Restriction on the strong coupling constant in the IR region from the 1D-1P splitting in bottomonium

The bb̄ spectrum is calculated with the use of a relativistic Hamiltonian where the gluon-exchange potential between a quark and an antiquark is taken as in background perturbation theory. We observed that the splittings Δ₁=Υ(1D)-χb(1P) and other splittings between low-lying states are very sensitive to the QCD constant ΛV(nf) which occurs in the vector scheme, and good agreement with the experimental data is obtained for ΛV(2-loop, nf=5)=325±10MeV which corresponds to the conventional ΛMS̄(2-loop,nf=5)=238±7MeV, αₛ(2-loop, MZ)=0.1189±0.0005, and to a large freezing value of the background coupling: ${{α}}crit(2{-}loop, {q}²=0)={{α}}crit(2{-}loop, {{→}}{r}{∞})=0.58±{}0.02.$ If the asymptotic freedom behavior of the coupling is neglected and an effective freezing coupling ${{α}}static=const$ is introduced, as in the Cornell potential, then precise agreement with ${{Δ}}₁(exp)$ and ${{Δ}}₂(exp)$ can be reached for the rather large Coulomb constant ${{α}}static=0.43±{}0.02.$ We predict a value for the mass $M(2D)=10451±{}2MeV.$