Bottom and charm mass determinations from global fits to Qoverline{Q} bound states at N3LO

Abstract

The bottomonium spectrum up to n = 3 is studied within Non-Relativistic Quantum Chromodynamics up to N3LO. We consider finite charm quark mass effects both in the QCD potential and the overline{mathrm{MS}} -pole mass relation up to third order in the Y-scheme counting. The u = 1/2 renormalon of the static potential is canceled by expressing the bottom quark pole mass in terms of the MSR mass. A careful investigation of scale variation reveals that, while n = 1, 2 states are well behaved within perturbation theory, n = 3 bound states are no longer reliable. We carry out our analysis in the nℓ = 3 and nℓ = 4 schemes and conclude that, as long as finite mc effects are smoothly incorporated in the MSR mass definition, the difference between the two schemes is rather small. Performing a fit to boverline{b} bound states we find {overline{m}}_bleft({overline{m}}_bright) = 4.216 ± 0.039 GeV. We extend our analysis to the lowest lying charmonium states finding {overline{m}}_cleft({overline{m}}_cright) = 1.273 ± 0.054 GeV. Finally, we perform simultaneous fits for {overline{m}}_b and αs finding {alpha}_s^{left({n}_f=5right)}left({m}_Zright)=0.1178pm 0.0051 . Additionally, using a modified version of the MSR mass with lighter massive quarks we are able to predict the uncalculated mathcal{O}left({alpha}_s^4right) virtual massive quark corrections to the relation between the overline{mathrm{MS}} and pole masses.