All-loop renormalizable Wess-Zumino model on bosonic-fermionic noncommutative superspace

We generalize the ordinary Wess-Zumino model to the bosonic-fermionic noncommutative (BFNC) superspace and study its renormalization. In our previous work that can be regarded as the key foundation of the present paper, we have proved that the BFNC Wess-Zumino model with the real mass and interacting constant is one-loop renormalizable up to the second order of BFNC parameters. Based on the result obtained, in the present paper we modify the one-loop renormalizable BFNC Wess-Zumino model by generalizing the mass and interacting constant to complex numbers, introduce the $U(1{)}_{\mathrm{R}}$ $R$ symmetry and $U(1{)}_{\mathrm{\Phi }}$ flavor symmetry in the modified model, analyze possible divergent operators in the effective action of the modified model by using the dimensional analysis method, and further give a new BFNC Wess-Zumino model that is renormalizable at all loops still up to the second order of BFNC parameters by imposing symmetries rather than doing a direct perturbative investigation.