Sensitivity Reach on Anomalous Higgs Couplings via Triphoton Production for the Post-LHC Circular High-energy Hadron Colliders

The potential of triphoton production to obtain limits on anomalous Higgs boson couplings at \(H\gamma \gamma \) and \(HZ\gamma \) vertices is studied in the Standard Model Effective Field Theory (EFT) framework for the post-LHC circular high-energy hadron colliders: High Luminosity-LHC (HL-LHC), High-Energy LHC (HE-LHC), and Low-Energy FCC (LE-FCC) which are designed with standard configurations of 14 TeV/3 ab\(^{-1}\), 27 TeV/15 ab\(^{-1}\), and 37.5 TeV/15 ab\(^{-1}\). Madgraph in which the effective Lagrangian of the SM EFT is implemented using FeynRules and UFO framework is used to generate both background and signal events. These events are then passed through PYTHIA 8 for parton showering and Delphes to include realistic detector effects. After optimizing cuts on kinematics of three photons as well as the reconstructed invariant mass of the two leading photons, invariant mass of three leading photons is used to obtain constraints on the Wilson coefficients of dimension-six operators. We report on the result of a two-dimensional scan of \(\bar {c}_{\gamma }\) and \(\tilde {c}_{\gamma }\) couplings at 95% confidence level and compare with the LHC results. Our obtained limits without systematic error on \(\bar {c}_{\gamma }\) ( \(\tilde {c}_{\gamma }\)) are \([-3.15;1.41]\times 10^{-2}\) (\([-2.12;2.12]\times 10^{-2}\)), \([-1.21;0.78]\times 10^{-2}\) (\([-0.98;0.98]\times 10^{-2}\)), and \([-0.89;0.66]\times 10^{-2}\) (\([-0.77;0.77]\times 10^{-2}\)) for HL-LHC, HE-LHC, and LE-FCC, respectively.