Infrared Freezing of Euclidean QCD observables

Abstract

We consider the leading one-chain term in a skeleton expansion for QCD observables and show that for energies Q^2>Λ^2, where Q^2=Λ^2 is the Landau pole in the coupling, the skeleton expansion result is equivalent to the standard Borel integral representation, with ambiguities related to infrared (IR) renormalons. For Q^2<Λ^2 the skeleton expansion result is equivalent to a previously proposed modified Borel representation where the ambiguities are connected with ultraviolet (UV) renormalons. We investigate the Q^2-dependence of the perturbative corrections to the Adler D function, the GLS sum rule, and the polarized and unpolarized Bjorken sum rules. In all these cases the one-chain result changes sign in the vicinity of Q^2=Λ^2, and then exhibits freezing behaviour, vanishing at Q^2=0. Finiteness at Q^2=Λ^2 implies specific relations between the residues of IR and UV renormalons in the Borel plane. These relations, only one of which has previously been noted (though it remained unexplained) are shown to follow from the continuity of the characteristic function in the skeleton expansion. By considering the compensation of non-perturbative and perturbative ambiguities we are led to a result for the Q^2 dependence of these observables at all Q^2, in which there is a single undetermined non-perturbative parameter, and which involves the skeleton expansion characteristic function. The observables freeze to zero in the infrared. We briefly consider the freezing behaviour of the Minkowskian R_{e+e-} ratio.