Electron-positron annihilation into hadrons at the higher-loop levels: Explicit form

A. V. Nesterenko

Published 2019-02-18Version 1

The paper constitutes the second part of the study of the R-ratio of electron-positron annihilation into hadrons [Eur. Phys. J. C77, 844 (2017)]. Specifically, the explicit expression for the R-ratio, which properly accounts for all the effects due to continuation of the spacelike perturbative results into the timelike domain, is obtained at an arbitrary loop level, that, in turn, substantially facilitates its application for practical purposes. Several equivalent ways to derive a commonly employed approximation of the R-ratio are recapped and the impact of the discarded in the latter higher-order pi2-terms on the evaluation of the strong running coupling is elucidated.