QCD result for the hyperfine splittingMΥ(1S)−Mηband the value ofαs

The measurement of the ${\ensuremath{\eta}}_{b}$ mass, together with a QCD result for the hyperfine splitting ${E}_{\mathrm{HFS}}={M}_{\ensuremath{\Upsilon}(1S)}\ensuremath{-}{M}_{{\ensuremath{\eta}}_{b}}$, allows us to determine the strong coupling constant ${\ensuremath{\alpha}}_{s}$ at a low energy scale. The result ${\ensuremath{\alpha}}_{s}({M}_{\ensuremath{\Upsilon}(1S)})=0.197\ifmmode\pm\else\textpm\fi{}0.002{|}_{\ensuremath{\Delta}{E}_{\mathrm{HFS}}^{\mathrm{exp} }}\ifmmode\pm\else\textpm\fi{}0.002{|}_{\mathrm{scheme}}\ifmmode\pm\else\textpm\fi{}0.002{|}_{\ensuremath{\delta}⟨{G}^{2}⟩}\ifmmode\pm\else\textpm\fi{}0.006{|}_{\ensuremath{\delta}{m}_{b}}\ifmmode\pm\else\textpm\fi{}0.005{|}_{\mathrm{ho}}$, ${\ensuremath{\alpha}}_{s}({M}_{{Z}^{0}})=0.124\ifmmode\pm\else\textpm\fi{}0.001{|}_{\ensuremath{\Delta}{E}_{\mathrm{HFS}}^{\mathrm{exp} }}\ifmmode\pm\else\textpm\fi{}0.001{|}_{\mathrm{scheme}}\ifmmode\pm\else\textpm\fi{}0.001{|}_{\ensuremath{\delta}⟨{G}^{2}⟩}\ifmmode\pm\else\textpm\fi{}0.003{|}_{\ensuremath{\delta}{m}_{b}}\ifmmode\pm\else\textpm\fi{}0.002{|}_{\mathrm{ho}}$ is compatible with the current world average of ${\ensuremath{\alpha}}_{s}$ reported by the Particle Data Group, and shows that the experimental lowest-lying $\overline{b}b$ hyperfine splitting can be reproduced in terms of a perturbative and nonperturbative QCD contribution.