Comment on "Infrared freezing of Euclidean QCD observables"

Details Comment on "Infrared freezing of Euclidean QCD observables" Comment on "Infrared freezing of Euclidean QCD observables"

2007-06-20

arxiv.org/abs/0706.2914v1

Phys.Rev.D76:018501,2007

Physics

High Energy Physics

High Energy Physics - Phenomenology

Scientific paper

10.1103/PhysRevD.76.018501

Recently, P. M. Brooks and C.J. Maxwell [Phys. Rev. D{\bf 74} 065012 (2006)] claimed that the Landau pole of the one-loop coupling at $Q^2=\Lambda^2$ is absent from the leading one-chain term in a skeleton expansion of the Euclidean Adler ${\cal D}$ function. Moreover, in this approximation one has 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.

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