Exact analytic two-loop expressions for some QCD observables in the time-like region

Abstract

The author of this work have got explicit expressions for the timelike region at Next-to-Leading-Order (NLO) as for the coupling function so for QCD observables. These expressions were compared with approximate ones obtained in terms of "double logarithms". Next-Next-to-Leading-Order (NNLO) Pade approximation was also discussed. In this paper some particular role of NLO was emphasised. It is related with the possibility to express any multi-loop expressions in terms of the two-loop ones. Thus we can use NLO functions as a basis of some functional expansion, where higher loop terms incorporation affects the expansion coefficients only.