Probing Higgs and Top Interactions through the Muon Lens at multi-TeV Muon Colliders

We investigate the sensitivity of a future 10 TeV muon collider to dimension-6 operators in the Standard Model Effective Field Theory (SMEFT), focusing on Higgs and top quark production processes. The analysis includes two-fermion and four-fermion operators that induce electroweak vector and axial-vector interactions, as well as dipole, scalar, and tensor interactions involving muons. Many of these operators are only weakly constrained or difficult to probe at the LHC due to limited sensitivity and large SM backgrounds. We study the processes $\mu^+\mu^- \to Zh$, $\mu^+\mu^- \to \mu^+\mu^-h$, $\mu^+\mu^- \to t\bar t$, and $\mu^+\mu^- \to t\bar t h$, exploiting the energy-enhanced SMEFT effects at multi-TeV scales accessible to a muon collider. Using detailed simulations that incorporate differential information and angular distributions, we derive projected bounds on the relevant Wilson coefficients. We find that a 10 TeV muon collider can strengthen existing limits on muon-Higgs-gauge and muon-top interactions by up to an order of magnitude, surpassing even FCC-ee projections. Finally, we interpret these bounds in the context of representative UV scenarios, including models with vector-like lepton and scalar leptoquarks, highlighting the potential of a muon collider to probe new physics at scales well beyond the LHC reach.