6,592 research outputs found
Analytic continuation and perturbative expansions in QCD
Starting from the divergence pattern of perturbative quantum chromodynamics,
we propose a novel, non-power series replacing the standard expansion in powers
of the renormalized coupling constant . The coefficients of the new
expansion are calculable at each finite order from the Feynman diagrams, while
the expansion functions, denoted as , are defined by analytic
continuation in the Borel complex plane. The infrared ambiguity of perturbation
theory is manifest in the prescription dependence of the . We prove
that the functions have branch point and essential singularities at
the origin of the complex -plane and their perturbative expansions in
powers of are divergent, while the expansion of the correlators in terms of
the set is convergent under quite loose conditionsComment: 18 pages, latex, 5 figures in EPS forma
Comment on "Infrared freezing of Euclidean QCD observables"
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 is
absent from the leading one-chain term in a skeleton expansion of the Euclidean
Adler 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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