Probing CP-violating Higgs-Gauge Boson Couplings at the Future Muon Collider

We explore the sensitivity of future muon colliders to CP-violating interactions in the Higgs sector, specifically focusing on the process $\mu <^>- \mu <^>+ \rightarrow h \bar{\nu _{l}} \nu _{l} \rightarrow b\bar{b} \bar{\nu _{l}}\nu _{l}$. Using a model-independent approach within the framework of the Standard Model effective field theory, we analyze the contribution of dimension-six operators to Higgs-gauge boson couplings, emphasizing CP-violating effects. To simulate the process, all signal and background events are generated through MadGraph. The analysis provides 95% confidence level limits on the relevant Wilson coefficients $\tilde{c}_{HB}$, $\tilde{c}_{HW}$, $\tilde{c}_{\gamma }$, with a comparative discussion of existing experimental and phenomenological constraints. Our best constraints on $\tilde{c}_{HB}$, $\tilde{c}_{HW}$, $\tilde{c}_{\gamma }$ with an integrated luminosity of 10 ab$<^>{-1}$ are $[-0.017\,428;0.018\,991]$, $[-0.002\,880;0.002\,586]$, and $[-0.010\,784;0.011\,381]$, respectively. In this context, this study highlights the capability of future muon collider experiments to probe new physics in the Higgs sector, potentially offering tighter constraints on CP-violating Higgs-gauge boson interactions than those provided by current colliders.