Renormalization Scheme and Mass Scale Independence

TL;DR

This paper shows that in mass independent renormalization schemes, the renormalization group equations lead to a cancellation of dependence on unphysical parameters, making the perturbative expansion scheme-independent, demonstrated through e+e- -> hadrons.

Contribution

It introduces a method to achieve scheme and scale independence in perturbative expansions using renormalization group equations.

Findings

Dependence on unphysical parameters cancels out in the scheme.

Perturbative expansion becomes independent of arbitrary parameters.

Application to e+e- -> hadrons demonstrates the approach.

Abstract

We demonstrate that in the mass independent renormalization scheme. the renormalization group equations associated with the unphysical parameters that characterize the renormalization scheme and the mass scale leads to summation that results in a cancellation between the implicit and explicit dependence on these parameters. The resulting perturbative expansion is consequently independent of these arbitrary parameters. We illustrate this by considering R, the cross section for e+e- -> hadrons.