Bounds on Elastic and Inelastic Form Factors of the Nucleon and the Pion

In this paper we derive bounds on the nucleon form factor, the anomalous magnetic moment of nucleons, and the pion form factor. By using sidewise dispersion relations and the Schwarz inequality, we are able to bound the elastic nucleon form factors $F_1\left(q^2\right)$ and $F_2\left(q^2\right)$ by integrals over the structure functions for inelastic electron-nucleon scattering, $W_{1,2}(q^2,\nu )$. At $q^2=0\mathrm{}$, we then use unitarity to bound the anomalous magnetic moment by an integral over the nucleon propagator spectral function. Finally, by dispersing in $q^2$, the photon virtual mass, we are able to bound the pion form factor $F_{\pi }\left(q^2\right)$ by an integral over the total electron-positron annihilation cross section.