Multiplicity Distributions and Kno Scaling in the Parton Branching Model.

We present multiplicity distributions based on QCD parton branching processes and relate them to KNO scaling. We obtain a new non-scaling law for the probability distribution P(,mn) for m quarks and n gluons. In the case when quark evolution is neglected, the probability P(,n) approaches the KNO scaling limit for large energy and large n. For this case and also for the simpler pure gluon branching case, the KNO limit is approached from below, in agreement with data. We contrast our branching model with the stochastic picture. We find that both stochastic and branching picture can be described by the Fokker-Planck type equation but with a different physical meaning of the evolution parameter. We also discuss KNO scaling violations in the context of a three step QCD interaction process.