On the BLM scale-fixing procedure, its generalizations and "genuine" higher order corrections

The question of the uniqueness of the Brodsky–Lepage–Mackenzie procedure for fixing the renormalization scale in perturbative QCD is discussed. It is shown that the resulting finite order approximants are as ambiguous as the original truncated perturbative expansions. This inherent ambiguity of the BLM procedure undermines the recent attempts to define ``genuine’’ higher order perturbative corrections.