Perturbation theory and renormalisation group equations

TL;DR

This paper examines the limitations of one-loop improved renormalisation group equations, showing that their integrated flows generally do not align with perturbation theory beyond the first loop.

Contribution

It reveals a fundamental discrepancy between integrated renormalisation group flows and higher-order perturbation theory, highlighting a key limitation of current methods.

Findings

Integrated RG flows often fail beyond one loop

Perturbation theory and RG flows diverge at higher loops

Highlights need for improved RG methods

Abstract

We discuss the perturbative expansion of several one-loop improved renormalisation group equations. It is shown that in general the integrated renormalisation group flows fail to reproduce perturbation theory beyond one loop.