Quadratic divergences in dimensional-regularization finite quantum field theories

In the search for finite quantum field theories, a set of (supersymmetric as well as non-supersymmetric) models has been singled out by demanding one-loop finiteness in dimensional regularization. We demonstrate that the additional requirement of absence of quadratic divergences provides a clear distinction within this set: Only the supersymmetric theories are also free from quadratic divergences whereas the non-supersymmetric models are still quadratically divergent. (orig.)