We study the asymptotic behavior of the ratio of Pauli and Dirac electromagnetic nucleon form factors, $F_2/F_1$, in time-like region for different parametrizations built for the space-like region. We investigate how fast the ratio $F_2/F_1$ approaches the asymptotic limits according to the Phragm\\`en-Lindel\\\"of 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 $e^++e^-\\to N+\\bar{N}$ (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 $F_2/F_1$ contradicts this theorem. |
