Discrete QCD, a new approximation for QCD cascades

We consider a new approximation scheme to the perturbative QCD cascades, discrete QCD, corresponding to an expansion in the phase space density of the emitted partons. It turns out that this density in phase space is very low and the reason can be traced to the physics behind the running coupling constant. The whole scheme only contains a single parameter, viz. the scale in the running coupling constant and is consequently strongly predictive. We show how to obtain analytical formulas for the multiplicity and the phase space distributions and compare to the results of the conventional cascade models (JETSET, ARIADNE and KERWIG) as well as earlier analytical approximation schemes.