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

Abstract

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∞. 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 β-terms which can be applied from either a numerical or an analytical calculations. We illustrate the PMC∞ 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∞ 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.