A Phenomenological Study of Heavy-Quark Fragmentation Functions in e+e- Annihilation

TL;DR

An analysis of heavy-quark fragmentation functions in e+e− annihilation merges fixed-order and resummed perturbative calculations with a non-perturbative Peterson fragmentation component. The authors develop an improved cross-section formula that retains mass terms up to O(αs^2) and resums leading logarithms to NLL, including a scheme to subtract double-counted contributions. Fits to ARGUS, OPAL, and ALEPH data show that mass effects are small at LEP energies and that NLL resummation reduces the need for a large non-perturbative input, lowering the Peterson epsilon parameter. The work provides a practical, interpolating framework for HQFF that improves heavy-flavor production predictions across a range of energies.

Abstract

We consider the computation of D and B fragmentation functions in e+e- annihilation. We compare the results of fitting present data using the next-to-leading-logarithmic resummed approach, versus the O(alpha_s^2) fixed-order calculation, including also mass-suppressed effects. We also propose a method for merging the fixed-order calculation with the resummed approach.

Figures (11)

• Figure 1: Fragmentation function $1/\sigma_{\rm tot} \, d\sigma^D/dx_p$ for ARGUS. The value of the Peterson $\epsilon$ parameter is fixed at 0.035.
• Figure 2: Fragmentation function $1/\sigma_{\rm tot} \, d\sigma^D/dx_E$ for OPAL. The value of the Peterson $\epsilon$ parameter is fixed at 0.035. The dashed curve is almost hidden by the solid one.
• Figure 3: Fragmentation function $1/\sigma_{\rm tot} \, d\sigma^B/dx_E$ for ALEPH. The value of the Peterson $\epsilon$ parameter is fixed at 0.0035.
• Figure 4: Fragmentation function $1/\sigma_{\rm tot} \, d\sigma^D/dx_p$ for ARGUS. The value of the Peterson $\epsilon$ parameter is fixed at 0.035.
• Figure 5: Fragmentation function $1/\sigma_{\rm tot} \, d\sigma^D/dx_E$ for OPAL. The value of the Peterson $\epsilon$ parameter is fixed at 0.035.