One-loop renormalizable Wess-Zumino model on a bosonic-fermionic noncommutative superspace

We construct a deformed Wess-Zumino model on the noncommutative superspace where the bosonic and fermionic coordinates are no longer commutative with each other. Using the background field method, we calculate the primary one-loop effective action based on the deformed action. By comparing the two actions, we find that the deformed Wess-Zumino model is not renormalizable. To obtain a renormalizable model, we combine the primary one-loop effective action with the deformed action, and then calculate the secondary one-loop effective action based on the combined action. After repeating this process a third time, we finally give the one-loop renormalizable action up to the second order of bosonic-fermionic noncommutative parameters by using our specific techniques of calculation.