What can new time-like data tell us about the electromagnetic structure of the proton and neutron?

Unsubtracted dispersion relations are used to link new data obtained in the time-like region with the electromagnetic structure of the nucleons as measured in the space-like region. Simple analytic representations of the magnetic form factor of the proton G^p_M( Q²) and the electric form factor of the neutron Gⁿ_E( Q²) are derived which have the following properties built-in: the correct normalization and slope at Q² = 0 and correct asymptotic behavior at | Q²| → ∞. The pred of perturbative QCD at asymptotic Q² and meson physics at low Q² are combined to fit the existing data in the entire range of the four-momentum transfer squared. This leads to the following observations: (i) Measurements of cross sections for the reaction p overlinep → e ⁺e ^- taken at the Fermilab E-760 match measurements made at the SLAC-136 experiment only if the logarithmic falloff of Q⁴G^p_M( Q²), expected from leading twist predictions of perturbative quantum chromodynamics, is included. (ii) Analytic continuation of the neutron time-like form factor into the space-like interval 0.1 GeV ² ≤ Q² ≤ 1 GeV ² using the limited FENICE data gives a factor of ∼ 2 inconsistency in Gⁿ_E( Q²) with the recent Saclay and Mainz measurements.