Pole mass renormalon and its ramifications

TL;DR

This paper reviews the infrared renormalon divergence in the pole mass of heavy quarks and discusses alternative short-distance mass definitions that avoid this divergence for precision calculations.

Contribution

It provides a detailed analysis of the leading infrared renormalon in the pole mass and explores renormalon-free mass definitions for heavy quarks.

Findings

Pole mass series diverges rapidly due to infrared renormalons.

Renormalon-free mass definitions are suitable for near on-shell heavy quark processes.

Abandoning pole mass is necessary for precision in heavy quark physics.

Abstract

I review the structure of the leading infrared renormalon divergence of the relation between the pole mass and the $\overline{\rm MS}$ mass of a heavy quark, with applications to the top, bottom and charm quark. That the pole quark mass definition must be abandoned in precision computations is a well-known consequence of the rapidly diverging series. The definitions and physics motivations of several leading renormalon-free, short-distance mass definitions suitable for processes involving nearly on-shell heavy quarks are discussed.