the usual complex conjugation. The notion of chirality is preserved in this model, i.e. the deformed product of two chiral superfields is again a chiral superfield. On the other hand, one half of ${\cal N}=1$ supersymmetry is broken and this is the so-called ${\cal N}=1/2$ supersymmetry. Another type of deformation is introduced in [@Ferrara] and [@D-def-us]. There the product of two chiral superfields is not a chiral superfield but the model is invariant under the full supersymmetry. Renormalizability of different models (both scalar and gauge theories) has been discussed in [@RenWZ], [@Penati], [@RenYM] and [@D-def-us]. The twist approach to nonanticommutativity was discussed in [@SUSYtwist].

In our previous paper [@miSUSY] we introduced a hermitian deformation of the usual superspace. The non(anti)commutative deformation was introduced via the twist $${\cal F} = e^{\frac{1}{2}C^{\alpha\beta}\p_\alpha \otimes\p_\beta
+ \frac{1}{2}\bar{C}_{\dot{\alpha}\dot{\beta}}
\bar{\p}^{\dot{\alpha}}\otimes\bar{\p}^{\dot{\beta}} } .\label{intro-twist}$$ Here $C^{\alpha\beta} = C^{\beta\alpha}$ is a complex constant matrix, $\bar{C}^{\dot{\alpha}\dot{\beta}}$ its complex conjugate and $\p_\alpha = \frac{\p}{\p \theta^\alpha}$ are fermionic partial derivatives. The twist (\[intro-twist\]) is hermitian under the usual complex conjugation. Due to this choice of the twist, the coproduct of the SUSY transformations becomes deformed, leading to the deformed Leibniz rule. The inverse of (\[intro-twist\]) defines the $\star$-product. It is obvious that 