Resummation of large logarithms in the VFN scheme for DIS heavy-quark production

TL;DR

This paper investigates how resumming large logarithms affects heavy-quark parton distribution functions in deep-inelastic scattering, revealing significant impacts at different orders and emphasizing the importance of consistent perturbative accuracy.

Contribution

It introduces a detailed analysis of large logarithm resummation effects in the VFN scheme for DIS heavy-quark production, highlighting the importance of matching conditions and perturbative order consistency.

Findings

Resummation significantly impacts LO and NLO heavy-quark PDFs.

NNLO distributions differ from NLO at low virtualities.

Mismatch in perturbative orders causes substantial excess in heavy-quark distributions.

Abstract

We consider the impact of the resummation of large logarithms, which appear in the QCD evolution of the heavy-quark distributions, on the phenomenology of deep-inelastic heavy-quark production. The heavy-quark PDFs are derived using the fixed-order matching conditions as a boundary for the QCD evolution and the result obtained is compared to the distributions defined by the matching conditions at all scales. With such an approach, the effect of heavy-quark PDF evolution is found to be sizable at LO and dramatically reduces at NLO. The NNLO evolved distributions are not very different from the NLO ones at large scales, however, show substantial differences at low virtualities, i.e. where the additional large logarithms are numerically not important, while a mismatch between the NLO accuracy of the matching conditions and the NNLO accuracy in the evolution kernels causes a substantial excess in the heavy-quark distributions. This excess propagates into the variable flavor number (VFN) scheme predictions for the deep-inelastic structure functions and has to be compensated by a decrease in the small-$x$ gluon distribution determined from PDF fits based on the VFN scheme, which should be considered as a theoretical uncertainty in VFN PDF fits and reaches $\sim 30\%$ for the small-$x$ gluon distribution extracted from the data on deep-inelastic charm-quark production.