The three loop relation between the \bar {MS} and the pole quark masses

TL;DR

This paper derives an exact three-loop relation between the ar{MS} and pole quark masses in QCD, critically evaluates approximation methods, and discusses implications for semileptonic B decays.

Contribution

It provides the first complete three-loop analytic relation between ar{MS} and pole quark masses, improving precision in QCD mass calculations.

Findings

The exact relation differs significantly from large eta_0 approximation.

The large eta_0 approximation's accuracy is critically assessed.

Implications for semileptonic B decay analyses are discussed.

Abstract

The analytic relation between the \bar {MS} and the pole quark masses is computed to O(\alpha_s^3) in QCD. Using this exact result, the accuracy of the large \beta_0 approximation is critically examined and the implications of the obtained relation for semileptonic B decays are discussed.