On exact account for heavy quark thresholds in hard processes

We study the problem of accurate account for heavy quark threshold effects in hard processes. We employ the direct perturbative Feynman diagram analysis and the Stueckelberg-Bogoliubov massive renormalization group formalism to show that both methods result in the same prescription for the ''smooth'' mass-dependent QCD effective coupling as an argument of anomalous dimensions that determine the evolution of structure functions (parton distributions). By considering a one-loop example, we discuss the difference between our smooth expression and a popular massless one in treating the anti αs(Q) behavior in the threshold vicinity. (orig.)