Fragmentation Functions from Flavour-inclusive and Flavour-tagged e^+e^- Annihilations

TL;DR

The paper aims to extract flavour-resolved fragmentation functions for identified hadrons from e+e- data at the Z0 pole, anchoring the nonperturbative input to the GRV radiative parton model. It develops a NLO QCD framework with timelike DGLAP evolution in Mellin space, using physically motivated light-flavour hierarchies and heavy-quark treatment above thresholds to constrain D_i^h(z, μ^2) for π±, K±, and Σh±. Fits to ALEPH, SLD, and TPC data reveal generally good agreement but leave substantial uncertainties in individual flavour and gluon fragmentation, especially for heavy quarks and gluons, with cross-checks from 3-jet data aiding and revealing limitations. The work highlights the delicate nature of energy-sum-rule interpretations in perturbative QCD FFs at low z and provides a practical FF set (FORTRAN package) for phenomenology, while underscoring the need for more precise flavour-tagged data to pin down the gluon and heavy-quark channels.

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$=π^\pm, K^\pm, \sum_h h^\pm$) fragmentation functions (FFs) at the low resolution scale of the radiative parton model of Glück, 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.

Figures (11)

• Figure 1: ALEPH aleph$\sum h^\pm$ inclusive particle spectra, measured at the $Z^0$ pole, and the corresponding fit results. Details to the individual data samples and curves are given in the text. The 'longitudinal' set has not been included in the fit.
• Figure 2: SLD sldpk$\pi^\pm$ and $K^\pm$ inclusive particle spectra, measured at the $Z^0$ pole, and the corresponding fit results. Details to the individual data samples are given in the text.
• Figure 3: $\sum h^\pm$ and $\pi^\pm$ inclusive particle spectra and flavour separated events over the range $0<z<0.9$ (inclusive) and $0<z<0.45$ ($\{u,d,s\}$, $c$, and $b$ events; $\beta=p_\pi/E_\pi\simeq 1$ for not too small $z$) as measured at $\sqrt{s}=29\ {\rm GeV}$ by TPC tpc. The corresponding curves are the fit results. Details to the individual data samples and curves are given in the text. Also included in the fit were inclusive $K^\pm$ data by TPC which are, however, not accompanied by flavour tagged samples and are therefore not shown in the Figure for clearness.
• Figure 4: The input fragmentation functions $D_i^{\pi^+}$ as given in Table \ref{['fitpars']} at their respective input scales.
• Figure 5: The input for light ($uds$) quarks and gluons of Fig. \ref{['input']} evolved upward to $Q^2=M_Z^2$.