Renormalons beyond the Borel plane

TL;DR

This paper explores the possibility of renormalon singularities existing beyond the traditional Borel plane in field theories, demonstrating an example with a scalar field theory that exhibits a Gevrey-3 asymptotic series.

Contribution

It introduces the concept of renormalons beyond the first Borel plane and provides an explicit example with a scalar field theory showing Gevrey-3 asymptotic behavior.

Findings

Identification of renormalons beyond the first Borel plane

Scalar field theory example with Gevrey-3 series

Implications for divergence analysis in quantum field theories

Abstract

The renormalon singularities are a known source of the divergent behavior of asymptotic perturbative series from field theoretical models. These singularities live in the Borel plane and are responsible for ambiguities in the physical plane. We propose that field theories can have renormalons beyond the usual first Borel plane. We show an example with a scalar field theory where, considering a chain of cat's eyes diagrams, the model develops a Gevrey-3 asymptotic series.