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 ${\ensuremath{\alpha}}_{s}({\ensuremath{\mu}}_{1})=0.33\ifmmode\pm\else\textpm\fi{}0.01(\mathrm{exp})\ifmmode\pm\else\textpm\fi{}0.02(\mathrm{th})$ at the scale ${\ensuremath{\mu}}_{1}=1.8\ifmmode\pm\else\textpm\fi{}0.1$ GeV, which corresponds to the QCD constant ${\ensuremath{\Lambda}}^{(4)}(2\ensuremath{-}\mathrm{loop})=338\ifmmode\pm\else\textpm\fi{}30$ MeV ${(n}_{f}=4)$ and ${\ensuremath{\alpha}}_{s}{(M}_{Z})=0.119\ifmmode\pm\else\textpm\fi{}0.002.$ For the $2P$ state the value ${\ensuremath{\alpha}}_{s}({\ensuremath{\mu}}_{2})=0.40\ifmmode\pm\else\textpm\fi{}0.02(\mathrm{exp})\ifmmode\pm\else\textpm\fi{}0.02(\mathrm{th})$ at the scale ${\ensuremath{\mu}}_{2}=1.02\ifmmode\pm\else\textpm\fi{}0.02$ 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 ${\ensuremath{\alpha}}_{s}(1.0)\ensuremath{\approx}0.40$ can be obtained in the framework of the background perturbation theory and appears to be compatible with the freezing of ${\ensuremath{\alpha}}_{s}(\ensuremath{\mu}).$ The relativistic corrections to ${\ensuremath{\alpha}}_{s}$ are found to be about 15%.