at the International Linear Collider (ILC)[@ilc]. At the ILC, the top Yukawa interaction is expected to be measured through the process $e^-e^+ \to t \bar t H$[@tth] for a relatively light Higgs boson when it is kinematically allowed. For a heavier Higgs boson, it can be measured via the vector boson fusion process $e^-e^+ \to  W^-W^+\nu\bar\nu \to t \bar t \nu\bar\nu$[@w-fusion; @Kauffman:1989aq; @alcaraz].

Impact of non-standard interactions on the coupling of the top quark with the Higgs boson is of central interest in this paper. Below the new physics scale (i.e., the cutoff scale of the SM), such a new interaction is effectively described in terms of higher dimensional operators after the heavy new physics particles are integrated out. In particular, the low energy effect of new physics is expressed at the leading order by dimension-six operators in a gauge invariant Lagrangian. These dimension-six operators have been systematically studied in the literature[@buchmuller; @gounaris1; @gounaris2]. Some of them effectively give modifications to the top Yukawa coupling. Han et al. have discussed the effect of the dimension-six operators on the process of $e^-e^+ \to t \bar t H$[@han].

We here calculate the cross section of the process $e^-e^+ \to W^-W^+ \nu \bar 