Fluctuations and anomalous dimensions in QCD cascades

Abstract

A recently proposed multiplicity measure is used to study the properties of QCD cascades. We show that it is possible to define anomalous dimensions locally in rapidity space for the QCD cascade ine ⁺ e ⁻-annihilation events and in deep inelastic lepton scattering. In this way it will be possible to differentiate between different suggested models for multiple gluon emission. We also show that the properties of an event are to a surprisingly large degree deterimined by the first one or two gluons. Thus e.g. the multiplicity fluctuations ine ⁺ e ⁻-annihilation at theZ ⁰-pole are to about 90% determined by the hardest gluon. This implies that it may be principally difficult to make a distinct separation between the hard perturbative phase and the soft hadronization phase.