Maximally Precise Tests of the Standard Model: Elimination of Perturbative QCD Renormalization Scale and Scheme Ambiguities

A central issue in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale of the QCD running coupling. The purpose of the running coupling in any gauge theory is to sum all terms involving the β function; in fact, when the renormalization scale is set properly, all non-conformal β terms in a perturbative expansion arising from renormalization are summed into the running coupling. The remaining terms in the perturbative series are then identical to that of a conformal theory, i.e., the corresponding theory with β = 0. The resulting scale-fixed predictions using the “Principle of Maximum Conformality” (PMC) are independent of the choice of renormalization scheme—a key requirement of renormalization group invariance. The results avoid renormalon resummation and agree with QED scale-setting in the Abelian limit. The PMC is also the theoretical principle underlying the BLM procedure, commensurate scale relations between observables, and the scale-setting method used in lattice gauge theory. The number of active flavors n_F in the QCD β function is also correctly determined. The elimination of the renormalization scale ambiguity and the scheme dependence using the PMC not only increases the precision of QCD tests, but it also increases the sensitivity of collider experiments to new physics beyond the SM…