ON SOME POSSIBLE EXTENSIONS OF THE BRODSKY-LEPAGE-MACKENZIE APPROACH BEYOND THE NEXT-TO-LEADING ORDER

Noting that the choice of renormalization point advocated by Brodsky, Lepage and Mackenzie (BLM) is the flavor independent prescription which removes all f-dependence from the next-to-leading order coefficients, we consider the possible generalization which requires all higher order coefficients r(i) to be f-independent constants r(i)*. We point out that in QCD, setting r(i) = r(i)* is always possible, but leaves us with an ambiguous prescription. We consider an alternative possibility within the framework of the BLM approach and apply the corresponding prescription to the next-to-next-to-leading approximation of sigma(tot)(e+e- --> hadrons) in QCD. The analogous questions and the special features of the BLM and effective charge approaches in QED are also discussed.