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 $\frac{\sigma ({\nu }_{\mu }e\to {\nu }_{\mu }e)}{\sigma ({\overline{\nu }}_{\mu }e\to {\overline{\nu }}_{\mu }e)}$ and of the absolute value of $\sigma ({\overline{\nu }}_{\mu }e\to {\overline{\nu }}_{\mu }e)$ are reported. These yield $R={1.38}_{-0.31\mathrm{}}^{+0.40\mathrm{}}\left(\mathrm{stat}\right)\pm 0.17\left(\mathrm{syst}\right)$ and $\frac{\sigma ({\overline{\nu }}_{\mu }e\to {\overline{\nu }}_{\mu }e)}{E_{{\overline{\nu }}_{\mu }}}=[1.16\mathrm{}\pm 0.20(\mathrm{stat})\pm 0.14(\mathrm{syst}\left)\right]\times {10}^{-42\mathrm{}}$ ${\mathrm{cm}}^2$/GeV. This value of $R$ determines the fundamental weak neutral-current parameter to be ${{sin}^2\theta }_W=0.209\mathrm{}\pm 0.029\left(\mathrm{stat}\right)\pm 0.013\left(\mathrm{syst}\right)$.