Unified QCD description of hadron and jet multiplicities

The evolution equation for parton multiplicities in quark and gluon jets which takes into account the soft gluon interference and energy conservation is solved numerically using the initial conditions at threshold. If the k⊥-cutoff Qc is lowered towards the hadronic scale Q0 of a few hundred MeV, the jets are fully resolved into hadrons. Both hadron and jet multiplicities in e+e− annihilation are well described with a common normalization. Evidence is presented within this perturbative approach that the coupling αs(k⊥) rises by an order of magnitude when approaching the low energy region. The ratio of hadron multiplicities in gluon and quark jets is found smaller than in previous approximate solutions of the evolution equation.