QCD explanation of oscillating hadron and jet multiplicity moments

Ratios of multiplicity moments, H_q (cumulant over factorial moments K_q/F_q), have been observed to show an oscillatory behaviour with respect to order, q. Recent studies of e^+e^- annihilations at LEP have shown, moreover, that the amplitude and oscillation length vary strongly with the jet resolution parameter y_{cut}. We study the predictions of the perturbative QCD parton cascade assuming low non-perturbative cut-off (Q_0\sim \Lambda_{QCD}\sim few 100 MeV) and derive the expectations as a function of the cms energy and jet resolution from threshold to very high energies. We consider numerical solutions of the evolution equations of gluodynamics in Double Logarithmic and Modified Leading Logarithmic Approximations (DLA,MLLA), as well as results from a parton MC with readjusted parameters. The main characteristics are obtained in MLLA, while a more numerically accurate description is obtained by the MC model. A unified description of correlations between hadrons and correlations between jets emerges, in particular for the transition region of small y_{cut}