Comment on "Infrared freezing of Euclidean QCD observables"

TL;DR

This paper critiques a recent claim that the Euclidean Adler function exhibits infrared freezing and lacks a Landau pole, demonstrating that the modified Borel summation used in that claim compromises the function's fundamental analyticity.

Contribution

The paper provides a critical analysis showing that the method used to argue for infrared freezing undermines the Adler function's analyticity, challenging previous conclusions.

Findings

Modified Borel summation affects analyticity

Infrared freezing does not hold under true analyticity

Landau pole remains a fundamental feature

Abstract

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.