The Vector Coupling α_V(r) and the Scales r_0, r_1 in the Background Perturbation Theory

摘要

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 GeV~2 and the QCD constants Λ_(MS~-)(n_f), taken from pQCD, while the infrared (IR) regulator MB 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_0Λ_(MS-)(n_f = 3) = 0.77 ± 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 Λ_(MS~-)(n_f = 3) = (325 ± 15) MeV and the frozen value of α_V = 0.57 ± 0.02. The mass splittings M~-(1D) ? M~- (1P) and M~- (2P) ? M~- (1P) are shown to be sensitive to the IR regulator used. The masses M(1 ~3D_3) = 10169(2) MeV andM(1 ~3D_1) = 10155(3) MeV are predicted.