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

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 $$ \boldsymbol{\Upsilon} (1S) $$ 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 $$ \overline{\mathrm{MS}} $$ mass reads $$ {\overline{m}}_b\left({m}_b\right)=4201(43) $$ MeV.