QCD Description of Particle Spectra up to LEP-1.5 Energies and the Running of $\alpha_s$

Abstract

Recent results on the energy spectra in QCD jets are reported. Within the Modified Leading Logarithmic Approximation (MLLA) and the Local Parton Hadron Duality (LPHD) model one finds a very good description of the $e^+e^-$ data from the lowest up to the LEP 1.5 energies. A model with fixed $\alpha_s$ can be excluded, already in certain finite energy intervals. The fits also extrapolate smoothly into the region of small particle energies, in particular, the data follow a scaling prediction for the low energy limit derived from the colour coherence of the soft gluon emission.