Callan–Symanzik and Weinberg equations: frame dependence of fixed points

Abstract

We discuss the relationship between the Weinberg and Callan–Symanzik equations and show that the fixed points of the β functions for the two equations are 'frame-independent' only when γθ(gR, mR/μ) = −1. We also obtain Weinberg's result in the asymptotic limit provided that γθ > −1 and certain explicit mass dependences in scaling factors are dropped.