Supersymmetric Scaling Violations (I). An Algorithm to Solve the Supersymmetric DGLAP Evolution

We discuss a method for the numerical solution of the renormalization group equations of supersymmetric QCD with N=1 for the evolution of parton distributions. After a discussion of the original algorithm in which we show its connection to other finite-step expansions, such as the Furmanski-Petronzio (FP) expansion, we extend it to include both regular regions and supersymmetric regions in the evolution. Here we focus on a scenario with broken susy, characterized by a lighter gluino coupled to the standard evolution and a decoupled scalar quark. The formulation of the method is illustrated to next to leading order, with approximate matching conditions at the gluino threshold mass. A leading order implementation is presented. Modifications on the standard evolution are shown to be small down to $x=10^{-2}$ both for gluinos and for the distributions of quarks and gluons.