Implications of the Veneziano Model to Vector - Meson Dominance for the Electromagnetic Form Factors

The Frampton Veneziano-type model for the nucleon form factor is studied in detail. It is found that the predictions of the model for $F_1^V\mathrm{}\left(t\right)\mathrm{}$ and $F_1^S\mathrm{}\left(t\right)\mathrm{}$ are almost indistinguishable from the vector-meson dominance (VMD) predictions in the region $0<t<\mathrm{}0.8\mathrm{}$ ${\mathrm{GeV}}^2$. Consequently, these two models imply the same relations for the Dirac coupling constants of $\rho$, $\omega$, and $\phi$ to the nucleon and to the photon. If the Frampton model has anything to do with reality, it also implies that no VMD assumption can be made for $F_2^V\mathrm{}\left(t\right)\mathrm{}$ and $F_2^S\mathrm{}\left(t\right)\mathrm{}$ even if we restrict ourselves to small regions around the $\rho$ and $\omega$. Finally, by making analogous assumptions for the pion form factor, we argue that higher $\rho$ mesons ${\rho }^{\prime }$, ${\rho }^{\prime \prime }$, etc.) are coupled more strongly to the nucleon than to the pion and that the pion form factor is vanishing asymptotically more slowly than the nucleon form factor. This suggests that it might be profitable to look for these mesons in backward production in $\pi -N$ scattering, and provides an explanation of the difficulty of discovering them up to now.