Measurement of the Elastic Scattering of Neutrinos and Antineutrinos by Protons

We have observed 217 (66) events of the process $\nu p\to \nu p$ ($\overline{\nu }p\to \overline{\nu }p$) with an estimated background of 82 (28). The neutral-to-charged-current ratios are $\frac{\sigma (\nu p\to \nu p)}{\sigma (\nu n\to {\mu }^{-}p)}=0.11\mathrm{}\pm 0.02$ and $\frac{\sigma (\overline{\nu }p\to \overline{\nu }p)}{\sigma (\overline{\nu }p\to {\mu }^{+}n)}=0.19\mathrm{}\pm 0.05$ for $0.40<\mathrm{}{Q}^2<0.90\mathrm{}$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$, where -$Q^2$ is the square of the momentum transfer to the nucleon. These yield $\frac{\sigma (\overline{\nu }p\to \overline{\nu }p)}{\sigma (\nu p\to \nu p)}=0.53\mathrm{}\pm 0.17$. The neutral-current form factors at $Q^2=0\mathrm{}$ are $G_E={0.5}_{-0.5\mathrm{}}^{+0.25\mathrm{}}$, $G_M={1.0}_{-0.04\mathrm{}}^{+0.35\mathrm{}}$, and $g_A={0.5}_{-0.15\mathrm{}}^{+0.2\mathrm{}}$.