Measurement of the Ratio of Cross Sections for Neutrino and Antineutrino Scattering from Electrons

Abstract

Measurements of the ratio $R$ of the purely leptonic weak neutral-current cross sections $\frac{\ensuremath{\sigma}({\ensuremath{\nu}}_{\ensuremath{\mu}}e\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\mu}}e)}{\ensuremath{\sigma}({\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}e\ensuremath{\rightarrow}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}e)}$ and of the absolute value of $\ensuremath{\sigma}({\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}e\ensuremath{\rightarrow}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}e)$ are reported. These yield $R={1.38}_{\ensuremath{-}0.31}^{+0.40}(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.17(\mathrm{syst})$ and $\frac{\ensuremath{\sigma}({\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}e\ensuremath{\rightarrow}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}e)}{{E}_{{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}}}=[1.16\ifmmode\pm\else\textpm\fi{}0.20(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.14(\mathrm{syst})]\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}42}$ ${\mathrm{cm}}^{2}$/GeV. This value of $R$ determines the fundamental weak neutral-current parameter to be ${{sin}^{2}\ensuremath{\theta}}_{W}=0.209\ifmmode\pm\else\textpm\fi{}0.029(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.013(\mathrm{syst})$.