A Measurement of alpha-s from the scaling violation in e+ e- annihilation

The hadronic fragmentation functionsof the various quark flavours and of gluons are measured in a study of the inclusive hadron production from Z0 decays with the DELPHI detector and are compared with the fragmentation functionsmeasured elsewhere at energies between 14 GeV and 91 GeV. A large scaling violation is observed, which is used to extract the strong coupling constant from a fit using a numerical integrationof the second order DGLAPevolution equations. The result is αs(MZ) = 0.124−0.007+0.006(exp) ± 0.009(theory) where the first error represents the experimental uncertainty and the second error is due to the factorization and renormalization scale dependence.