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The reactions of electron-positron to nucleon-antinucleon pair at energythreshold are studied in a non-perturbative quark model. The puzzlingexperimental result that the ratio of the cross section of electron-positron toproton-antiproton to the one of electron-positron to neutron-antineutron issmaller than 1 can be understood in the framework of the phenomenologicalnonrelativistic quark model and the theoretical predictions for the time-likeproton form factor at energy threshold are well consistent with theexperimental data. The work suggests that the two-step process, in which theprimary quark-antiquark pair forms first a vector meson which in turn decaysinto a hadron pair, is dominant over the one-step process in which the primaryquark-antiquark pair is directly dressed by additional quark-antiquark pairs toform a hadron pair. The experimental data on the reactions of electron-positronto 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 amixture of 3S and 2D states.

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