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 i n the time-like region with the electromagnetic structure of the nucle ons as measured in the space-like region. Simple analytic representati ons of the magnetic form factor of the proton G(M)(p)(Q(2)) and the el ectric form factor of the neutron G(E)(n)(Q(2)) are derived which have the following properties built-in: the correct normalization and slop e at Q(2) = 0 and correct asymptotic behavior at \Q(2)\ --> infinity. The predictions of perturbative QCD at asymptotic Q(2) and meson physi cs at low Q(2) are combined to fit the existing data in the entire ran ge of the four-momentum transfer squared. This leads to the following observations: (i) Measurements of cross sections for the reaction p (p ) over bar --> e(+)e(-) taken at the Fermilab E-760 match measurements made at the SLAC-136 experiment only if the logarithmic falloff of Q( 4)G(M)(p)(Q(2)), expected from leading twist predictions of perturbati ve quantum chromodynamics, is included. (ii) Analytic continuation of the neutron time-like form factor into the space-like interval 0.1 GeV 2 less than or equal to Q(2) less than or equal to 1 GeV2 using the li mited FENICE data gives a factor of similar to 2 inconsistency in G(E) (n)(Q(2)) with the recent Saclay and Mainz measurements.