Year: 2000
Type: preprint
Abstract: We analyze two sets of specific functions, that/which form the basis of the nonpower asymptotic expansions both in the timelike and spacelike regions for single scale dependent QCD observables in the Shirkov--Solovtsov's Analytic Perturbation Theory (APT) free of unphysical singularities. These functions are explicitly derived up to the third order in the closed form in terms of the Lambert-W function. As an input we used the exact two loop and the three loop (corresponding to Padé transformed beta-function) RG solutions for common invariant coupling α_s. The elegant recurrence formulas, helpful for numerical analysis, are obtained for the both sets of the APT functions. Then we construct the global versions of APT functions using the continuity conditions (at the quark thresholds) on the α_s in the \bar{MS} scheme and give numerical results. For first three of these functions \mathfrak{A}_n(s) and {\cal A}_n(Q^2); n=1,2,3 in the large interval of the momentum transfer and energy (1 GeV
Source: arXiv (Cornell University)
Author: Magradze, B. A.
Institution: Joint Institute for Nuclear Research
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2963528075