Determining alpha_s from the hyperfine splitting mUpsilon(1S)-mEta(b)

Abstract

The measurement of the eta_b mass, together with a QCD result for the hyperfine splitting E_{HFS}=M_{Upsilon(1S)}-M_{eta_b}, allows us to determine the strong coupling constant alpha_s at a low energy scale. The result alpha_s(M_{Upsilon(1S)})=0.197\pm 0.002_{Delta E_{HFS}^{exp}} \pm 0.002_{scheme} \pm 0.002_{delta <G^2>} \pm 0.006_{delta m_b} \pm 0.005_{ho}, alpha_s(M_{Z^0})=0.124\pm 0.001_{Delta E_{HFS}^{exp}} \pm 0.001_{scheme} \pm 0.001_{delta <G^2>} \pm 0.003_{delta m_b} \pm 0.002_{ho}, is compatible with the current world average of alpha_s reported by the Particle Data Group, and shows that the experimental lowest-lying \bar b b hyperfine splitting can be reproduced in terms of a perturbative and nonperturbative QCD contribution.

9 pages, 3 figure. Analysis of the errors reconsidered, one figure added, title modified, accepted for publication in Phys. Rev. D