Comment on “Infrared freezing of Euclidean QCD observables”

Abstract

Recently, P. M. Brooks and C. J. Maxwell [Phys. Rev. D 74, 065012 (2006)] claimed that the Landau pole of the one-loop coupling at ${Q}^{2}={\ensuremath{\Lambda}}^{2}$ is absent from the leading one-chain term in a skeleton expansion of the Euclidean Adler $\mathcal{D}$ function. Moreover, in this approximation one has, allegedly, continuity along the Euclidean axis and a smooth infrared freezing, properties known to be satisfied by the ``true'' Adler function. We show that crucial in the derivation of these results is the use of a modified Borel summation, which leads simultaneously to the loss of another fundamental property of the true Adler function: the analyticity implied by the K\"allen-Lehmann representation.