The vector coupling α V((r) and the scales r 0, r 1 in the background perturbation theory

Abstract

We study the universal static potential V st(r) and the force, which are fully determined by two fundamental parameters: the string tension σ = 0.18 ± 0.02 GeV2 and the QCD constants $$\Lambda _{\overline {MS} } (n_f )$$ , taken from pQCD, while the infrared (IR) regulator M B is taken from the background perturbation theory and expressed via the string tension. The vector couplings α V(r) in the static potential and α F(r) in the static force, as well as the characteristic scales, r 1(n f = 3) and r 0(n f = 3), are calculated and compared to lattice data. The result $$r_0 \Lambda _{\overline {MS} } (n_f = 3) = 0.77 \pm 0.03$$ , which agrees with the lattice data, is obtained for M B = (1.15 ± 0.02) GeV. However, better agreement with the bottomonium spectrum is reached for a smaller $$\Lambda _{\overline {MS} } (n_f = 3) = (325 \pm 15)$$ MeV and the frozen value of α V = 0.57 ± 0.02. The mass splittings $$\bar M(1D) - \bar M(1P)$$ and $$\bar M(2P) - \bar M(1P)$$ are shown to be sensitive to the IR regulator used. The masses M(1 3 D 3) = 10169(2) MeV andM(1 3 D 1) = 10155(3) MeV are predicted.