Strong coupling constant from bottomonium fine structure - art. no. 094031

From a fit to the experimental data on the b (b) over bar fine structure, t he two-loop strong coupling constant is extracted. For the 1P state the fit ted 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 2 P state the value alpha (s)(mu (2))=0.40+/-0.02 (exp)+/-0.02(th) at the sca le mu (2)=1.02 +/- 0.02 GeV is extracted, which is significantly larger tha n in the previous analysis, but about 30% smaller than the value given by t he standard perturbation theory. This value alpha (s)(1.0)approximate to0.4 0 can be obtained in the framework of the background perturbation theory an d appears to be compatible with the freezing of alpha (s)(mu). The relativi stic corrections to alpha (s) are found to be about 15%.