Measurement of the quark and gluon fragmentation functions in Z$^0$ hadronic decays

Abstract.

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 $\sigma_T/\sigma_{tot}=0.949\pm 0.001(stat.)\pm 0.007(syst.)$ and $\sigma_L/\sigma_{tot}=0.051\pm 0.001(stat.)\pm 0.007(syst.)$ 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.