Heavy Quark Fragmentation in $e^+e^-$ Collisions to NNLO+NNLL Accuracy in Perturbative QCD

TL;DR

This paper advances the precision of heavy quark fragmentation predictions in electron-positron collisions by incorporating NNLO+NNLL corrections, analyzing their dependence on various schemes, and extracting non-perturbative effects from experimental data.

Contribution

It provides a detailed analysis of perturbative QCD corrections at NNLO+NNLL accuracy for heavy quark fragmentation, highlighting scheme dependencies and extracting non-perturbative contributions from experimental data.

Findings

Significant dependence of results on matching schemes and regularisations.

Standard perturbative predictions do not match $D^{*+}$ data from CLEO/BELLE and LEP.

Extracted non-perturbative contributions can predict fragmentation in other processes.

Abstract

Fragmentation of heavy quarks into heavy-flavoured hadrons receives both perturbative and non-perturbative contributions. We consider perturbative QCD corrections to heavy quark production in $e^+e^-$ collisions to next-to-next-to-leading order accuracy in QCD with next-to-next-to-leading-logarithmic resummation of quasi-collinear and soft emissions. We study multiple matching schemes, and multiple regularisations of the soft resummation, and observe a significant dependence of the perturbative results on these ingredients, suggesting that NNLO+NNLL perturbative accuracy may not lead to real gains unless the interface with non-perturbative physics is properly analysed. We confirm previous evidence that $D^{*+}$ experimental data from CLEO/BELLE and from LEP are not reconcilable with perturbative predictions employing standard DGLAP evolution. We extract non-perturbative contributions from $e^+e^-$ experimental data for both $D$ and $B$ meson fragmentation. Such contributions can be used to predict heavy-quark fragmentation in other processes, e.g. DIS and proton-proton collisions.