Measurement of elasticνμandν¯μscattering on protons

We have measured elastic ${\nu }_{\mu }$ and ${\overline{\nu }}_{\mu }$ scattering on protons at the Brookhaven National Laboratory Alternating Gradient Synchrotron. We find $R_{\mathrm{NC}}=\frac{\sigma ({\overline{\nu }}_{\mu }p\to {\overline{\nu }}_{\mu }p)}{\sigma ({\nu }_{\mu }p\to {\nu }_{\mu }p)}=0.44\mathrm{}\pm 0.12$ and $R_{{\nu }_{\mu }}=\frac{\sigma ({\nu }_{\mu }p\to {\nu }_{\mu }p)}{\sigma ({\nu }_{\mu }n\to {\mu }^{-}p)}=0.11\mathrm{}\pm 0.03$. The elastic $Q^2$ distribution is in good agreement with present knowledge of form factors and the Weinberg-Salam model. We find ${{sin}^2\theta }_W=0.26\mathrm{}\pm 0.06$.