QCD Perturbation Theory: It's not what you were taught

Abstract

Physical quantities in QCD do not depend upon $\alpha_s(Q)$. There is no way to measure $\alpha_s(Q)$ experimentally. If those statements sound shocking, please read on. They are actually well-known facts, though ones that are constantly being ignored in the QCD literature. Renormalized perturbation theory is not an ordinary power-series expansion; its renormalization-scheme ambiguity is not merely a minor nuisance. Rather, it is a structure in which invariance under redefinitions of the coupling is a fundamental symmetry -- a symmetry that, like any other, deserves respect. I speak bluntly because without a change in mindset perturbative QCD can never become a proper, scientific enterprise.