Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2005-06-29
Phys.Rev. D72 (2005) 074014; Erratum-ibid. D72 (2005) 119908
Physics
High Energy Physics
High Energy Physics - Phenomenology
23 pages, 6 figures (figure 4a corrected), Eq.(B13) corrected; incorporates Erratum sent to PRD. See also hep-ph/0504275
Scientific paper
10.1103/PhysRevD.72.074014
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.
Bakulev Alexander P.
Mikhailov S. V.
Stefanis N. G.
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