we extend their study and examine the effect of these operators for the process $e^-e^+ \to W^-W^+ \nu\bar \nu \to  t \bar t \nu \bar \nu$: see Fig. \[fig:diagram-full\].

![ The top pair production via $W$ boson fusion []{data-label="fig:diagram-full"}](feynman-diagram-w-fusion-tt.eps){width="8cm"}

We note that ${\mathcal O}_{t1}$ yields the anomalous dimension-five interaction $W^-W^+ \bar t t$ in the large Higgs-boson mass limit via the $s$-channel process $W^-W^+ \to H^{\ast} \to t \bar t$. In Ref. [@larios], impact of dimension-five anomalous couplings $W^- W^+  \bar t t$ and $W_\mu^- W_\nu^+ \bar t \sigma^{\mu\nu}  t$ is studied on the cross section of $W^-W^+ \to t \bar t$ at an $e^- e^+$ linear collider. The tensor operator $W_\mu^- W_\nu^+ \bar t \sigma^{\mu\nu} t$ is not relevant to the new interaction between the Higgs boson and the top quark. In this paper, we concentrate on the effect of ${\mathcal O}_{t1}$ and ${\mathcal O}_{Dt}$ with the Higgs boson mass $m_H^{}$ to be at the electroweak scale and the SM cutoff $\Lambda$ to be at TeV scales.

Let us discuss possible allowed values for the anomalous couplings $C_{t1}$ and $C_{Dt}$ under theoretical consistencies and current experimental data. The coefficients $C_i/\Lambda^2$ of the dimension-six operators ${\cal O}_i$ can be constrained 