Abstract
Fitting $Z^0$-pole data from ALEPH and SLD, and TPC data at a lower c.m.s.\ energy, we fix the boundary condition for NLO parton$\to$hadron (hadron$=\pi^\pm, K^\pm, \sum_h h^\pm$) fragmentation functions (FFs) at the low resolution scale of the radiative parton model of Gl\"{u}ck, Reya and Vogt (GRV). Perturbative LO$\leftrightarrow$NLO stability is investigated. The emphasis of the fit is on information on the fragmentation process for individual light ($u,d,s$) and heavy ($c,b$) quark flavours where we comment on the factorization scheme for heavy quarks in $e^+e^-$ annihilations as compared to deep inelastic production. Inasmuch as the light quark input parameters are not yet completely pinned down by measurements we assume power laws to implement a physical hierarchy among the FFs respecting valence enhancement and strangeness suppression both of which are manifest from recent leading particle measurements. Through the second Mellin moments of the input functions we discuss the energy-momentum sum rule for massless FFs. We discuss our results in comparison to previous fits and recent 3-jet measurements and formulate present uncertainties in our knowledge of the individual FFs.
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