to the SM case. The decay modes $H\to t\bar t$ (tree), $H \to
  \gamma\gamma$, $H \to \gamma Z$ and $H \to gg$ (one loop) are largely modified at the leading order by the inclusion of ${\cal O}_{t1}$ and ${\cal O}_{Dt}$. The results for the decay branching ratios are shown in Fig. \[fig:plot-br\] for Set A, Set B, $\cdot\cdot\cdot$, and Set E.

![ Feynman diagrams for the subprocess $W^-W^+ \to t \bar t$ in the SM. []{data-label="fig:diagram-sm"}](feynman-diagram-WWtt.eps){width="14cm"}

Subprocess {#Sec:Subprocess}
==========

We here study the cross section for the subprocess $W^-W^+ \to t \bar t$[@RuizMorales:1999kz]. By using the results in this section, we evaluate the cross section of the full process $e^-e^+ \to W^-W^+ \nu \bar \nu \to t \bar t \nu \bar \nu$ in the the effective $W$ approximation (EWA)[@ewa] in Sec. IV, and compare it to the numerical results of calculation of the full matrix elements by the full use of the packages CalcHEP[@calchep] and LanHEP[@lanhep].

In the SM, Feynman diagrams for the subprocess are shown in Fig. \[fig:diagram-sm\]. Cross sections $\hat{\sigma}_{\lambda\bar\lambda}^{\rm SM}$ for the helicity amplitudes of $W_\lambda^- W_{\bar \lambda}^+ \to t\bar{t}$ with helicity sets ($\lambda$, $\bar \lambda$) are shown as a function of $\sqrt{\hat{s}}$ (the energy of the 