Constraints on the anomalous Higgs boson couplings in $Z\gamma\gamma$ production at muon collider

We investigate the sensitivities on the Wilson coefficients of dimension-six operators associated with the anomalous $H\gamma\gamma$, $H\gamma Z$ and $HZZ$ vertices through the process $\mu^- \mu^+ \rightarrow Z\gamma\gamma$ at future muon collider. Signal events involving Higgs-gauge boson interactions and relevant backgrounds events at the muon collider designed with center-of-mass energy of 10 TeV and integrated luminosity of 10 ab$^{-1}$ are generated in Madgraph within the framework of the model-independent Standard Model effective field theory and detector effects are also included with corresponding detector cards in Delphes. The limits at 95% C.L. on the coefficients $\overline{c}_{HB}$ and $\overline{c}_{HW}$ are reported to be [-0.0052; 0.0040] and [-0.0034; 0.0023], respectively, and compared with the experimental and phenomenological limits.