theoretically by using the idea of partial wave unitarity[@pwu]. Due to the structure of a dimension-six operator, the two-body elastic scattering amplitudes is proportional to the square of the scattering energy, so that the coefficient becomes strong at some energy scale, and violate tree-level unitarity. The unitarity bounds for the coefficients $C_i/\Lambda^2$ are obtained by setting the scale of unitarity violation to be above $\Lambda$. The bounds for $C_{t1}$ and $C_{Dt}$ are evaluated as $$\begin{aligned}
&\left| C_{t1} \right| \le \frac{16\pi}{3\sqrt{2}} 
\left( \frac{\Lambda}{v} \right), 
\label{eq:pu-t1} \\
&-6.2 \le C_{Dt} \le 10.2.\label{eq:pu-Dt}\end{aligned}$$ These results are almost the same as those in Ref. [@gounaris2].

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The value of the anomalous coupling $C_{t1}$ is free from the constraint from current experimental data[@pdg; @hikasa], because it only affects the genuine interaction between the top quark and the Higgs boson which has not been measured yet. Therefore, only the theoretical consideration such as perturbative unitarity is important to constrain this operator. On the other hand, $C_{Dt}$ turns out to receive strong experimental limits from the electroweak rho parameter result[@pdg; @lep; @Barbieri:1999tm], since the operator ${\cal O}_{Dt}$ changes the interaction of the top quark with weak gauge bosons through the covariant derivative. The contribution of ${\cal O}_{Dt}^{}$ 