Callan-Symanzik and renormalization group equation in a model with spontaneous breaking of the symmetry

In a simple model with spontaneous breaking of the axialU(1)-symmetry via the Higgs mechanism we construct the Callan-Symanzik and renormalization group equation in the Goldstone mode. Aiming at questions of renormalization group improvement and the like we compare two different parametrizations the model can be described with. We show that in the presence of fermions a β-function for a physical mass or some equivalent of it enters unavoidably the Callan-Symanzik equation, which leads to significant differences to the symmetric theory starting with two loops. On the other hand in the asymptotic region the equivalence to the symmetric theory is manifest.