Some properties of renormalons in gauge theories

TL;DR

This paper explicitly characterizes the operator structure of renormalon singularities in abelian gauge theories, showing how local and non-local operators address UV and IR issues and cancel non-physical imaginary parts in perturbation series.

Contribution

It provides the explicit operatorial form of renormalon singularities and demonstrates their role in canceling non-physical imaginary parts in the effective Lagrangian.

Findings

Local operators of dimension six handle UV renormalons.

Non-local operators are required for IR renormalons.

The constructed effective Lagrangian cancels non-physical imaginary parts.

Abstract

We find the explicit operatorial form of renormalon-type singularities in abelian gauge theory. Local operators of dimension six take care of the first U.V. renormalon, non local operators are needed for I.R. singularities. In the effective lagrangian constructed with these operators non local imaginary parts appearing in the usual perturbative expansion at large orders are cancelled.