Higher logarithms and ε-poles for the MS-like renormalization prescriptions

Abstract

We consider a version of dimensional regularization (reduction) in which the dimensionful regularization parameter Λ is in general different from the renormalization scale μ. Then in the scheme analogous to the minimal subtraction the renormalization constants contain ε-poles, powers of ln Λ/μ, and mixed terms of the structure ε−q lnp Λ/μ. For the MS-like schemes we present explicit expressions for the coefficients at all these structures which relate them to the coefficients in the renormalization group functions, namely in the β-function and in the anomalous dimension. In particular, for the pure ε-poles we present explicit solutions of the ’t Hooft pole equations. Also we construct simple all-loop expressions for the renormalization constants (also written in terms of the renormalization group functions) which produce all ε-poles and logarithms and establish a number of relations between various coefficients at ε-poles and logarithms. The results are illustrated by some examples.