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

TL;DR

This paper refines the determination of charm and bottom quark masses using perturbative QCD predictions for quarkonium 1S states, incorporating higher-order effects and charm mass corrections, resulting in values consistent with current standards.

Contribution

It provides updated quark mass values from high-order perturbative calculations, including effects of non-zero charm mass, improving precision over previous estimates.

Findings

Determined charm quark mass as 1246 ± 23 MeV.

Determined bottom quark mass as 4197 ± 20 MeV.

Results agree with Particle Data Group values.

Abstract

We update determination of the $\overline{\rm MS}$ 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 $\varepsilon$ expansion and using the $\overline{\rm MS}$ 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.} )~{\rm MeV} $ and $\overline m_b=4197\pm 2 (d_3) \pm 6 (\alpha_s) \pm 20 (\text{h.o.} )\pm 5 (m_c)~ {\rm MeV} $, which agree with the current Particle Data Group values.