Two-loop renormalization group equations for soft supersymmetry-breaking scalar interactions: Supergraph method

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