Treatment of heavy quarks in QCD

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) over bar factorization 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 formulas for the explicit m(h) dependence of the splitting functions, and for alpha(s), are presented.