The charm/bottom quark mass from heavy quarkonium at N3LO

Abstract

We determine the charm and bottom quark masses using the N33LO perturbative expression of the ground state (pseudoscalar) energy of the bottomonium, charmonium and Bcc​ systems: the ηbb​, ηcc​ and Bcc​ 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 MS‾MS masses reads m‾c(m‾c)=1223(33)mc​(mc​)=1223(33) MeV and m‾b(m‾b)=4186(37)mb​(mb​)=4186(37) MeV. We also extract a value of αss​ from a renormalon-free combination of the ηbb​, ηcc​ and Bcc​ masses: αss​(Mzz​) = 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.