The effects of Higgs boson couplings through HZZ production at future lepton colliders

We focus on the sensitivity of the anomalous Higgs-gauge boson couplings at $H\gamma Z$ and $HZZ$ vertices through the process $\ell^- \ell^+ \rightarrow HZZ$ at CLIC and Muon Collider. Signal and relevant backgrounds events are generated in MadGraph within Standard Model Effective Field Theory (SMEFT) framework. These events are passed through Pythia for parton showering, and realistic detector effects are simulated by Delphes. The limits at 95% C.L. on the coefficients $\overline{c}_{HB}$ and $\overline{c}_{HW}$ are obtained at two b-tagging working points; loose and medium containing the Delphes card from CLIC and Muon Collider, corresponding to b-tagging efficiencies of 90% and 70%, respectively. We report that our best 95% C.L. limits on $\overline{c}_{HB}$ and $\overline{c}_{HW}$ coefficients are $[-0.00138; 0.00090]$ and $[-0.00162; 0.00026]$, respectively, at 3 TeV CLIC with an integrated luminosity of 5 ab$^{-1}$, and $[-0.00024; 0.00023]$ and $[-0.00020; 0.00009]$, respectively, at 10 TeV Muon Collider with an integrated luminosity of 10 ab$^{-1}$. These limits are compared with the present experimental and various phenomenological limits.