Pion form factor in QCD sum rules, local duality approach, and O(A_2) fractional analytic perturbation theory

TL;DR

This paper combines QCD sum rules, local duality, and fractional analytic perturbation theory to improve the estimation of the pion form factor, providing a more accurate theoretical prediction.

Contribution

It introduces a novel method to determine the effective continuum threshold and applies fractional analytic perturbation theory at O(α_s^2) for pion form factor estimation.

Findings

Effective continuum threshold determined for local duality approach

Constructed O(α_s^2) estimation of pion form factor

Enhanced theoretical accuracy in pion form factor prediction

Abstract

Using the results on the electromagnetic pion Form Factor (FF) obtained in the $O(\alpha_s)$ QCD sum rules with non-local condensates \cite{BPS09} we determine the effective continuum threshold for the local duality approach. Then we apply it to construct the $O(\alpha_s^2)$ estimation of the pion FF in the framework of the fractional analytic perturbation theory.