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 ∼30% for the small-x gluon
distribution extracted from the data on deep-inelastic charm-quark production.Comment: 6 pages, 3 figures, proceedings of XXVII International Workshop on
Deep-Inelastic Scattering and Related Subjects (DIS2018), 8-12 Apr, Torino
(Italy