\[fig:WW-tt-cDt\](a) and \[fig:WW-tt-cDt\](b), respectively. The cross sections of the corresponding processes $\omega^-\omega^+ \to t \bar t$ are also plotted by dotted curves for a test of the calculation by using the equivalence theorem. It can be seen that the cross sections for $W^-_L W^+_L \to t \bar t$ and $\omega^-\omega^+ \to t \bar t$ agree with each other at high energies $\sqrt{\hat{s}} \gg m_W^{}$. The Higgs boson mass is fixed as $m_H=500$ GeV.

In Fig. \[fig:WW-tt-ct1\](a), the coefficient of ${\cal O}_{t1}$ is taken to be $C_{t1} = \pm \frac{16\pi}{3\sqrt{2}} 
\left( \frac{\Lambda}{v} \right)$ (Set B and Set C), corresponding to the upper and lower bounds determined from perturbative unitarity in Eq. (\[eq:pu-t1\]). The effect of the other operator ${\cal O}_{Dt}$ is switched off. The SM prediction (Set A) is also shown for comparison. The cutoff scale $\Lambda$ is set to be $1$ TeV. It is found that the effect of ${\cal O}_{t1}$ can enhance the cross section from its SM prediction significantly. In particular, for $\sqrt{\hat{s}}$ higher than 400 GeV, values of the cross section can even be one order of magnitude greater than its SM results.

In Fig. \[fig:WW-tt-ct1\](b), the helicity cross sections for $W^-_\lambda W^+_{\bar\lambda} \to t \bar t$ 