Renormalizations in softly broken SUSY gauge theories

The supergraph technique for calculations in supersymmetric gauge theories where supersymmetry is broken in a "soft" way (without introducing quadratic divergencies) is reviewed. By introducing an external spurion field the set of Feynman rules is formulated and explicit connections between the UV counterterms of a softly broken and rigid SUSY theories are found, It is shown that the renormalization constants of softly broken SUSY gauge theory also become external superfields depending on the spurion field, Their explicit form repeats that of the constants of a rigid theory with the redefinition of the couplings, The method allows us to reproduce all known results on the renormalization of soft couplings and masses in a softly broken theory, As an example the renormalization group functions for soft couplings and masses in the Minimal Supersymmetric Standard Model up to the three-loop level are calculated. (C) 1998 Elsevier Science B.V.