Multiplicity Moments in Qcd and Experiment

QCD predictions for moments of parton multiplicity distributions are discussed. The next-to-leading terms and conservation law give rise to the peculiar oscillating shape of some ratio of the moments. The similar shape has been found by moment analysis of hadron multiplicities. Experimental data, theoretical Monte Carlo models and phenomenological fits have been used for ee, hh, hA, AA reactions at high energies. In multiparticle production the primary observable is the multiplicity distribution Pn which contains in the integrated form all the correlations of the system. First attempts to derive parton multiplicities in the double logarithmic approximation (DLA) of QCD provided extremely wide distributions compared to those found experimentally for hadrons. Later, the solution of the QCD equation for the generating function which takes into account higher order terms of the perturbative expansion and conservation law was found [1] and more efficient way of studying the distribution shape based on moment analysis was proposed (see review [2]). When applied to hadron multiplicities, it shows peculiar oscillating curves first derived for partons in QCD [3]. Their stability for reactions initiated by different projectiles and targets is rather astonishing [4]. Let us describe briefly the theoretical findings. The generating function is defined by