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 ${\Lambda }_{\overline{MS}}(2$-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.

8 pages. The talk presented at the workshop "QUARKS-2004"