Heavy Flavoured Meson Fragmentation Functions in $e^+e^-$ annihilation up to NNLO + NNLL

TL;DR

This paper presents the first NNLO + NNLL theoretical predictions for heavy quark fragmentation in electron-positron annihilation, incorporating resummation techniques and comparing with experimental data to analyze non-perturbative effects.

Contribution

It provides the first combined NNLO and NNLL calculation for heavy quark fragmentation functions in $e^+e^-$ annihilation, including analytical Mellin-space computation and detailed resummation.

Findings

Significant differences found due to matching schemes and Landau pole prescriptions.

Discrepancies observed between charm meson data and standard DGLAP evolution.

Extracted non-perturbative fragmentation functions for $B$ and $D^*$ mesons.

Abstract

In this contribution, we make use of the QCD perturbative fragmentation function formalism to describe the one-particle inclusive fragmentation of a heavy quark produced in $e^+e^-$ annihilation at $\mathcal{O}(\alpha_S^2)$. We perform the computation analytically in Mellin-space. We resum soft-gluons effects in initial conditions and coefficient functions and perform evolution up to NNLL accuracy, obtaining the first NNLO + NNLL prediction for charm quark production. We study the impact of different matching schemes and Landau pole prescriptions in soft-gluon resummation, finding significant differences. We extract simple non-perturbative fragmentation functions for $B$ and $D^*$ mesons by comparing the perturbative prediction with the data from CLEO, BELLE and LEP experiments. We find that for charm mesons the experimental results from CLEO/BELLE and from LEP are not reconcilable with the standard DGLAP evolution.