Nuclear Physics B 163 (1980) 477-518 © North-Holland Publishing Company INELASTIC DISTRIBUTIONS AND COLOR STRUCTURE IN PERTURBATIVE QCD A. BASSETTO* Dipt~rtimento di Fisica, Libera Universitfi di Trento, Italy M. CIAFALONI Scuola Normale Superiore, Pisa e Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, Italy G. MARCHESINI Istituto di Fisica dell' Universitfi di Parma e Istituto Nazionale di Fisica Nucleate, Sezione di Milano, Italy Received 2 August 1979 The tree-like evolution of a QCD jet in a planar gauge is studied, with particular emphasis on the soft parton region of the phase space. We calculate (in a gauge- invariant way) multiplicities and multiplicity distributions, and find a Q2 dependence which is more than logarithmic but less than a power. We also compute the resulting KNO scaling function, thus confirming the existence of long-range correlations. A general method for selecting semi-inclusive distributions is given, and applied to the study of colorless clusters. The mass of such clusters is of order of the confinement scale Qo, and their distributions are simply related to the ones of partons of off-shell mass Qo (a(Q2) ~ 1). We also give the general structure of the tree evolution at the "exclusive" level, and we find p± spectra which are damped in all relative transverse momenta. Nevertheless, the integrated exclusive probabilities sum up correctly to one in a non-trivial way. 1. Introduction The range of applicability of perturbative QCD has been recently extended to an increasing variety of hard and semihard processes. It is known [1-4] that a perturbative approach to hard processes (a(Q 2) small for large Q2>> m E) is restricted by the existence of mass singularities, i.e., by the fact that the limit of m 2 (light quark mass)-~ 0 is possibly not smooth because of infrared collinear diver- gences. Various efforts have therefore been made in looking for singularity-free processes. Such are, e.g., O'tot(e+e-), the jet cross sections at fixed angular and energy resolution [2], the energy flow [5], etc. Such quantities are calculable in * Associato all'Istituto Nazionale di Fisica Nucleare, Italy. 477