Wilsonian proof for renormalizability of $\mathcal{N}=1/2\mathrm{}$ supersymmetric field theories

We provide a Wilsonian proof for the renormalizability of four-dimensional quantum field theories with $\mathcal{N}=1/2\mathrm{}$ supersymmetry. We argue that the non-Hermiticity inherent to these theories permits assigning a noncanonical scaling dimension both for the Grassman coordinates and superfields. This reassignment can be done in such a way that the non(anti)commutativity parameter is dimensionless, and then the rest of the proof amounts to power counting. The renormalizability is also stable against adding standard four-dimensional soft-breaking terms to the theory. However, with the new scaling dimension assignments, some of these terms are not just relevant deformations of the theory but become marginal.