Should we worry about renormalons in the epsilon-expansion?

TL;DR

This paper investigates whether renormalons affect the divergence of the epsilon-expansion in quantum field theories, using the large N limit of the O(N) model, and finds no evidence of non-analyticity caused by renormalons.

Contribution

The study provides an explicit analytic analysis of the O(N) model at large N, showing that renormalons do not induce non-analytic behavior in the epsilon-expansion.

Findings

No sign of non-analyticity from renormalons in the model

Renormalons do not significantly affect the epsilon-expansion divergence

Supports the validity of the epsilon-expansion despite renormalon concerns

Abstract

Turning the divergent epsilon-expansion into a numerically sensible algorithm, relies on the knowledge of the behaviour of the large order contributions. Two different pictures are known to compete there. The first one was based on Lipatov's instantons, which is known to deal with the multiplicity of Feynman diagrams which grows factorially at high orders. However this was challenged by 't Hooft's renormalons who pointed out that renormalization could yield a similar growth through one single diagram. We study here a well-known model, the $O(N)$ model, in the large $N$ limit. The reason for returning to this familiar model, is that it deals with diagrams known to give renormalon effects.Through an explicit analytic result, we find no sign of a non-analyticity of perturbation theory due to these renormalons.