Renormalons

TL;DR

This paper discusses the impact of renormalons on higher twist corrections in quantum field theory, comparing dimensional regularization and lattice cut-off methods, and illustrates the concepts with heavy quark effective theory calculations.

Contribution

It clarifies how different regularization schemes affect renormalon ambiguities and provides a framework for extracting physical predictions from lattice measurements.

Findings

Renormalon ambiguities arise in dimensional regularization but are absent with lattice cut-offs.

Cancellations between divergent terms ensure well-defined predictions in lattice regularization.

Illustration using heavy quark effective theory demonstrates practical application of these ideas.

Abstract

The calculation of higher twist (or dimension) corrections to physical quantities using operator product expansions is delicate. If dimensional regularization is used to regulate the ultra-violet divergences then there are ambiguities in the Wilson coefficient functions due to infra-red renormalon singularities. With a hard ultra violet cut-off, such as the inverse lattice spacing $a$, there are no renormalon ambiguities, as a result of cancellations between terms which in finite orders of perturbation theory diverge as inverse powers of $a$, and those which diverge at most logarithmically. In this lecture I review these questions, explaining the steps necessary to obtain predictions for physical quantities from lattice measurements of matrix elements of higher dimensional operators. The ideas are illustrated by considering quantities computed using the heavy quark effective theory beyond leading order in the heavy quark mass.