Mean multiplicity and fluctuations of the multiplicity of particles in hard jets

Analytic expressions which are not asymptotic at high energy are obtained in QCD for the mean multiplicity and for the dispersion of the multiplicity of quarks and gluons in hard jets. The deviation from the asymptotic expressions is very large, and the approach to the asymptotic behavior is very slow. In particular, it is found that in the region of energies E< or approx. =100 GeV the second correlation moment f2 is negative. To describe the experimental data obtained in the process of e+e- annihilation into hadrons, it is necessary to assume that each parton formed as the result of a quark-gluon cascade fragments on the average into several hadrons and that the dispersion of the number of hadrons is rather large