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The Top Yukawa coupling profoundly influences several core mysteries linkedto the electroweak scale and the Higgs boson. We study the feasibility ofmeasuring the Top Yukawa coupling at high-energy muon colliders by examiningthe high-energy dynamics of the weak boson fusion to top quark pair processes.A deviation of the Top Yukawa coupling from the Standard Model would leadmodified $V V \rightarrow t\bar{t}$ process, violating unitarity at highenergy. Our analysis reveals that utilizing a muon collider with acenter-of-mass energy of 10 TeV and an integrated luminosity of 10 ab$^{-1}$allows us to investigate the Top Yukawa coupling with a precision surpassing1.5\%, more than one order of magnitude better than the precision from $t\bar th$ channel at muon colliders. This precision represents a notable enhancementcompared to the anticipated sensitivities of the High-Luminosity LHC (3.4\%)and those at muon colliders derived from the $t\bar{t} H$ process.

Top Yukawa Coupling Determination at High Energy Muon Collider