Top Yukawa Coupling at the Muon Collider

We have presented a detailed study about the prospects for the measurement of the top Yukawa coupling in the vector boson fusion (VBF) production of a top quark pair at high energy muon colliders. By employing the effective $W$ approximation and the high energy limit for the helicity amplitudes of the subprocess $W^+ W^- \rightarrow t \bar t$, we have derived the energy scaling of the statistical signal significance in the presence of the anomalous couplings. The sensitivity on the top Yukawa coupling decreases as the bin energy increases. For the anomalous triple gauge boson couplings and the gauge-boson-fermion couplings with $E^2$ energy growing behavior for the interference term, the signal significance has mild increase at the beginning and start to decrease for $\hat s_{t \bar t} \sim 0.2 \, s_{\mu^+ \mu^-}$. The 95\% C.L. on the anomalous top Yukawa coupling is projected to be 5.6\% (1.7\%) at a 10 (30) TeV muon collider, which is comparable to the sensitivity of 2\% at the 100 TeV collider.