$\int {\mbox{d}}^8 z \theta\theta\bar{\theta}\bar{\theta} D^2 \Phi$ and $\int {\mbox{d}}^8 z \theta\theta\bar{\theta}\bar{\theta} (D^2 \Phi)^2$ were added in order to absorb divergences produced by $\int {\mbox{d}}^4 x F^3 
= \int {\mbox{d}}^8 z \theta\theta\bar{\theta}\bar{\theta} (D^2 \Phi)^3$ term. Since the model we work with is more complicated than the models of [@D-def-us] and [@Penati], it is not obvious which terms should be added. Let us list possible terms. Note that the new terms have to be invariant under the deformed SUSY transformations (\[defsusytr\]). This requirement gives three possibilities: $$\begin{aligned}
T_1 &=& \int {\mbox{d}}^4 x\hspace{1mm} 
P_1(\Phi\star\Phi)\Big|_{\bar{\theta}\bar{\theta}} 
\label{T1}\\
&=& \frac{1}{2} K^{ab}K_{ab}\int {\mbox{d}}^4 x\hspace{1mm} \big( 
\frac{1}{2}(\p_m\psi)\sigma^m\bar{\sigma}^n(\p_n\psi)-F\Box A
\big). \nonumber\\
T_2 &=& \int {\mbox{d}}^4 x\hspace{1mm} P_1(\Phi\star P_2(\Phi\star\Phi))\Big|_{\bar{\theta}\bar{\theta}} 
\label{T2}\\
&=& \frac{1}{4}K^{ab}K_{ab}\int {\mbox{d}}^4 x\hspace{1mm} \big(
-AF \Box A - \frac{1}{2}F\Box A^2 \nonumber\\
&& + \frac{1}{2}\psi\psi\Box A +
\p_m(A\psi)\sigma^m\bar{\sigma}^n(\p_n\psi)  \big).
\nonumber\\
T_3 &=& \int {\mbox{d}}^4 x\hspace{1mm} \Phi\star P_1(\Phi\star\Phi))
\Big|_{\theta\theta\bar{\theta}\bar{\theta}} 
\label{T3}\\
&=& \frac{3}{4}K^{ab}K_{ab} \int {\mbox{d}}^4 x\hspace{1mm} \Big(
F(\p_m\psi)\sigma^m\bar{\sigma}^l(\p_l\psi) - F^2\Box A \Big)\nonumber\\
&& + K^{m}_{\ a}K^{*na} \int {\mbox{d}}^4 x\hspace{1mm} \Big(
A(\Box A)(\p_m\p_n A) + A(\p_m\p_l A)(\p_n\p^l A)
\Big). \nonumber\end{aligned}$$ The term $T_1$ produces divergences of the type $\int {\mbox{d}}^4 x\hspace{1mm} \Phi^+ \Phi$ so it would not spoil the renormalizability of the model. However, it cannot improve renormalizability since divergences appearing in (\[2pointAll\]) 