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 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 α s , are presented.