Pion form factor in QCD sum rules, local duality approach, and O(A2) fractional analytic perturbation theory

Using the results on the electromagnetic pion Form Factor (FF) obtained in the O(αs) QCD sum rules with non-local condensates [A.P. Bakulev, A.V. Pimikov, and N.G. Stefanis, Phys. Rev. D79 (2009) 093010] we determine the effective continuum threshold for the local duality approach. Then we apply it to construct the estimation of the pion FF in the framework of the fractional analytic perturbation theory.