Measurements of the forward-angle differential cross section for elastic electron-proton scattering were made in the range of momentum transfer from $Q^2=2.9\mathrm{} \mathrm{to} 31.3$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$ using an electron beam at the Stanford Linear Accelerator Center. The data span six orders of magnitude in cross section. Combinded statistical and systematic uncertainties in the cross section measurements ranged from 3.6% at low $Q^2$ to 19% at high $Q^2$. These data have been used to extract the proton magnetic form factor $G_M^p\left(Q^2\right)$ and Dirac form factor $F_1^p\left(Q^2\right)$ by using form factor scaling. The logarithmic falloff of $Q^4{F}_1^p$ expected from leading twist predictions of perturbative quantum chromodynamics is consistent with the new data at high $Q^2$. Some nonperturbative and hybrid calculations also agree with our results.

• Received 23 November 1992

DOI:https://doi.org/10.1103/PhysRevD.48.29