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

DELPHI Collaboration:     P. Abreu - et al.

doi:doi:10.1007/s100529801013

2020 Impact factor 4.590

Particles and Fields

Eur. Phys. J. C 6, 19-33
DOI 10.1007/s100529801013

Measurement of the quark and gluon fragmentation functions
in Z⁰ hadronic decays

DELPHI Collaboration
P.Abreu²¹ et al.

²¹ LIP, IST, FCUL - Av. Elias Garcia, 14-1^o, P-1000 Lisboa Codex, Portugal

Received: 12 September 1997 / Published online: 19 October 1998

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

$\begin{displaymath} \alpha_s(M_Z)=0.120\pm 0.002(stat.)\pm 0.013(syst.)\pm 0.007(scale)\ .\end{displaymath}$

Including non-perturbative power corrections leads to

$\begin{displaymath} \alpha_s(M_Z)=0.101\pm 0.002(stat.)\pm 0.013(syst.)\pm 0.007(scale)\ .\end{displaymath}$

The measured transverse and longitudinal components of the fragmentation function are used to estimate the mean charged multiplicity,

$\begin{displaymath} \langle n^{ch}\rangle = 21.21 \pm 0.01(stat.)\pm 0.20(syst.)\end{displaymath}$

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.