Neutral current in the Weinberg-Salam gauge model and elastic scattering of neutrinos and antineutrinos on nucleons

Abstract

We study the elastic scattering of neutrinos and antineutrinos on nucleons in the Weinberg-Salam model of the neutral current. In particular, we incorporate into our calculation the experimental cuts relevant to the two recent BNL experiments and also fold in the BNL $\ensuremath{\nu}$ and $\overline{\ensuremath{\nu}}$ spectra. Sensitivity of the calculation to the changes in the axial-vector-meson mass and the Weinberg angle are explored. We conclude that the Weinberg-Salam-model prediction for ${R}_{\mathrm{el}}=\frac{〈\ensuremath{\sigma}({\ensuremath{\nu}}_{\ensuremath{\mu}}+p\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\mu}}+p)〉}{〈\ensuremath{\sigma}({\ensuremath{\nu}}_{\ensuremath{\mu}}+n\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}+p)〉}$ and the differential-cross-section measurements are not inconsistent with the data provided the uncertainty in the mass of the axial-vector meson ${M}_{A}$ is taken into account. Similar predictions are given for $\overline{\ensuremath{\nu}}N$ scattering.