This paper projects how well a proposed 100 TeV proton‑proton collider (the Future Circular Collider – hadron‑hadron, FCC‑hh) could constrain tiny deviations from the Standard Model in four‑boson interactions. The authors focus on the process pp → ZZγ where one Z decays to a same‑flavor, opposite‑sign lepton pair (electrons or muons), the other Z decays invisibly to neutrinos, and a photon is radiated. Those final states are written as ℓℓννγ and are sensitive to so‑called anomalous quartic gauge couplings (aQGCs) that would point to new physics beyond the Standard Model.

To make this projection the team simulated the FCC‑hh detector and event reconstruction and generated large samples of signal and background events. Events were produced at leading order with MadGraph5_aMC@NLO and showered with PYTHIA, using the FCC‑hh Delphes detector card and the NNPDF parton distributions. They included the main backgrounds (WWγ, WZγ, tt̄γ, Zγγ and ZZZ) and scanned four dimension‑8 effective‑field‑theory operator coefficients commonly used to parametrize neutral quartic gauge deviations: fT0/Λ4, fT8/Λ4, fT9/Λ4 and fM2/Λ4. For each coupling they varied only that one at a time and generated up to one anomalous vertex per simulated event.

The analysis uses three multivariate classifiers — Boosted Decision Trees (BDT), a decorrelated variant (BDTD), and Deep Neural Networks (DNN) — to separate possible aQGC signals from the Standard Model backgrounds. They preserve unitarity (the requirement that probabilities stay physical at high energy) by applying an operator‑dependent bound on the total transverse mass of the event. Expected sensitivities were computed in the Asimov approximation and for assumed background systematic uncertainties between 0% and 10%. The DNN gave the best signal‑background separation. For an integrated luminosity of 30 ab−1 the 95% confidence limits (no systematic uncertainty, combined electron+muon channel) are |fT0/Λ4| < 2.83×10−3 TeV−4, |fT8/Λ4| < 1.65×10−3 TeV−4, |fT9/Λ4| < 3.81×10−3 TeV−4 and |fM2/Λ4| < 8.97×10−3 TeV−4. With a 5% background systematic assumption they estimate about an order of magnitude improvement over current LHC limits.