Analytic perturbation theory in QCD and Schwinger’s connection between the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi></mml:math>function and the spectral density

Milton, Kimball A.; Solovtsov, I. L.

doi:10.1103/physrevd.55.5295

Cited by 128 publications

(243 citation statements)

References 11 publications

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“…(11) hereinafter, which makes Eq. (10) identical to that of both the foregoing DPT [31][32][33][34] and the so-called analytic perturbation theory 2 (APT) [54][55][56][57]. It has to be noted that, in general, the perturbative spectral function at small values of its argument may be altered by the terms of an intrinsically nonperturbative nature.…”

Section: R-ratio Of Electron-positron Annihilation Into Hadronsmentioning

confidence: 99%

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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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Section: R-ratio Of Electron-positron Annihilation Into Hadronsmentioning

confidence: 99%

“…[120] and only afterwards was derived in Refs. [9,10,12,54,55]. Figure 3A displays the one-loop "timelike" effective couplant a (1) TL (s) (17) and the "naive" continuation of the oneloop perturbative couplant a (1) s (Q 2 ) (13) into the timelike domain (12).…”

Section: Figmentioning

confidence: 99%

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

Нестеренко

2017

Eur. Phys. J. C

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“…We emphasize that in this approach, the higher order quantities A k (µ 2 ) (k ≥ 2) are not as basic, they are defined via Eqs. (26) for convenience of having closer notational analogy with pQCD formulas (and a k ↔ A k ). In these definitions (26), as well as in β j -running Eqs.…”

Section: Analytization Of Higher Powers Of the Coupling Parametermentioning

confidence: 99%

“…(27) are, in contrast to Eqs. (26), not definitions, but in general approximations for the evolution under RSch-changes. The RSch-dependence of A 1 (µ 2 ) is treated in more detail later in this work.…”

Section: Analytization Of Higher Powers Of the Coupling Parametermentioning

confidence: 99%

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Various versions of analytic QCD and skeleton-motivated evaluation of observables

Cvetič

Valenzuela

2006

Phys. Rev. D

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We present skeleton-motivated evaluation of QCD observables. The approach can be applied in analytic versions of QCD in certain classes of renormalization schemes. We present two versions of analytic QCD which can be regarded as low-energy modifications of the "minimal" analytic QCD and which reproduce the measured value of the semihadronic τ decay ratio rτ . Further, we describe an approach of calculating the higher order analytic couplings A k (k = 2, 3, . . .) on the basis of logarithmic derivatives of the analytic coupling A1(Q 2 ). This approach can be applied in any version of analytic QCD. We adjust the free parameters of the afore-mentioned two analytic models in such a way that the skeleton-motivated evaluation reproduces the correct known values of rτ and of the Bjorken polarized sum rule (BjPSR) d b (Q 2 ) at a given point (e.g., at Q 2 = 2 GeV 2 ). We then evaluate the low-energy behavior of the Adler function dv(Q 2 ) and the BjPSR d b (Q 2 ) in the afore-mentioned evaluation approach, in the three analytic versions of QCD. We compare with the results obtained in the "minimal" analytic QCD and with the evaluation approach of Milton et al. and Shirkov. Changes in v3: the values of parameters of analytic QCD models M1 and M2 were refined and the numerical results modified accordingly; the penultimate paragraph of Sec. II and the ultimate paragraph of Sec. III are new; discussion of Figs. 4 was extended; new references were added.

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Ghost-Free APT Analysis of Perturbative QCD Observables

Shirkov

2003

Particle Physics in the New Millennium

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We establish direct connection between ghost-free formulations of RG-invariant perturbation theory in the both Euclidean and Minkowskian regions.By combining the trick of resummation of the π 2 -terms for the invariant QCD coupling and observables in the time-like region with fresh results on the "analyticized" coupling α an (Q 2 ) and observables in the space-like domain we formulate a self-consistent scheme, free of ghost troubles. The basic point of this joint construction is the "dipole spectral relation" (1) emerging from axioms of local QFT.Then we consider the issue of the heavy quark thresholds and devise a global scheme for the data analysis in the whole accessible space-like and time-like domain with various numbers of active quarks. Observables in both the regions are presented in a form of non-power perturbation series with improved convergence properties.Preliminary estimates indicate that this global scheme produces results a bit different -on a few per cent level forᾱ s -from the usual one, thus influencing the total picture of the QCD parameters correlation.

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Analytic perturbation theory in QCD and Schwinger’s connection between theβfunction and the spectral density

Cited by 128 publications

References 11 publications

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

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

Various versions of analytic QCD and skeleton-motivated evaluation of observables

Ghost-Free APT Analysis of Perturbative QCD Observables

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