Renormalization Scheme Dependence and the Renormalization Group Beta Function

TL;DR

This paper explores how different renormalization schemes affect the renormalization group beta function and the determination of infrared fixed points, emphasizing the scheme dependence in quantum field theory calculations.

Contribution

It demonstrates the relationship between renormalization scheme changes and shifts in the mass scale, and argues that physical quantities' fixed points are scheme-dependent and best determined when series expansions terminate.

Findings

Renormalization scheme changes induce shifts in the mass scale.

Infrared fixed points depend on the chosen renormalization scheme.

Physical quantities' series expansions should terminate at fixed points.

Abstract

The renormalization that relates a coupling "a" associated with a distinct renormalization group beta function in a given theory is considered. Dimensional regularization and mass independent renormalization schemes are used in this discussion. It is shown how the renormalization $a^*=a+x_2a^2$ is related to a change in the mass scale $\mu$ that is induced by renormalization. It is argued that the infrared fixed point is to be a determined in a renormalization scheme in which the series expansion for a physical quantity $R$ terminates.