The bottom quark mass from the ${\rm Y}(1S)$ 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 ${\rm Y}(1S)$ 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 ${\overline{m}}_b({\overline{m}}_b)=4201(43)$ MeV.

Comments: 37 pages, 11 figures, minor changes in presentation, version to appear in JHEP