The vector coupling in IR region from splittings in bottomonium

Abstract

The splittings $1D-1P, 1F-1P, 2D-2P$ are shown to be the most convenient characteristics to determine the vector coupling in IR region. In background perturbation theory the splitting $\Delta =1D -1P$ appears to be in agreement with $\Delta (\exp) =261.1 \pm 2.2$ MeV only for large freezing value, $\alpha_{crit} \cong 0.60$, which corresponds to $\Lambda_{\bar{MS}} (2$-loop, $n_f=5)\cong 240$ MeV $(\alpha_s(M_Z) =0.1193(2)$. The masses $M_{cog} (1F)=10362\pm 3$ MeV and $M_{cog} (2D) =10452\pm 4 $ MeV are predicted.