High-Energy Behavior of Nucleon Electromagnetic Form Factors

Theoretical implications of the suggestion that the observed nucleon electromagnetic form factors indicate the existence of a nucleon "core" are discussed. On the basis of physical arguments concerning the nature of such a core, it is shown that, for the neutron, both the charge form factor, ${F_{\mathrm{ch}}}^n\left(q^2\right)$, and the magnetic form factor, ${F_{\mathrm{mag}}}^n\left(q^2\right)$, must vanish as $q^2$, the invariant momentum transfer, increases without limit. On the other hand, for the proton ${F_{\mathrm{ch}}}^p\left(q^2\right)\to {Z_2}^{\mathrm{}\left(s\right)\mathrm{}}$ and ${F_{\mathrm{mag}}}^p\left(q^2\right)\to \frac{{Z_2}^{\mathrm{}\left(s\right)\mathrm{}}}{2M}$, where ${Z_2}^{\mathrm{}\left(s\right)\mathrm{}}$ is the wave function renormalization constant for strong interactions, which is a measure of the probability of the "core state." In terms of the Dirac form factor, $F_1\left(q^2\right)$, and the Pauli form factor, $F_2\left(q^2\right)$, these results read ${F_1}^n\left(q^2\right)\to 0$, ${F_1}^p\left(q^2\right)\to {Z_2}^{\mathrm{}\left(s\right)\mathrm{}}$, and $q^2{F}_2\left(q^2\right)\to 0$ for both neutron and proton. The results for $F_1\left(q^2\right)$ are the same as those obtained by Hiida, Nakanishi, Nogami, and Uehara. The other result implies the existence of a relationship which may be used to eliminate one parameter in the analysis of $F_2$. The generality of the interpretation of $F_{\mathrm{ch}}$ and $F_{\mathrm{mag}}$ as Fourier transforms of distributions of charge and magnetization, respectively, is demonstrated in the Appendix.