The influence of the analytical continuation effects on the value of the QCD scale parameter Λ extracted from the data on charmonium and upsilon hadron decays

Krasnikov, N.; Пивоваров, А. А.

doi:10.1016/0370-2693(82)91001-2

Cited by 91 publications

(105 citation statements)

References 10 publications

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“…The latter can be obtained by integrating Eq. (4) in finite limits, which yields [9][10][11] R(s) = 1 2πi lim…”

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

confidence: 99%

“…The one-loop spectral functionρ (1) 1 (σ ) (16) ρ(σ ) (11), which enters the pertinent integral representation (10), is required. Since the involved strong correction to the Adler function (8) takes a simple form at the one-loop level, (13) and…”

Section: Figmentioning

confidence: 99%

“…Specifically, it proves to be convenient to express the spectral function ρ ( ) (σ ) (11) in terms of the so-called "partial" spectral functionsρ ( ) j (σ ) corresponding to the jth power of the -loop perturbative couplant (9), namely…”

Section: Spectral Function At the Higher-loop Levelsmentioning

confidence: 99%

“…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%

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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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“…The latter can be obtained by integrating Eq. (4) in finite limits, which yields [9][10][11] R(s) = 1 2πi lim…”

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

confidence: 99%

Section: Figmentioning

confidence: 99%

Section: Spectral Function At the Higher-loop Levelsmentioning

confidence: 99%

Section: R-ratio At the Higher-loop Levelsmentioning

confidence: 99%

See 2 more Smart Citations

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

Нестеренко

2017

Eur. Phys. J. C

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“…Aside from these nice features, this function cannot entirely sum up the π 2 -terms. In order to deal with these corrections a somewhat different approach, known as RKP (Radyushkin-Krasnikov-Pivovarov) procedure, has been suggested [40,41] (see also [42]), which is firmly based upon the analytical properties of the polarization tensor Π h (−q 2 ) and of the related D-function (44), summarized by the dispersion relations, respectively…”

Section: Time-like Couplingmentioning

confidence: 99%

On the running coupling constant in QCD

Prosperi

Raciti

Simolo

2007

Progress in Particle and Nuclear Physics

165

234

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We try to review the main current ideas and points of view on the running coupling constant in QCD. We begin by recalling briefly the classic analysis based on the Renormalization Group Equations with some emphasis on the exact solutions for a given number of loops, in comparison with the usual approximate expressions. We give particular attention to the problem of eliminating the unphysical Landau singularities, and of defining a coupling that remains significant at the infrared scales. We consider various proposal of couplings directly related to the quark-antiquark potential or to other physical quantities (effective charges) and discuss optimization in the choice of the scale parameter and of the renormalization scheme. Our main focus is, however, on dispersive methods, their application, their relation with non-perturbative effects. We try also to summarize the main results obtained by Lattice simulations in particular in various MOM schemes. We conclude briefly recalling the traditional comparison with the experimental data.

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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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The influence of the analytical continuation effects on the value of the QCD scale parameter Λ extracted from the data on charmonium and upsilon hadron decays

Cited by 91 publications

References 10 publications

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

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

On the running coupling constant in QCD

Ghost-Free APT Analysis of Perturbative QCD Observables

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