Supergraph Techniques and Two-Loop Beta-Functions for Renormalizable and Non-Renormalizable Operators

We present a construction kit for calculating two-loop beta functions in N=1 supersymmetric theories for the operators of the superpotential using supergraph techniques. In particular, it allows to compute the beta functions for every desired, even higher dimensional, operator of the superpotential from the wavefunction renormalization constants of the theory. We apply this method to calculate the two-loop beta functions for the lowest-dimensional effective neutrino mass operator in the Minimal Supersymmetric Standard Model (MSSM) and for the Yukawa couplings in the MSSM extended by singlet superfields and the mass matrix for the latter. Our method can be applied to any N=1 supersymmetric theory.