The bottom quark mass from the $\Upsilon(1S)$ system at NNNLO

TL;DR

This paper refines the bottom quark mass measurement using high-order perturbative calculations of the $
S$ bottomonium state, addressing renormalon effects and charm quark contributions for improved precision.

Contribution

It provides an improved determination of the infrared renormalon normalization constant and a precise bottom quark mass value at NNNLO, incorporating charm effects and renormalon subtraction.

Findings

Bottom quark mass: 4201(43) MeV in MSbar scheme

Renormalon normalization constant: 0.563(26) for Nf=3

Controlled divergence of perturbation series using renormalon subtraction

Abstract

We obtain an improved determination of the normalization constant of the first infrared renormalon of the pole mass (and the singlet static potential). For $N_f=3$ it reads $N_m=0.563(26)$. Charm quark effects in the bottom quark mass determination are carefully investigated. Finally, we determine the bottom quark mass using the NNNLO perturbative expression for the $\Upsilon(1S)$ mass. We work in the renormalon subtracted scheme, which allows us to control the divergence of the perturbation series due to pole mass renormalon. Our result for the ${\overline {\rm MS}}$ mass reads ${\overline m}_{b}({\overline m}_{b})=4201(43)$ MeV.