Soft and hard processes in QCD

Abstract

QCD equations for the generating functions are applied to separate soft and hard jets in $e^+e^-$-processes of multiparticle production. The dependence of average multiplicities and higher moments of multiplicity distributions of particles created in a "newly born" soft subjets on the share of energy devoted to them is calculated in fixed coupling gluodynamics. This dependence is the same as for the total multiplicity up to a constant factor if soft jets are defined as those carrying out a fixed share of initial energy at all energies. The constant factor depends on this share in a non-trivial way. Other definitions are also proposed. The relation between these quantities for soft and hard processes is discussed.