Determination of m c and m b from quarkonium 1 S energy levels in perturbative QCD

Abstract We update determination of the MS ‾ masses of the charm and bottom quarks, from comparisons of the masses of the charmonium and bottomonium 1 S states with their perturbative predictions up to next-to-next-to-next-to-leading order in e expansion and using the MS ‾ masses. Effects of non-zero charm-quark mass in the bottomonium masses are incorporated up to next-to-next-to-leading order. We obtain m ‾ c = 1246 ± 2 ( d 3 ) ± 4 ( α s ) ± 23 ( h.o. )  MeV and m ‾ b = 4197 ± 2 ( d 3 ) ± 6 ( α s ) ± 20 ( h.o. ) ± 5 ( m c )  MeV , which agree with the current Particle Data Group values.