Two-loop renormalization group equations for soft SUSY breaking scalar interactions: supergraph method

We obtain the one- and two-loop renormalization group equations for soft SUSY breaking scalar interactions in general, semi-simple SUSY gauge model, by using the supergraph method. We find that the method simplifies the calculation significantly because of the non-renormalization theorem and also because of the property that the relevant divergences are derived by simple algebra from those in exact SUSY case. A disagreement with the existing result is found in ${\beta }^{(2)}(m^2)$ and its cause is briefly discussed.