Callan-Symanzik and renormalization group equation in theories with spontaneously broken symmetry

TL;DR

This paper examines the Callan-Symanzik and renormalization group equations in theories with spontaneous symmetry breaking, revealing differences in asymptotic behavior and similarities in equation form across models.

Contribution

It demonstrates that the symmetric model is not the asymptotic limit of the spontaneously broken model due to mass logarithms affecting the beta functions.

Findings

Symmetric and broken models differ in asymptotic behavior.

Mass logarithms influence the beta functions in broken symmetry models.

The standard model's Callan-Symanzik equation mirrors that of simpler models.

Abstract

Callan-Symanzik and renormalization group equation are discussed for the $U(1)$-axial model and it is shown that the symmetric model is not the asymptotic version of the spontaneously broken one due to mass logarithms in the $\beta$-functions. The Callan-Symanzik equation of the standard model is seen to have the same form as the one of the simple model.