High-Momentum-Transfer Behavior of the Electromagnetic Form Factor of the Nucleon

Abstract

A possible mechanism for the observed rapid falloff of the electromangetic form factor of the nucleon for large momentum transfer is outlined and a heuristic calculation is given. The conjecture is adopted that the observed falloff is a consequence of a damping via unitarity by soft-meson production processes, and that recoil effects of these soft mesons can be neglected. The consequences of these assumptions are combined with a perturbation-theoretic model calculation to all orders for the one-meson production cross section. As a result we obtain $\frac{G_{\mathrm{Mp}}}{{\mu }_p}\approx \exp \{-A[{\ln }^2\mathrm{}(-at)\left]\right\}$ for the magnetic form factor of the proton. This is in good agreement with experiment for $-t>\mathrm{}0.3\mathrm{}$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$. If we correct the analytic behavior of this function by shifting the branch point from $t=0\mathrm{}$ to the usual position of the lowest branch point t $\mathrm{a}t=4\mathrm{}{M_{\pi }}^2$, we are led to $\frac{G_{\mathrm{Mp}}}{{\mu }_p}\approx \exp \{-A[{\ln }^2(-a(t-4\mathrm{}{M_{\pi }}^2\left)\right)-{\ln }^2\left(a4\mathrm{}{M_{\pi }}^2\right)\left]\right\}.\mathrm{}$ Choosing the free parameters as $A=0.172\mathrm{}$ and $a4\mathrm{}{M_{\pi }}^2=1.65\mathrm{}$, we obtain good agreement with experiment for all $t<\mathrm{}0\mathrm{}$. A general connection between breaking of dilatation symmetry, soft-meson emission, and $t$ dependence of the form factor is pointed out briefly.