  I elaborate on the implementation of analyticity of hadronic quantities at
the amplitude level and show that it amounts to the extension of Analytic
Perturbation Theory of Shirkov and Solovtsov to non-integer (fractional) powers
of the strong running coupling. I give evidence that at the NLO of the
factorized pion's electromagnetic form factor this framework diminishes the
uncertainty due to the renormalization-scheme choice and nearly removes the
dependence on both the renormalization and the factorization scale. I
supplement this discussion by considering effects caused by retaining
transverse momenta that give rise to Sudakov factors.
