We show that to correctly describe the effects of the heavy-quark mass, m_h,
in DGLAP evolution, it is necessary to work in the so-called `physical' scheme.
In this way, we automatically obtain a smooth transition through the
heavy-quark thresholds. Moreover, we show that to obtain NLO accuracy, it is
sufficient to account for the heavy-quark mass, m_h, just in the LO (one-loop)
splitting function. The use of the MS-bar factorisation scheme is not
appropriate, since at NLO we deal with a mixture of quarks and gluon (that is,
the mass of the heavy parton is not well-defined). The formulae for the
explicit m_h dependence of the splitting functions, and for alpha_s, are
presented.Comment: 14 pages, 3 figures, references updated, version to be published in
EPJ
