Strong coupling constant from bottomonium fine structure

From a fit to the experimental data on the b (b) over bar fine structure, the two-loop strong coupling constant is extracted. For the 1P state the fitted value is alpha (s)(mu (1)) = 0.33+/-0.01 (exp)+/-0.02(th) at the scale mu (1)=1.8 +/-0.1 GeV, which corresponds to the QCD constant Lambda ((4))(2-loop) = 338+/-30 MeV (n(f)=4) and alpha (s)(M-z) =0.119+/-0.002. For the 2P state the value alpha (s)(mu (2))=0.40+/-0.02 (exp)+/-0.02(th) at the scale mu (2)=1.02 +/- 0.02 GeV is extracted, which is significantly larger than in the previous analysis, but about 30% smaller than the value given by the standard perturbation theory. This value alpha (s)(1.0)approximate to0.40 can be obtained in the framework of the background perturbation theory and appears to be compatible with the freezing of alpha (s)(mu). The relativistic corrections to alpha (s) are found to be about 15%.