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

TL;DR

This paper determines the strong coupling constant alpha_s from the hyperfine splitting of bottomonium states, showing compatibility with the world average and highlighting the interplay of perturbative and nonperturbative QCD effects.

Contribution

It provides a novel extraction of alpha_s at low energy from bottomonium hyperfine splitting measurements, combining experimental data with QCD calculations.

Findings

Alpha_s(M_{Upsilon(1S)})=0.197 ± uncertainties

Alpha_s(M_{Z^0})=0.124 ± uncertainties

Reproduction of hyperfine splitting with perturbative and nonperturbative QCD

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.