are shown as a function of the anomalous coupling $C_{t1}$ for $\sqrt{\hat s} = m_H^{}=500$ GeV with $C_{Dt}$ being switched off. The SM prediction corresponds to the point of $C_{t1}=0$. The dimension-six operator ${\mathcal O}_{t1}$ only contributes to $\lambda \bar \lambda = LL,
$ and $\pm\pm$.

In Fig. \[fig:WW-tt-cDt\](a), the coefficient of ${\cal O}_{Dt}$ is taken to be $C_{Dt} = 10.2$ (Set D) and $-6.2$ (Set E) which are the lower and upper bounds from perturbative unitarity in Eq. (\[eq:pu-Dt\]). $C_{t1}$ is set to be zero. The SM prediction (Set A) is also shown for comparison. For higher $\sqrt{\hat s}$, cross sections with large dimension-six coupling $C_{Dt}$ are enhanced due to its momentum dependence.

In Fig. \[fig:WW-tt-cDt\](b), the helicity cross sections for $W^-_\lambda W^+_{\bar \lambda} \to t \bar t$ are plotted as a function of $C_{Dt}$ for all $W$ polarizations with $\sqrt{\hat s} = m_H^{}=500$ GeV. Again $C_{t1}$ is switched off.

As already discussed, although $C_{Dt}$ receives relatively strong constraint under the LEP precision data, $C_{t1}$ is free from them. Therefore, we conclude that the effect of ${\cal O}_{t1}$ can be really large as compared to the SM prediction. One might suspect why the correction due to ${\cal O}_{t1}$ can 