Determination of $m_c$ and $m_b$ from quarkonium 1S energy levels in perturbative QCD

Abstract

We update determination of the $\overline{\mathrm{MS}}$ 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 $\epsilon$ expansion and using the $\overline{\mathrm{MS}}$ masses. Effects of non-zero charm-quark mass in the bottomonium masses are incorporated up to next-to-next-to-leading order. We obtain ${\overline{m}}_c=1246\pm 2(d_3)\pm 4({\alpha }_s)\pm 23(\text{h.o.})\mathrm{MeV}$ and ${\overline{m}}_b=4197\pm 2(d_3)\pm 6({\alpha }_s)\pm 20(\text{h.o.})\pm 5(m_c)\mathrm{MeV}$, which agree with the current Particle Data Group values.

Comments: 12 pages, 5 figures, 1 table. v2: Typo corrected in Eq.(3); no change of final results