Measurement of neutrino-proton and antineutrino-proton elastic scattering

We report here new measurements of neutrino-proton and antineutrino-proton elastic scattering, performed in the BNL neutrino beam. We observed a net signal of 212 neutrino events and 110 antineutrino events which lead to determination of the values $R_{\nu }\equiv \frac{\sigma ({\nu }_{\mu }+p\to {\nu }_{\mu }+p)}{\sigma ({\nu }_{\mu }+n\to {\mu }^{-}+p)}=0.11\mathrm{}\pm 0.015$, $R_{\overline{\nu }}\equiv \frac{\sigma ({\overline{\nu }}_{\mu }+p\to {\overline{\nu }}_{\mu }+p)}{\sigma ({\overline{\nu }}_{\mu }+p\to {\mu }^{+}+n)}=0.19\mathrm{}\pm 0.035$, and $R^{\mathrm{NC}}\equiv \frac{\sigma ({\overline{\nu }}_{\mu }+p\to {\overline{\nu }}_{\mu }+p)}{\sigma ({\nu }_{\mu }+p\to {\nu }_{\mu }+p)}=0.41\mathrm{}\pm 0.09$ 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. The differential cross sections as functions of $Q^2$, $\frac{d{\sigma }^{\nu }}{d{Q}^2}$ and $\frac{d{\sigma }^{\overline{\nu }}}{d{Q}^2}$, are also determined. Our results are in good agreement with the Weinberg-Salam-Glashow-Iliopoulos-Maiani model of the weak and electromagnetic interactions and yield ${{sin}^2\theta }_W=0.28\mathrm{}\pm 0.03$.