Algorithm for the Fermionic Lines in Grace-susy* (revised Version**)

Algorithm of constructing Feynman amplitudes in the framework of minimal supersymmetic extension of the standard model is presented, which can be easily implemented in GRACE, the program of automatic generation of Feynman amplitudes. The equivalence of our method with the prescription given by Denner et al. is proved. 1.Introduction The fundamental theory of elementary particle physics is described by lagrangians. Given a lagrangian, the important task is to calculate the reaction rates, such as production rates, scattering cross sections or production cross sections of elementary particles, which should be confronted with experimental data to confirm that the theory based on the lagrangian is correct. As the S matrix is a nonlinear functional of the lagrangian, we usually cannot calculate the reaction rates exactly. The conventional approach is, therefore, to use the perturbative expansion of the S matrix in the power of the coupling constants and to calculate reaction rates to a certain order of coupling constants. Given the order of perturbation, one draws all the Feynman diagrams consistent with the theory and write down the corresponding Feynman amplitudes. The reaction rates are obtained by squaring the sum of the amplitudes and integrating over the phase space. It is this part of the calculation that is straightforward but very tedious. For example, for the process e + e − → W + W − , in the lowest order in perturbation there are only three Feynman diagrams and the computation of the cross section is rather easy. Already at the next order, however, there are as many as 140 Feynman diagrams (in a covariant gauge) and the calculation of the cross section by hand is a very