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

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 $D^{\ast +}$ 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.

43 pages, 15 figures, 2 tables; v2 matches the published version

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