On the Proton Form Factors in the Time-Like Region

The process $\bar{p} p \rightarrow e^{-} e^{+}$ is considered in the general case of polarized initial particles. A relation between the difference of the phases of the electromagnetic form factors $G_M$ and $G_E$ in the time-like region and measurable asymmetries is derived. It is shown that the moduli of the form factors can be determined from measurements of the total unpolarized cross section and of the integral asymmetry for longitudinally polarized (or transversely polarized) $\bar{p}$ and $p$. The behaviour of the proton form factors at high $q^2$ in the time-like region is also discussed. From the Phragm\'en-Lindel\"of's theorem it follows that the asymptotical behaviour of the form factors in the space-like and time-like regions must be the same. An analysis of experimental data in both regions based on perturbative QCD is presented.