Analysis of anomalous Hγγ coupling in light-by-light collision at future muon collider

In this study, the process $\gamma\gamma \to \gamma\gamma$ is investigated to establish constraints on anomalous Higgs boson couplings at $H\gamma\gamma$ vertex within the framework of the Standard Model Effective Field Theory (SMEFT). The study is performed for a future muon collider operating at CoM energies of 10 and 30 TeV with integrated luminosities of 10 and 90 ab$^{-1}$, respectively, where the incoming photons are modeled using the Weizs\"acker-Williams approximation. Signal and background events are simulated using MadGraph, with the SMEFT Lagrangian implemented via FeynRules and UFO frameworks. Parton showering is evaluated with PYTHIA 8, and detector effects are accounted for using Delphes. Limits on the Wilson coefficients $\bar{c}_\gamma$ and $\tilde{c}_\gamma$ of the dim-6 operators without and with systematic uncertainties of 5% and 10% are reported at the 95% confidence level, demonstrating the potential of a high-energy muon collider to provide precise constraints on these couplings and presenting a significant improvement over experimental and related phenomenological results.