The charm/bottom quark mass from heavy quarkonium at N³LO

© 2018, The Author(s). We determine the charm and bottom quark masses using the N3LO perturbative expression of the ground state (pseudoscalar) energy of the bottomonium, charmonium and Bc systems: the ηb, ηc and Bc 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 M S ¯ masses reads m¯c(m¯c)=1223(33) MeV and m¯b(m¯b)=4186(37) MeV. We also extract a value of αs from a renormalon-free combination of the ηb, ηc and Bc masses: αs(Mz) = 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.