Higher ε-poles and logarithms in the MS-like schemes from the algebraic structure of the renormalization group

We investigate the structure of renormalization constants within the MS-like renormalization prescriptions for a version of dimensional regularization in which the dimensionful regularization parameter Λ differs from the renormalization point μ. Namely, we rewrite the all-loop equations relating coefficients at higher ε-poles and higher powers of lnΛ/μ to the coefficients of the renormalization group functions in a simple unified form. It is argued that this form follows from the algebraic structure of the renormalization group.