The static force in background perturbation theory

Abstract

The static force $F_B(r)$ and the strong coupling $α_F(r)$, which defines the gluon-exchange part of $F_B(r)$, are studied in QCD background perturbation theory (BPT). In the region $r\la 0.6 $ fm $α_F(r)$ turns out to be essentially smaller than the coupling $α_B(r)$ in the static potential. For the dimensionless function $Φ_B(r) = r^2 F_B(r)$ the characteristic values $Φ_B(r_1) =1.0$ and $Φ_B(r_0)=1.65$ are shown to be reached at the following $Q\bar Q$ separations: $r_1\sqrtσ =0.77, r_0\sqrtσ =1.09$ in quenched approximation and $r_1\sqrtσ=0.72, r_0\sqrtσ=1.04$ for $n_f =3$. The numbers obtained appear to be by only 8% smaller than those calculated in lattice QCD while the values of the couplings $α_F(r_1)$ and $α_F(r_0)$ in BPT are by $\sim 30% (n_f =3)$ and $50% (n_f=0)$ larger than corresponding lattice couplings. With the use of the BPT potential good description of the bottomonium spectrum is obtained.