On the Light Massive Flavor Dependence of the Top Quark Mass

TL;DR

This paper develops a systematic renormalization group approach to analyze how lighter massive quarks influence the top quark's mass, providing precise predictions and understanding of mass ambiguities.

Contribution

It introduces a novel formalism combining matching and evolution to study light flavor effects on heavy quark masses, improving precision and understanding of mass ambiguities.

Findings

Predicted ${ m O}(eta_s^4)$ virtual quark mass corrections.

Calculated pole mass differences with ~20 MeV accuracy.

Determined the pole mass ambiguity to be 250 MeV.

Abstract

We provide a systematic renormalization group formalism to study the mass effects in the relation of the pole mass and short-distance masses such as the $\overline{\mathrm{MS}}$ mass of a heavy quark $Q$, coming from virtual loop insertions of massive quarks lighter than $Q$ with the main focus on the top quark. The formalism reflects the constraints from heavy quark symmetry and entails a combined matching and evolution procedure that allows to disentangle and successively integrate out the corrections coming from the lighter massive quarks and the momentum regions between them and also to precisely control the large order asymptotic behavior. The formalism is used to study the asymptotic behavior of light massive flavor contributions and is applied to predict the ${\cal O}(\alpha_s^4)$ virtual quark mass corrections, calculate the pole mass differences for massive quark flavors with a precision of around 20 MeV, and determine the pole mass ambiguity which amounts to 250 MeV in the physical case of three massless quark flavors.