Asymptotic behavior of nucleon electromagnetic form factors in time-like region

We study the asymptotic behavior of the ratio of Pauli and Dirac electromagnetic nucleon form factors, F₂/F₁, in time-like region, for different parametrizations built for the space-like region. We investigate how fast the ratio F₂/F₁ approaches the asymptotic limits according to the Phragmèn-Lindel?f theorem. We show that the QCD-inspired logarithmic behavior of this ratio results in very far asymptotics, experimentally unachievable. This is also confirmed by the normal component of the nucleon polarization, P_y, in e⁺ + e^-↦N + ˉ (in collisions of unpolarized leptons), which is a very interesting observable, with respect to this theorem. Finally we observe that the 1/Q parametrization of F₂/F₁ contradicts this theorem.