Calculation of binding energies and masses of quarkonia in analytic QCD models

We extract quark masses (m) over bar (q) (q = b, c) from the evaluation of the masses of quarkonia Upsilon(1S) and J/psi (1S), performed in two analytic QCD models, and in perturbative QCD in two renormalization schemes. In analytic QCD the running coupling has no unphysical singularities in the low-momentum regime. We apply the analytic model of Shirkov et al. [analytic perturbation theory (APT)], extended by Bakulev et al. [fractional analytic perturbation theory (FAPT)], and the two-delta analytic model (2 delta anQCD). The latter, in contrast to (F) APT, at higher energies basically coincides with the perturbative QCD (in the same scheme). We use the renormalon-free mass (m) over bar (q) as input. The separation of the soft and ultrasoft parts of the binding energy E-q (q) over bar is performed by the requirement of the cancellation of the leading infrared renormalon. The analysis in the 2 delta anQCD model indicates that the low-momentum ultrasoft regime is important for the extraction of the masses (m) over bar (q), especially (m) over bar (b). The 2 delta anQCD model gives us clues on how to estimate the influence of the ultrasoft sector on (m) over bar (q) in general. These effects lead to relatively large values (m) over bar (b) approximate to 4.35 +/- 0.08 GeV in the 2 delta anQCD model, which, however, are compatible with recent lattice calculations. In perturbative QCD in the (MS) over bar scheme these effects are even stronger and give larger uncertainties in (m) over bar (b). The (F) APT model gives small ultrasoft effects and the extracted values of (m) over bar (b) agree with those in most of the literature ((m) over bar (b) approximate to 4.2 GeV). The extracted values of (m) over bar (c) in all four models are about 1.26-1.27 GeV and agree well with those in the literature. DOI: 10.1103/PhysRevD.87.054008