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

The b (b) over bar 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 Delta(1)=Y(1D)-chi(b)(1P) and other splittings between low-lying states are very sensitive to the QCD constant Lambda(V)(n(f)) which occurs in the vector scheme, and good agreement with the experimental data is obtained for Lambda(V)(2-loop, n(f)=5)=325+/-10 MeV which corresponds to the conventional Lambda((MS) over bar)(2-loop, n(f)=5)=238+/-7 MeV, alpha(s)(2-loop, M-Z)=0.1189+/-0.0005, and to a large freezing value of the background coupling: alpha(crit)(2-loop, q(2)=0)=alpha(crit)(2-loop, r-->infinity)=0.58+/-0.02. If the asymptotic freedom behavior of the coupling is neglected and an effective freezing coupling alpha(static)=const is introduced, as in the Cornell potential, then precise agreement with Delta(1)(exp) and Delta(2)(exp) can be reached for the rather large Coulomb constant alpha(static)=0.43+/-0.02. We predict a value for the mass M(2D)=10451+/-2 MeV.