Hadron Multiplicities

We review results on hadron multiplicities in high energy particle collisions. Both theory and experiment are discussed. The general procedures used to describe particle multiplicity in Quantum Chromodynamics (QCD) are summarized. The QCD equations for the generating functions of the multiplicity distributions are presented both for fixed and running coupling strengths. The mean multiplicities of gluon and quark jets, their ratio, higher moments, and the slopes of multiplicities as a function of energy scale, are among the main global features of multiplicity for which QCD results exist. Recent data from high energy e+e- experiments, including results for separated quark and gluon jets, allow rather direct tests of these results. The theoretical predictions are generally quite successful when confronted with data. Jet and subjet multiplicities are described. Multiplicity in limited regions of phase space is discussed in the context of intermittency and fractality. The problem of singularities in the generating functions is formulated. Some special features of average multiplicities in heavy quark jets are described.Comment: 140 pages, 33 figures, version for Physics Report

Multiparticle production and perturbative QCD

The perturbative quantum chromodynamics (QCD) is quite successful in the description of main features of multiparticle production processes. Ten most appealing characteristics are described in this brief review talk and compared with QCD predictions. The general perturbative QCD approach is demonstrated and its problems are discussed. It is shown that the analytical calculations at the parton level with the low-momentum cut-off reproduce experimental data on the hadronic final state surprisingly accurately even though the perturbative expansion parameter is not very small. Moreover, the perturbative QCD has been able not only to {\it describe} the existing data but also to {\it predict} many new bright qualitative phenomena.Comment: 22 pages, 10 Figs, LATEX. Talk given at the conference "From the smallest to largest distances", ITEP, Moscow, 24-26 May 200

Multiparticle production and quantum chromodynamics

The theory of strong interactions, quantum chromodynamics (QCD), is quite successful in the prediction and description of main features of multiparticle production processes at high energies. The general perturbative QCD approach to these processes (mainly to e+e- -annihilation) is briefly formulated and its problems are discussed. It is shown that the analytical calculations at the parton level with the low-momentum cut-off reproduce experimental data on the hadronic final state in multiparticle production processes at high energies surprisingly accurately even though the perturbative expansion parameter is not very small. Moreover, it is important that the perturbative QCD has been able not only to describe the existing data but also to predict many bright qualitatively new phenomena.Comment: 30 pages, LATEX, 12 Figs available at www.ufn.ru; the review pap er to be published in Physics-Uspekhi 45 (5) (2002

Fractal Inspired Models of Quark and Gluon Distributions and Longitudinal Structure Function FL(x, Q2) at small x

In recent years, Fractal Inspired Models of quark and gluon densities at small x have been proposed. In this paper, we investigate longitudinal structure function F-L (x, Q2) within this approach. We make predictions using the QCD based approximate relation between the longitudinal structure function and the gluon density. As the Altarelli-Martinelli equation for the longitudinal structure function cannot be applied to Model I due to the presence of a singularity in the Bjorken x-space we consider Model II only. The qualitative feature of the prediction of Model II is found to be compatible with the QCD expectation.Comment: 11 pages, 4 figures, Accepted for publication on 10-07-2010 in Indian Journal of Physic

Fractal Propagators in QED and QCD and Implications for the Problem of Confinement

We show that QED radiative corrections change the propagator of a charged Dirac particle so that it acquires a fractional anomalous exponent connected with the fine structure constant. The result is a nonlocal object which represents a particle with a roughened trajectory whose fractal dimension can be calculated. This represents a significant shift from the traditional Wigner notions of asymptotic states with sharp well-defined masses. Non-abelian long-range fields are more difficult to handle, but we are able to calculate the effects due to Newtonian gravitational corrections. We suggest a new approach to confinement in QCD based on a particle trajectory acquiring a fractal dimension which goes to zero in the infrared as a consequence of self-interaction, representing a particle which, in the infrared limit, cannot propagate.Comment: To appear in Brazilian Journal of Physics, special edition for the proceedings of IRQCD, Rio de Janeiro, 5-9 June 200