QCDMAPT: Program package for Analytic approach to QCD

Нестеренко, А. В.; Simolo, C.

doi:10.1016/j.cpc.2010.06.040

Cited by 39 publications

(29 citation statements)

References 49 publications

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“…Numerical programs were constructed to calculate A (APT) ν (Q 2 ) up to four-loop level of the underlying MS pQCD coupling a, in [75,76] in Maple and/or Fortran, and in [23,77] in Mathematica.…”

Section: Discussionmentioning

confidence: 99%

Bjorken polarized sum rule and infrared-safe QCD couplings

et al. 2018

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Experimental data obtained for the polarized Bjorken sum rule (BSR) Γ p−n 1 (Q 2 ) are fitted by using predictions derived within a truncated operator product expansion (OPE) approach to QCD. Four QCD versions are considered: perturbative QCD (pQCD) in the MS scheme, Analytic Perturbation Theory (APT), and 2δ and 3δ analytic QCD versions. In contrast to pQCD, these QCD variants do not have Landau singularities at low positive Q 2 , which facilitates the fitting procedure significantly. The fitting procedure is applied first to the experimental data of the inelastic part of BSR, and the known elastic contributions are added after the fitting. In general, when 2δ and 3δ QCD coupling is used the fitted curves give the best results, within the Q 2 -range of the fit as well as in extended Q 2intervals. When the fitting procedure is applied to the total BSR, i.e., to the sum of the experimental data and the elastic contribution, the quality of the results deteriorates significantly.

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Section: Discussionmentioning

confidence: 99%

Bjorken polarized sum rule and infrared-safe QCD couplings

et al. 2018

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“…As for the four-loop first-order function (76), it can be represented as [122,123] [which, being based on a less universal method of calculation of the relevant spectral function (11) than that of Eq. (71), is applicable at first four loop levels only] and [124].…”

Section: R-ratio At the Higher-loop Levelsmentioning

confidence: 99%

Electron–positron annihilation into hadrons at the higher-loop levels

Нестеренко

2017

Eur. Phys. J. C

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The strong corrections to the R-ratio of electronpositron annihilation into hadrons are studied at the higherloop levels. Specifically, the derivation of a general form of the commonly employed approximate expression for the Rratio (which constitutes its truncated re-expansion at high energies) is delineated, the appearance of the pertinent π 2 -terms is expounded, and their basic features are examined. It is demonstrated that the validity range of such approximation is strictly limited to √ s/Λ > exp(π/2) 4.81 and that it converges rather slowly when the energy scale approaches this value. The spectral function required for the proper calculation of the R-ratio is explicitly derived and its properties at the higher-loop levels are studied. The developed method of calculation of the spectral function enables one to obtain the explicit expression for the latter at an arbitrary loop level. By making use of the derived spectral function the proper expression for the R-ratio is calculated up to the five-loop level and its properties are examined. It is shown that the loop convergence of the proper expression for the R-ratio is better than that of its commonly employed approximation. The impact of the omitted higher-order π 2 -terms on the latter is also discussed.

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“…Firstly, the analytization in the general analytic QCD frameworks [13] can be performed for powers of a(Q 2 ), but not for the expression of the type (16). 1 Secondly, we will be working at the two-loop level; in the general n-loop case the coefficient d 1 of the expansion (17) depends only on the two-loop coefficients β 1 and γ 1 , while the full next coefficient d 2 involves also the three-loop (MS) coefficients β 2 and γ 2 which are not included in this work.…”

Section: Gluon Propagator In the Landau Gauge A Propagator In Pqcdmentioning

confidence: 99%

“…Mathematical packages for numerical calculations in APT and FAPT are given in Refs. [16]. We will use the numerical approach (5) for the calculation of the FAPT coupling, with the underlying pQCD coupling being the two-loop coupling [14,17,18] (see also [19,20])…”

Section: Fractional Analytic Perturbation Theory (Fapt) Modelmentioning

confidence: 99%

Gluon propagator in fractional analytic perturbation theory

2014

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We consider the gluon propagator in the Landau gauge at low spacelike momenta and with the dressing function Z(Q 2 ) at the two-loop order. We incorporate the nonperturbative effects by making the (noninteger) powers of the QCD coupling in the dressing function Z(Q 2 ) analytic (holomorphic) via the Fractional Analytic Perturbation Theory (FAPT) model, and simultaneously introducing the gluon dynamical mass in the propagator as motivated by the previous analyses of the Dyson-Schwinger equations. The obtained propagator has behavior compatible with the unquenched lattice data (N f = 2 + 1) at low spacelike momenta 0.4 GeV < Q 10 GeV. We conclude that the removal of the unphysical Landau singularities of the powers of the coupling via the (F)APT prescription, in conjunction with the introduction of the dynamical mass M ≈ 0.62 GeV of the gluon, leads to an acceptable behavior of the propagator in the infrared regime.

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QCDMAPT: Program package for Analytic approach to QCD

Cited by 39 publications

References 49 publications

Bjorken polarized sum rule and infrared-safe QCD couplings

Bjorken polarized sum rule and infrared-safe QCD couplings

Electron–positron annihilation into hadrons at the higher-loop levels

Gluon propagator in fractional analytic perturbation theory

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