Determination of mc and mb from quarkonium 1S energy levels in perturbative QCD

We update determination of the MS‾ masses of the charm and bottom quarks, from comparisons of the masses of the charmonium and bottomonium 1S states with their perturbative predictions up to next-to-next-to-next-to-leading order in ε 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(d3)±4(αs)±23(h.o.) MeV and m‾b=4197±2(d3)±6(αs)±20(h.o.)±5(mc) MeV, which agree with the current Particle Data Group values