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

Understand

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.