Analyticity properties of three-point functions in QCD beyond leading order

Abstract

The removal of unphysical singularities in the perturbatively calculable part of the pion form factor-a classic example of a three-point function in QCD-is discussed. Different "analytization" procedures in the sense of Shirkov and Solovtsov are examined in comparison with standard QCD perturbation theory. We show that demanding the analyticity of the partonic amplitude as a whole, as proposed before by Karanikas and Stefanis, one can make infrared finite not only the strong running coupling and its powers, but also cure potentially large logarithms (that first appear at next-to-leading order) containing the factorization scale and modifying the discontinuity across the cut along the negative real axis. The scheme used here generalizes the Analytic Perturbation Theory of Shirkov and Solovtsov to non-integer powers of the strong coupling and diminishes the dependence of QCD hadronic quantities on all perturbative scheme and scale-setting parameters, including the factorization scale.

Erratum: QCD analytic perturbation theory: From integer powers to any power of the running coupling [Phys. Rev. D72, 074014 (2005)]

“…A first example of the present framework is discussed in [40], focusing on the topic of the renormalization-scheme and factorization-scale independence of the electromagnetic pion form factor, relative to its treatment within the standard QCD perturbation theory or original APT. The methods presented here are intended to be used in the low-to-medium momentum range where the standard perturbative approach faces the problem of the Landau pole and in processes or under circumstances where the original APT is insufficient because it is tied to integer powers of the coupling.…”

“…An example of the first kind in connection with a NLO calculation of the electromagnetic pion form factor is treated in [40], while the investigation of such terms in the context of light-cone sum rules will be considered in a future publication. To be more specific, we will consider below terms of the form a (2) ν L and a (2) ν L 2 -rather than deal with the series containing the constant coefficients f n , given in Eq.…”

On the running coupling constant in QCD

“…[89]). Computation of the functional sets has been recently extended to include analytic images of any real power of the coupling (Fractional Analytic Perturbation Theory) on the grounds of properties of the transcendental Lerch function [120]. The APT algorithm can also include thresholds effects [113] in a real description, by modifying the k-th spectral density (144) discontinuously at the heavy quark thresholds m f…”

Synthetic Running Coupling of QCD

“…Indicate Refs. 5,6,7,8,9,10,11,12 in which the analytic approach and its applications to QCD are considering. The analyticity requirement, which follows from the general principles of QFT, enables one to resolve the difficulties connected with nonphysical singularities of the perturbation theory in the infrared region.…”