Measurement of the quark and gluon fragmentation functions in Z0 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 \mbox{$\sigma_T/\sigma_{tot}=0.949\pm 0.001(stat.)\pm 0.007(syst.)$} and \mbox{$\sigma_L/\sigma_{tot}=0.051\pm 0.001(stat.)\pm 0.007(syst.)$} 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\pm 0.002(stat.)\pm 0.013(syst.)\pm 0.007(scale)\ . Including non-perturbative power corrections leads to alpha_s(M_Z)=0.101\pm 0.002(stat.)\pm 0.013(syst.)\pm 0.007(scale)\ . The measured transverse and longitudinal components of the fragmentation function are used to estimate the mean charged multiplicity, langle n^{ch}\rangle = 21.21 \pm 0.01(stat.)\pm 0.20(syst.) The fragmentation functions and multiplicities in $b\overline{b}$ and light quark events are compared. The measured transverse and longitudinal components of the fragmentation function allow the gluon fragmentation function to be evaluated.