Top-quark Yukawa coupling with a dimension-6 operator

We extend the standard top-quark Yukawa coupling with a dimension-6 operator in order to accommodate a CP violating complex phase with manifest gauge invariance. This leads to a new $ttHH$ contact interaction, along with many Goldstone boson couplings. We investigate the impact of the new interactions on a muon collider process ${\mu }^{-}{\mu }^{+}\to {\nu }_{\mu }{\bar{\nu }}_{\mu }t\bar{t}H$ compared with the standard dimension-4 top-Yukawa coupling. The unitarity bounds on the coefficient of the new physics operator is obtained from $W_L^{-}{W}_L^{+}$ and $HH$ initiated processes.