Infinite-order scale-setting using the principle of maximum conformality: A remarkably efficient method for eliminating renormalization scale ambiguities for perturbative QCD

We identify a property of renormalizable SU(N)/U(1) gauge theories, intrinsic conformality (iCF), which underlies the scale invariance of physical observables and leads to a remarkably efficient method to solve the conventional renormalization scale ambiguity at every order in perturbative QCD (pQCD): the PMC infinity. This new method reflects the underlying conformal properties displayed by pQCD at next-to-next-to-leading order, eliminates the scheme dependence of pQCD predictions, and is consistent with the general properties of the principle of maximum conformality (PMC). We introduce a new method to identify conformal and beta-terms which can be applied from either a numerical or an analytical calculations. We illustrate the PMC infinity for the thrust and C-parameter distributions in e(+)e(-) annihilation and then show how to apply this new method to general observables in QCD. We point out how the implementation of the PMC infinity can significantly improve the precision of pQCD predictions; its implementation in a multiloop analysis also simplifies the calculation of higher order corrections in a general renormalizable gauge theory.