Heavy-flavor PDF evolution and variable-flavor number scheme uncertainties in deep-inelastic scattering

TL;DR

This paper investigates the construction of heavy-quark PDFs and compares fixed-flavor and variable-flavor schemes in deep-inelastic scattering, finding minimal impact of resummation effects within current data ranges.

Contribution

It provides a detailed analysis of heavy-quark PDF construction, compares different VFN implementations, and assesses uncertainties in DIS charm-quark production.

Findings

Resummation effects have little impact in current DIS data ranges.

FFN scheme describes charm production well without large resummation.

Theoretical uncertainties in VFN schemes are significant at small Q^2.

Abstract

We consider a detailed account on the construction of the heavy-quark parton distribution functions for charm and bottom, starting from $n_f=3$ light flavors in the fixed-flavor number (FFN) scheme and by using the standard decoupling relations for heavy quarks in QCD. We also account for two-mass effects. Furthermore, different implementations of the variable-flavor-number (VFN) scheme in deep-inelastic scattering (DIS) are studied, with the particular focus on the resummation of large logarithms in $Q^2/m_h^2$, the ratio the virtuality of the exchanged gauge-boson $Q^2$ to the heavy-quark mass squared $m_h^2$. A little impact of resummation effects if found in the kinematic range of the existing data on the DIS charm-quark production so that they can be described very well within the FFN scheme. Finally, we study the theoretical uncertainties associated to the VFN scheme, which manifest predominantly at small $Q^2$.