Cesar Ayala

Simple analytic QCD model with perturbative QCD behavior at high momenta

In contrast to perturbative QCD, the analytic QCD models have running coupling whose analytic properties correctly mirror those of spacelike observables. The discontinuity (spectral) function of such running coupling is expected to agree with the perturbative case at large timelike momenta; however, at low timelike momenta it is not known. In the latter regime, we parametrize the unknown behavior of the spectral function as a sum of (two) delta functions; while the onset of the perturbative behavior of the spectral function is set to be 1.0-1.5 GeV. This is in close analogy with the “minimal hadronic ansatz” used in the literature for modeling spectral functions of correlators. For the running coupling itself, we impose the condition that it basically merges with the perturbative coupling at high spacelike momenta. In addition, we require that the well-measured nonstrange semihadronic (V + A) tau decay ratio value be reproduced by the model. We thus obtain a QCD framework which is basically indistinguishable from perturbative QCD at high momenta (Q > 1 GeV), and at low momenta it respects the basic analyticity properties of spacelike observables as dictated by the general principles of the local quantum field theories.

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/\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 (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.

The bottom quark mass from the

A bstractWe obtain an improved determination of the normalization constant of the first infrared renormalon of the pole mass (and the singlet static potential). For Nf = 3 it reads Nm = 0.563(26). Charm quark effects in the bottom quark mass determination are carefully investigated. Finally, we determine the bottom quark mass using the NNNLO perturbative expression for the ϒ1S

system at NNNLO

\boldsymbol{\Upsilon} (1S)

anQCD: A Mathematica package for calculations in general analytic QCD models☆

mass. We work in the renormalon subtracted scheme, which allows us to control the divergence of the perturbation series due to pole mass renormalon. Our result for the MS¯

\boldsymbol{\Upsilon} (1S)

\overline{\mathrm{MS}}