Asymptotic normalization properties and mass independent renormalization group functions

Mass independent renormalization group functions in massive theories are related to normalization properties of the Green functions in the asymptotic region, where mass effects are neglected. In this special form the renormalization group invariance is restricted to the asymptotic region and consequently mass effects cannot be recoverd by a integration of the renormalziation group equation. It is shown, that mass independence results in the limit of a large normalization point, whenever a Callan-Symanzik equation exists and contains the same differential operators as the renormalization group equation.