Running coupling at low momenta, renormalization schemes, and renormalons

We propose a method for summing a perturbation-theory asymptotic series that is related to infrared (IR) renormalons in QCD using special renormalization schemes in which the running coupling constant can be integrated over the small momenta. For our method to work, we should consider higher order perturbation-theory corrections to the standard bubble-chain diagrams. High-order corrections allow one to choose a scheme in which the coupling-constant evolution can be smoothly extrapolated to low momenta. In these schemes, the sum of an (extended) IR-renormalon asymptotic series is defined as an integral of the running coupling constant over the IR region. We present explicit examples of renormalization schemes of QCD that can be used to sum IR-renormalon asymptotic series according to our definition.