Exact results for soft supersymmetry-breaking parameters in supersymmetric gauge theories

We obtain exact relations (valid to all orders in the coupling constant) for the running gaugino mass in supersymmetric gauge theories, treating the soft supersymmetry-breaking effects in the linear approximation. If a supersymmetry-breaking squark (selectron) mass term is introduced, our relation connects the renormalization group equation for this term with that for the gaugino mass. Exact relations for the threshold effects in the gaugino masses are derived. The key ingredients of our analysis are the use of the Wilsonian action and holomorphy of this action with respect to relevant parameters.