An Analytic Approach to Perturbative QCD

Magradze, B. A.

doi:10.1142/s0217751x00001117

Cited by 42 publications

(78 citation statements)

References 49 publications

(115 reference statements)

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“…At the two-loop level, one should, strictly speaking, deal with the imaginary part of the Lambert function W −1 (see [20]) because the exact solution of Eq. (B4) can be realized in terms of the Lambert function.…”

Section: Discussionmentioning

confidence: 99%

“…Let us emphasize at this point that the extension of this procedure to the two-loop order for the first integer values of ν has been done in Refs. [4,5,20], while the inclusion of still higher-loops [46] seems feasible. 2 However, this approach, based on the spectral density (2.13), is restricted to the specific structure of the Shirkov-Solovtsov APT.…”

Section: Original Analytic Perturbation Theorymentioning

confidence: 99%

“…At zero-momentum transfer the Shirkov-Solovtsov coupling assumes a universal value that depends solely on renormalization-group constants. Using dispersion relations, this scheme was both generalized (in approximate form) to higher-loop orders and also extended to the timelike regime [6,7,[13][14][15][16][17][18][19][20][21][22][23], encompassing previous incomplete attempts [24,25] in this direction, and amounting to the theoretical framework of Analytic Perturbation Theory (APT). There have been a number of parallel developments by various authors during the past several years to avoid the Landau pole using different "analytization" techniques, prime examples being Refs.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Erratum: QCD analytic perturbation theory: From integer powers to any power of the running coupling [Phys. Rev. D72, 074014 (2005)]

Bakulev¹,

Михайлов²,

Stefanis³

2005

Phys. Rev. D

182

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We propose a new generalized version of the QCD Analytic Perturbation Theory of Shirkov and Solovtsov for the computation of higher-order corrections in inclusive and exclusive processes. We construct non-power series expansions for the analytic images of the running coupling and its powers for any fractional (real) power and complete the linear space of these solutions by constructing the index derivative. Using the Laplace transformation in conjunction with dispersion relations, we are able to derive at the one-loop order closed-form expressions for the analytic images in terms of the Lerch function. At the two-loop order we provide approximate analytic images of products of powers of the running coupling and logarithms-typical in higher-order perturbative calculations and when including evolution effects. Moreover, we supply explicit expressions for the two-loop analytic coupling and the analytic images of its powers in terms of one-loop quantities that can strongly simplify two-loop calculations. We also show how to resum powers of the running coupling while maintaining analyticity, a procedure that captures the generic features of Sudakov resummation. The algorithmic rules to obtain analytic coupling expressions within the proposed Fractional Analytic Perturbation Theory from the standard QCD power-series expansion are supplied ready for phenomenological applications and numerical comparisons are given for illustration.

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Section: Discussionmentioning

confidence: 99%

Section: Original Analytic Perturbation Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Erratum: QCD analytic perturbation theory: From integer powers to any power of the running coupling [Phys. Rev. D72, 074014 (2005)]

Bakulev¹,

Михайлов²,

Stefanis³

2005

Phys. Rev. D

182

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“…(109). Despite the implicit form of (111), its symmetry property β (1) an (x) = β (1) an (1 − x) reveals the existence of a IR fixed point at x = 1, corresponding to α an (0) = 1/β 0 (see also [88]). Finally, we just mention here that the relation between the β-function structure and the analytical properties of the running coupling has been investigated in ref.…”

Section: One-loop Analytic 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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“…4 Secondly, while many examples from physics where the Lambert W function arises have now been found (see, e.g., Refs. [18,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]), the problem of determining closed-form expressions for the Wien peaks provides what is undoubtedly the simplest illustration of the use of this function in physics.…”

Section: Introductionmentioning

confidence: 99%

Wien peaks and the Lambert W function

Stewart¹

2011

Rev. Bras. Ensino Fís.

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Exact expressions for the wavelengths where maxima occur in the spectral distribution curves of blackbody radiation for a number of different dispersion rules are given in terms of the Lambert W function. These dispersion rule dependent "Wien peaks" are compared to those wavelengths obtained in a setting independent of the dispersion rule chosen where the "peak" wavelengths are taken to be those obtained on dividing the total radiation intensity emitted from a blackbody into a given percentile. The account provides a simple yet accessible example of the growing applicability of the Lambert W function in physics. Keywords: blackbody radiation, Wien peaks, Lambert W function, polylogarithm.São apresentadas em termos das funções W de Lambert as expressões exatas para os comprimentos de onda para os quais ocorrem máximos das curvas espectrais do corpo negro para algumas diferentes regras de dispersão. Estes "picos de Wien", dependentes da regra de dispersão, são comparadosàqueles obtido independentes desta regra, onde os comprimentos de onda de "pico" são obtidos dividindo-se a intensidade de radiação total emitida por um corpo negro em um dado percentil. Isto fornece um exemplo simples e acessível da crescente aplicabilidade das funções W de Lambert. Palavras-chave: radiação de corpo negro, picos de Wien, função W de Lambert, polylogarithm.

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An Analytic Approach to Perturbative QCD

Cited by 42 publications

References 49 publications

Erratum: QCD analytic perturbation theory: From integer powers to any power of the running coupling [Phys. Rev. D72, 074014 (2005)]

Erratum: QCD analytic perturbation theory: From integer powers to any power of the running coupling [Phys. Rev. D72, 074014 (2005)]

On the running coupling constant in QCD

Wien peaks and the Lambert W function

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