II, we introduce dimension-six operators which directly affect the Higgs boson interaction with the top quark. Theoretical and experimental bounds for these anomalous couplings are also discussed. In Sec. III, we calculate the cross section of the subprocess $W^-W^+ \to t \bar t$ for each helicity set of the gauge bosons. A test of the amplitudes by using the equivalence theorem is also performed. In Sec. IV, we present the numerical evaluation of the deviation from the SM predictions. Conclusions are given in Sec. V. Some detailed analytic expressions are shown in Appendix.

Dimension-six operators {#Sec:Dimension-six operators}
=======================

The effect of new physics can be expressed in terms of higher dimensional operators, which are induced by integrating out the heavy non-standard particles. We here discuss such dimension-six operators which are relevant to the interaction between the Higgs boson and the top quark[^1].

Below the new physics scale (i.e., the SM cutoff scale) $\Lambda$, the non-standard interaction can be written in the effective Lagrangian as $$\begin{aligned}
{\mathcal L}^{\rm eff} =& {\mathcal L}_{\rm SM}^{}
              + {\mathcal L}_{\rm dim.6}^{}
              + {\mathcal L}_{\rm dim.8}^{} + \cdot\cdot\cdot,\end{aligned}$$ where ${\mathcal L}_{\rm SM}^{}$ is the SM Lagrangian, and $$\begin{aligned}
{\mathcal L}_{{\rm dim.}n} =& 
\frac{1}{\Lambda^{n-4}} \sum_i C_i^{(n)} {\mathcal 