Testing the running of the QCD coupling in particle energy spectra

The spectra of charged particles in the energy variable xi = log 1/x (''the hump backed plateau'') are analyzed in terms of moments in order to investigate the sensitivity to the running of alpha(s) in particular towards small scales, and to further test thereby the local parton hadron duality picture. The modified leading log approximation (MLLA) of QCD provides a very satisfying description of the e(+)e(-) data in the full range of c.m. energies from about 1 up to 91 GeV. The same calculation but with fixed coupling alpha(s) yields moments which are inconsistent with the data already close to threshold. In particular the soft particles (E less than or equal to 1 GeV) reflect directly the running of alpha(s).