Soflty broken supersymmetry and the fine-tuning problem

The supersymmetry of the simple Wess-Zumino model is broken, in the tree-approximation, by adding all possible parity-even[mass]-dimension 2 and 3 terms. The model is then renormalized using BPHZ and the normal product algorithm, such that supersymmetry is only softly broken (in the original sense of Schroer and Symanzik). We show that, within the above renormalization scheme, none of the added breaking terms give rise to technical fine-tuning problems (defined in the sense of Gildener) in larger models, with scalar multiplets and hierarchy of mass scales, which is in contrast to what we obtain via analytic schemes such as dimensional renormalization, or supersymmetry extension of which. The discrepancy (which can be shown to persist in more general models) originates in the inherent local ambiguity in the finite parts of subtracted Feynman integrals. Emphasizing that the issue is purely technical (as opposed to physical) in origin, and that all physical properties are scheme-independent (as they should be), we conclude that the technical fine-tuning problem, in the specific sense used in this paper, being scheme dependent, is not a well-defined issue within the context of renormalized perturbation theory. (orig.)