On the ultimate uncertainty of the top quark pole mass

TL;DR

This paper estimates the fundamental limit of precision in determining the top quark pole mass due to QCD renormalon effects, finding an intrinsic uncertainty of about 110 MeV, with additional higher-order contributions around 300 MeV.

Contribution

It combines asymptotic QCD series analysis with exact four-loop coefficients to quantify the ultimate uncertainty in the top quark pole mass.

Findings

Ultimate uncertainty in top quark pole mass is approximately 110 MeV.

Higher-order corrections beyond four loops contribute around 300 MeV.

The analysis is robust across variations in QCD parameters.

Abstract

We combine the known asymptotic behaviour of the QCD perturbation series expansion, which relates the pole mass of a heavy quark to the MSbar mass, with the exact series coefficients up to the four-loop order to determine the ultimate uncertainty of the top-quark pole mass due to the renormalon divergence. We perform extensive tests of our procedure by varying the number of colours and flavours, as well as the scale of the strong coupling and the MSbar mass. Including an estimate of the internal bottom and charm quark mass effect, we conclude that this uncertainty is around 110 MeV. We further estimate the additional contribution to the mass relation from the five-loop correction and beyond to be around 300 MeV.