O_i^{(n)}},
 \;\;\;\; (n \geq 6), \end{aligned}$$ where ${\mathcal O}^{(n)}_i$ are dimension-$n$ operators which are $SU_C (3)\times SU_L(2) \times U_Y(1)$ invariant, and $C^{(n)}_i$ are the constants which represent the coupling strengths of ${\mathcal O}^{(n)}_i$. Leading effects of new physics can well be described by the dimension-six operators ${\mathcal O}^{(6)}_i$. The higher order operators can only become important at the scale close to $\Lambda$. In this paper, we concentrate on the effect of the dimension-six operators neglecting additional contributions from the higher order operators such as dimension-eight ones.

A systematic study for dimension-six operators has been given in the literature[@buchmuller]. The complete list of the dimension-six gauge invariant operators is given in Refs. [@buchmuller; @gounaris1]. In this paper, we only consider the CP-conseving operators. Then, the operators which directly modify the top-Yukawa interaction are the followings[@whisnant; @FengLiMaalampi]: $$\begin{aligned}
{\mathcal O}_{t1} =& \left(\Phi^\dag \Phi - \frac{v^2}{2}\right) 
\left( \bar{q}_L t_R \tilde{\Phi} + \mbox{h.c.}\right),\label{eq:Ot1}\\
{\mathcal O}_{Dt} =& \left( \bar{q}_L D_\mu t_R \right) 
 D^\mu \tilde{\Phi} + \mbox{h.c.}, \label{eq:ODt}\end{aligned}$$ where $q_L^{}=(t_L^{},b_L^{})^T$, $\Phi$ is the scalar isospin doublet (the Higgs doublet) with hypercharge $Y=1/2$, and $\tilde{\Phi} \equiv i \tau_2 \Phi^\ast$ with $\tau_i$ ($i=$1-3) being the Pauli matrices. The doublet filed $\Phi$ is parameterized as $$\begin{aligned}
 \Phi = \left[ 