The charm/bottom quark mass from heavy quarkonium at N3LO

Abstract

Abstract We determine the charm and bottom quark masses using the N3LO perturbative expression of the ground state (pseudoscalar) energy of the bottomonium, charmonium and B c systems: the η b , η c and B c masses. We work in the renormalon subtracted scheme, which allows us to control the divergence of the perturbation series due to the pole mass renormalon. Our result for the $$ \overline{\mathrm{MS}} $$ M S ¯ masses reads $$ {\overline{m}}_c\left({\overline{m}}_c\right)=1223(33) $$ m ¯ c m ¯ c = 1223 33 MeV and $$ {\overline{m}}_b\left({\overline{m}}_b\right)=4186(37) $$ m ¯ b m ¯ b = 4186 37 MeV. We also extract a value of α s from a renormalon-free combination of the η b , η c and B c masses: α s (M z ) = 0.1195(53). We explore the applicability of the weak coupling approximation to bottomonium n = 2 states. Finally, we consider an alternative computational scheme that treats the static potential exactly and study its convergence properties.