Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2004-07-07
Phys.Atom.Nucl. 68 (2005) 582-590; Yad.Fiz. 68 (2005) 612-620
Physics
High Energy Physics
High Energy Physics - Phenomenology
21 pages, 1 figure. To be publised in Phys. Atom. Nucl. dedicated to the 70-th birthday of Yu.A. Simonov
Scientific paper
10.1134/1.1903088
The static force $F_B(r)$ and the strong coupling $\alpha_F(r)$, 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 $\alpha_F(r)$ turns out to be essentially smaller than the coupling $\alpha_B(r)$ in the static potential. For the dimensionless function $\Phi_B(r) = r^2 F_B(r)$ the characteristic values $\Phi_B(r_1) =1.0$ and $\Phi_B(r_0)=1.65$ are shown to be reached at the following $Q\bar Q$ separations: $r_1\sqrt{\sigma} =0.77, r_0\sqrt{\sigma} =1.09$ in quenched approximation and $r_1\sqrt{\sigma}=0.72, r_0\sqrt{\sigma}=1.04$ 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 $\alpha_F(r_1)$ and $\alpha_F(r_0)$ 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.
Badalian A. M.
Veselov A. I.
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