Abstract

The relation between the infrared renormalons, the Borel resummation prescriptions, and the analyticity structure of Green's functions in perturbative QCD is investigated. A specific recently suggested Borel resummation prescription resulted in a principal value and an additional power-suppressed correction that is consistent with operator product expansion. Arguments requiring the finiteness of the result for any power coefficient of the leading infrared renormalon, and consistency in the case of the absence of that renormalon, require that this prescription be modified. The apparently most natural modification leads to the result represented by the principal value. The analytic structure of the amplitude in the complex coupling plane, obtained in this way, is consistent with that obtained in the literature by other methods. © 2003 The American Physical Society.