Nonperturbative Renormalon Structure of Infrared Unstable Theories

TL;DR

This paper investigates the nonperturbative structure of infrared unstable theories using a generalized Borel Transform, exploring methods to extract singularities and discussing implications for QCD's infrared renormalons.

Contribution

It introduces an unambiguous reconstruction method for the nonperturbative structure and evaluates techniques for analyzing Borel singularities in lattice formulations.

Findings

Explicit illustration with the O(N) sigma model.

Assessment of the first infrared renormalon in QCD.

Feasibility of analytic continuation techniques from lattice data.

Abstract

The properties of a generalized version of the Borel Transform in infrared unstable theories with dynamical mass generation are studied. The reconstruction of the nonperturbative structure is unambiguous in this version. Various methods for extracting the singularity structure of the Borel Transform for lattice formulations of such theories are explored, and illustrated explicitly with the O(N) sigma model. The status of the first infrared renormalon in QCD is discussed. The feasibility of a proposed technique for analytically continuing from the left hand Borel plane (where nonperturbative information is available via simulation of lattice field theory) to the positive real axis is examined using the sigma model.