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

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