2000/10/31 by B. A. Magradze
Physics and Astronomy · #hep-ph
published as Communication of the Joint Institute for Nuclear Research, E2-2000-222, Dubna 2000 · 21 pages, Latex, 12 tables. Abstract is changed. The recurrence formulas (18)-(20) are added. Formula (35) corrected and Table 2 is revised. Misprint in formula (37) is corrected. Formula (38) added
arxiv created 2001/01/07 · arxiv updated 2009/11/30
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 αs. 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 αs in the MS scheme and give numerical results. For first three of these functions \mathfrakAn(s) and \cal An(Q2); n=1,2,3 in the large interval of the momentum transfer and energy (1 GeV <Q,√ s< 170 GeV), numerical tables are presented. From these we observe that, for the timelike arguments, the differences between functions \mathfrakAn(s) and the corresponding powers of the standard iteratively approximated coupling αsn(s) are not negligible even for moderate energies in the five--flavor region.