Measurement of the quark and gluon fragmentation functions in Z(0) hadronic decays

The transverse, longitudinal and asymmetric components of the fragmentation function are measured from the inclusive charged particles produced in e(+)e(-) collisions at LEP. As in deep inelastic scattering, these data are important for tests of QCD. The transverse sigma(T) and longitudinal sigma(L) components of the total hadronic cross section sigma(tot) are evaluated from the measured fragmentation functions. They are found to be a sigma(T)/sigma(tot) = 0.949 +/- 0.001(stat.) +/- 0.007(syst.) and sigma(L)/sigma(tot) = 0.051 +/- 0.001(stat.) +/- 0.007(syst.) respectively. The strong coupling constant is calculated from sigma(L)/sigma(tot) in next-to-leading order of perturbative QCD, giving alpha(s)(M-Z) = 0.120 +/- 0.002(stat.) +/- 0.013(syst.) +/- 0.007(scale). Including non-perturbative power corrections :leads to alpha(s)(M-Z) = 0.101 +/- 0.002(stat.) +/- 0.013(syst.) +/- 0.007(scale). The measured transverse and longitudinal components of the fragmentation function are used to estimate the mean charged multiplicity, [n(ch)] = 21.21 +/- 0.01(stat.)+/- 0.20(syst.) The fragmentation functions and multiplicities in bb and light quark events are compared. The measured transverse and longitudinal components of the fragmentation function allow the gluon fragmentation function to be evaluated.