(Non)renormalizability of the $D$-deformed Wess-Zumino model

We continue the analysis of the $D$-deformed Wess-Zumino model that we introduced in M. Dmitrijevic and V. Radovanovic, J. High Energy Phys. 04 (2009) 108. The model is defined by a deformation that is non-Hermitian and given in terms of the covariant derivatives $D_{\alpha }$. We calculate one-loop divergences in the two-point, three-point, and four-point Green functions. Possibilities to render the model renormalizable are discussed.