Low and high energy limits of particle spectra in QCD jets

Charged particle energy spectra in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $e^+e^-$\end{document} annihilation are compared with the analytical predictions from the QCD evolution equation in the Modified Leading Log Approximation. With the nonperturbative initial condition shifted down to threshold as suggested by the Local Parton Hadron Duality picture a good description of the data from the lowest up to highest available energies results. The two essential parameters in this approach are determined from a moment analysis. The sensitivity of the fit to the running of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\alpha_s$\end{document} and to the number of active flavours (including a light gluino) is demonstrated. For very high energies the theory predicts a scaling behaviour in certain rescaled variables (“\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\zeta$\end{document}-scaling”). The data show an approximate behaviour of this type in the present energy range and come close to the predicted asymptotic scaling function for the small particle energies.