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→hadron (hadronϭ Ϯ ,K Ϯ , ͚ h h Ϯ ) fragmentation functions ͑FFs͒ at the low resolution scale of the radiative parton model of Glück, Reya and Vogt ͑GRV͒. Perturbative LO↔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 flavors where we comment on the factorization scheme for heavy quarks in e ϩ e Ϫ 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.PACS number͑s͒: 13.87.Fh, 13.65.ϩi II. PARTON FRAGMENTATION IN e ¿ e À COLLISIONS BEYOND THE LEADING ORDERThe next-leading order ͑NLO͒ framework 1 for onehadron-inclusive e ϩ e Ϫ annihilations has been well known 1 The formulas below include the LO framework in an obvious way by dropping subleading terms.

Abstract. Heavy flavor production is an important QCD process both in its own right and as a key component of precision global QCD analysis. Apparent disagreements between fixed-flavor scheme calculations of b-production rate with experimental measurements in hadro-, lepto-, and photo-production provide new impetus to a thorough examination of the theory and phenomenology of this process. We review existing methods of calculation, and place them in the context of the general PQCD framework of Collins. A distinction is drawn between scheme dependence and implementation issues related to quark mass effects near threshold. We point out a so far overlooked kinematic constraint on the threshold behavior, which greatly simplifies the variable flavor number scheme. It obviates the need for the elaborate existing prescriptions, and leads to robust predictions. It can facilitate the study of current issues on heavy flavor production as well as precision global QCD analysis.

Previously published CTEQ6 parton distributions adopt the conventional zero-mass parton scheme since the corresponding hard cross sections are universally available. For precision observables which are sensitive to charm and bottom quark mass effects, we provide in this paper an improved CTEQ6HQ parton distribution set determined in the more general variable flavor number scheme that incorporates heavy flavor mass effects. We describe in detail the QCD scheme and analysis procedure used, examine the predominant features of the new distributions, and compare them with previous distributions.