Electron-Positron to Nucleon-Antinucleon Pair at Threshold and Proton Form Factor

The reactions of electron-positron to nucleon-antinucleon pair at energy threshold are studied in a non-perturbative quark model. The puzzling experimental result that the ratio of the cross section of electron-positron to proton-antiproton to the one of electron-positron to neutron-antineutron is smaller than 1 can be understood in the framework of the phenomenological nonrelativistic quark model and the theoretical predictions for the time-like proton form factor at energy threshold are well consistent with the experimental data. The work suggests that the two-step process, in which the primary quark-antiquark pair forms first a vector meson which in turn decays into a hadron pair, is dominant over the one-step process in which the primary quark-antiquark pair is directly dressed by additional quark-antiquark pairs to form a hadron pair. The experimental data on the reactions of electron-positron to nucleon-antinucleon strongly suggest the reported vector meson omega(1930) to be a 2D-wave particle, while the vector meson rho(2000) is preferred to be a mixture of 3S and 2D states.