Infrared freezing of Euclidean QCD observables in the one-chain approximation

Abstract

We consider the one-chain term in a skeleton expansion for Euclidean QCD observables. Focusing on the particular example of the Adler D function, we show that although there is a Landau pole in the coupling at Q^2=\Lambda^2 which renders fixed-order perturbative results infinite, the Landau pole is absent in the all-orders one-chain result. In this approximation one has finiteness and continuity at Q^2=\Lambda^2, and a smooth freezing as Q^2 decreases to 0.