The static force in background perturbation theory

The static force FB(r) and the strong coupling αF(r), which defines the gluon-exchange part of FB(r), are studied in QCD background perturbation theory (BPT). In the region r ≤ 0.6 fm αF(r) turns out to be essentially smaller than the coupling αB(r) in the static potential. For the dimensionless function ΦB(r) = r2FB(r) the characteristic values ΦB(r1) = 1.0 and ΦB(r0) = 1.65 are shown to be reached at the following QQ separations: r1√σ = 0.77, r0√σ = 1.09 in quenched approximation and r1√σ = 0.72, r0√σ = 1.04 for nf = 3. The numbers obtained appear to be only 8% smaller than those calculated in lattice QCD while the values of the couplings αF(r1) and αF(r0) in BPT are by ∼ 30% (nf = 3) and 50% (nf = 0) larger than corresponding lattice couplings. With the use of the BPT potential good description of the bottomonium spectrum is obtained