Strong coupling constant from bottomonium fine structure

From a fit to the experimental data on the $b\overline{b}$ fine structure, the two-loop strong coupling constant is extracted. For the $1P$ state the fitted value is ${\alpha }_s\left({\mu }_1\right)=0.33\mathrm{}\pm 0.01\left(\exp \right)\pm 0.02\left(\mathrm{th}\right)$ at the scale ${\mu }_1=1.8\mathrm{}\pm 0.1$ GeV, which corresponds to the QCD constant ${\Lambda }^{\mathrm{}\left(4\right)\mathrm{}}(2-\mathrm{loop})=338\mathrm{}\pm 30$ MeV ${(n}_f=4)$ and ${\alpha }_s{(M}_Z)=0.119\mathrm{}\pm \mathrm{0.002.}$ For the $2P$ state the value ${\alpha }_s\left({\mu }_2\right)=0.40\mathrm{}\pm 0.02\left(\exp \right)\pm 0.02\left(\mathrm{th}\right)$ at the scale ${\mu }_2=1.02\mathrm{}\pm 0.02$ 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 ${\alpha }_s\mathrm{}\left(1.0\right)\mathrm{}\approx 0.40$ can be obtained in the framework of the background perturbation theory and appears to be compatible with the freezing of ${\alpha }_s\left(\mu \right).\mathrm{}$ The relativistic corrections to ${\alpha }_s$ are found to be about 15%.