Renormalization Group Invariance and Optimal QCD Renormalization Scale-Setting

Understand

A valid prediction for a physical observable from quantum field theory should be independent of the choice of renormalization scheme -- this is the primary requirement of renormalization group invariance (RGI).

• Satisfying scheme invariance is a challenging problem for perturbative QCD (pQCD), since a truncated perturbation series does not automatically satisfy the requirements of the renormalization group.
• Two distinct approaches for satisfying the RGI principle have been suggested in the literature.
• One is the "Principle of Maximum Conformality" (PMC) in which the terms associated with the $\beta$-function are absorbed into the scale of the running coupling at each perturbative order; its predictions are scheme and scale independent at every finite order.