition: The inclusive sample contains approximately 38% triboson events and 62% FSR events.

Systematic Uncertainties

• Dominant systematic uncertainties for the inclusive measurement arise from renormalization/factorization scales, electron efficiency, and non-prompt photon background modeling.
• For the triboson measurement, the dominant systematics are the normalization of the non-prompt photon background and electron efficiency.

5. Significance

• SM Validation: The measurements are in good agreement with Standard Model predictions, validating the theoretical calculations of triboson production and gauge couplings at the LHC.
• Sensitivity to New Physics: The $ZZ\gamma$ channel is sensitive to anomalous quartic gauge couplings (aQGCs). Establishing a baseline measurement is crucial for future searches for deviations that could indicate new physics.
• Record Low Cross-Section: The measured $ZZ\gamma$ cross-section of 60 ab is noted as the smallest cross-section ever measured at the LHC, highlighting the CMS experiment's capability to probe extremely rare processes with high luminosity.
• Future Prospects: These results pave the way for more precise measurements in the High-Luminosity LHC (HL-LHC) era, where the statistical precision will improve significantly, allowing for tighter constraints on BSM physics.

In summary, this paper represents a milestone in electroweak physics at the LHC, successfully isolating and measuring the rare $ZZ\gamma$ production mode and the inclusive $4\ell\gamma$ final state, confirming the Standard Model's predictions in a regime of extreme rarity.