A Fixed-Order Calculation of the Heavy-Quark Fragmentation Function in e+e- Collisions

TL;DR

The paper develops a fixed-order QCD framework to extract the heavy-quark fragmentation function in e+e- collisions by convolving a ${ m O}(\, ext{α_s}^2)$ heavy-quark production cross section with a Peterson non-perturbative fragmentation function. It systematically analyzes mass effects and the absence of gluon-splitting contributions, and compares with resummed NLL/NNLL approaches. Fitting to ARGUS and OPAL data yields ε values around 0.036–0.041, illustrating how fixed-order mass terms influence the fragmentation parameter and how resummation can push ε in the opposite direction. The work clarifies the interplay between fixed-order calculations and resummation in charm fragmentation and highlights energy-dependent behavior in the extracted fragmentation function.

Abstract

We use a recently completed O(alpha_s^2) fixed-order calculation of the heavy-flavour production cross section in e+e- collisions to compute the heavy-quark fragmentation function. We fit the result of our calculation, convoluted with a Peterson fragmentation function, to available data for charm production, and thus obtain a value for the parameter epsilon in the Peterson function. We discuss the relevance of mass effects and of subleading terms in our calculation.

Figures (2)

• Figure 1: Best fit for the ${\cal O}(\alpha s$α_s$^2)$ fragmentation function at ARGUS.
• Figure 2: The ${\cal O}(\alpha s$α_s$^2)$ fragmentation function plotted together with OPAL data.