On the Seiberg-Witten map of $\mathcal{N}=2$ SYM theory in Non(anti)commutative Harmonic Superspace

We consider $\mathcal{N}=2$ supersymmetric U(1) gauge theory in a nonanticommutative $\mathcal{N}=2$ harmonic superspace with the singlet deformation. We generalize analytic superfield and gauge parameter to the nonanticommutative theory so that gauge transformations act on the component fields in a canonical form (Seiberg-Witten map). This superfield, upon a field redefinition transforms under supersymmetry in a standard way.