Optimization for factorized quantities in perturbative QCD

Abstract

Perturbative calculations of factorized physical quantities, such as moments of structure functions, suffer from renormalization- and factorization-scheme dependence. The application of the principle of minimal sensitivity to "optimize" the scheme choices is reconsidered, correcting deficiencies in the earlier literature. The proper scheme variables, RG equations, and invariants are identified. Earlier results of Nakkagawa and Niegawa are recovered, even though their starting point is, at best, unnecessarily complicated. In particular, the optimized coefficients of the coefficient function C are shown to vanish, so that C^opt=1. The resulting simplifications mean that the optimization procedure is as simple as that for purely-perturbative physical quantities.