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We present in detail a new systematic method which can be used toautomatically eliminate the renormalization scheme and scale ambiguities inperturbative QCD predictions at all orders. We show that all of thenonconformal \beta-dependent terms in a QCD perturbative series can be readilyidentified by generalizing the conventional renormalization schemes based ondimensional regularization. We then demonstrate that the nonconformal series ofpQCD at any order can be resummed systematically into the scale of the QCDcoupling in a unique and unambiguous way due to a special degeneracy of the\beta-terms in the series. The resummation follows from the principal ofmaximum conformality (PMC) and assigns a unique scale for the running couplingat each perturbative order. The final result is independent of the initialchoices of renormalization scheme and scale, in accordance with the principlesof the renormalization group, and thus eliminates an unnecessary source ofsystematic error in physical predictions. We exhibit several examples known toorder \alpha_s^4; i.e. i) the electron-positron annihilation into hadrons, ii)the tau-lepton decay to hadrons, iii) the Bjorken and Gross-Llewellyn Smith(GLS) sum rules, and iv) the static quark potential. We show that the finalseries of the first three cases are all given in terms of the anomalousdimension of the gluon field, in accordance with conformality, and with allnon-conformal properties encoded in the running coupling. The final expressionsfor the Bjorken and GLS sum rules directly lead to the generalized Crewtherrelations, exposing another relevant feature of conformality. The static quarkpotential shows that PMC scale setting in the Abelian limit is to all ordersconsistent with QED scale setting. Finally, we demonstrate that the methodapplies to any renormalization scheme and [...]

Systematic Scale-Setting to All Orders: The Principle of Maximum Conformality and Commensurate Scale Relations