Relations between Electron and Proton Excitation ofN*Resonances

We have taken various theories which relate the elastic electromagnetic form factors of the proton to the proton-proton scattering amplitude and, after briefly reviewing their content, have extended them in turn to diffractive excitation processes. We consider only very high-energy scattering $s\gg m^2$, $M^2$, where $m \mathrm{}\left(M\right)\mathrm{}$ is the proton (resonance) mass. For large momentum transfer we find $X={G_E}^{-2\mathrm{}}\mathrm{}\left(t\right)\left(\frac{{\left|f_c\right|}^2+a{\left|f_t\right|}^2}{\mathrm{}\left|t\right|\mathrm{}}\right)\frac{m}{M}+O\left(\frac{1}{s}\right)$, where $X$ is the ratio of $\frac{d\sigma }{\mathrm{dt}} \mathrm{for} p+p\to p+N$ to that for $p+p\to p+p$, and the $f$'s are the standard inelastic electromagnetic form factors. $a=\frac{\mathrm{}(2J+1)\mathrm{}}{J}$. For small momentum transfer we employ both an additive quark model and an eikonal scattering model. In both models a direct connection is found between $X$ and the electromagnetic form factors. The comparison of these theories with available data is very encouraging.