Multiplicity distributions from branching equations with constant vertex probabilities

We present multiplicity distributions which are solutions to branching equations, based on the assumption that the shapes and energy dependence of multiplicity distributions are principally determined by hard parton scattering and subsequent branching. We consider the four processes g gg, q qg, g qq, and in a few cases g ggg. All vertex probabilities for these processes are taken to be constant. In this simple approximation, we find that Koba-Nielsen-Olesen scaling is systemically violated. We compare the properties of branching distributions with the properties of the widely used negative-binomial distribution and of the stochastic approach.