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

César Ayala, Gorazd Cvetič

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25 Citations (Scopus)


We extract quark masses m̄q (q=b, c) from the evaluation of the masses of quarkonia Υ(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 (2δanQCD). 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 ̄q as input. The separation of the soft and ultrasoft parts of the binding energy Eqq̄ is performed by the requirement of the cancellation of the leading infrared renormalon. The analysis in the 2δanQCD model indicates that the low-momentum ultrasoft regime is important for the extraction of the masses m̄q, especially m̄b. The 2δanQCD model gives us clues on how to estimate the influence of the ultrasoft sector on m̄q in general. These effects lead to relatively large values m̄b≈4.35±0.08 GeV in the 2δanQCD model, which, however, are compatible with recent lattice calculations. In perturbative QCD in the MS̄ scheme these effects are even stronger and give larger uncertainties in m̄b. The (F)APT model gives small ultrasoft effects and the extracted values of m ̄b agree with those in most of the literature (m ̄b≈4.2 GeV). The extracted values of m̄c in all four models are about 1.26-1.27 GeV and agree well with those in the literature. © 2013 American Physical Society.
Original languageEnglish
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Publication statusPublished - 5 Mar 2013

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