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

We extract MSbar quark masses mqbar (q=b,c) from the evaluation of the masses of quarkonia Upsilon(1S) and J/ψ(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 (2delanQCD). 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 mqbar as input. The separation of the soft and ultrasoft parts of the binding energy E is performed by the requirement of the cancellation of the leading infrared renormalon. The analysis in the 2delanQCD model indicates that the low-momentum ultrasoft regime is important for the extraction of the masses mqbar, especially mbbar. The 2delanQCD model gives us clues on how to estimate the influence of the ultrasoft sector on mqbar in general. These effects lead to relatively large values mbbar(mbbar) =approx (4.35 +- 0.08) GeV in the 2delanQCD model, which, however, are compatible with recent lattice calculations. In perturbative QCD in MSbar scheme these effects are even stronger and give larger uncertainties in mbbar. The (F)APT model gives small ultrasoft effects and the extracted values of mbbar agree with those in most of the literature: mbbar(mbbar) =approx 4.2 GeV. The extracted values of mcbar(mcbar) in all four models are about 1.26-1.27 GeV and agree well with those in the literature.