Precision Measurement of the Weak Mixing Angle in Møller Scattering

We report on a precision measurement of the parity-violating asymmetry in fixed target electron-electron (Møller) scattering: $A_{\mathrm{PV}}=[-131\pm 14(\mathrm{stat})\pm 10(\mathrm{syst})]\times {10}^{-9}$, leading to the determination of the weak mixing angle ${sin}^2{\theta }_{\mathrm{W}}^{\mathrm{eff}}=0.2397\pm 0.0010(\mathrm{stat})\pm 0.0008(\mathrm{syst})$, evaluated at $Q^2=0.026{\mathrm{GeV}}^2$. Combining this result with the measurements of ${sin}^2{\theta }_{\mathrm{W}}^{\mathrm{eff}}$ at the $Z^0$ pole, the running of the weak mixing angle is observed with over $6\sigma$ significance. The measurement sets constraints on new physics effects at the TeV scale.

Figure 1

$A_{\mathrm{phys}}$ for each of 75 data samples. Data collected with half-wave plate inserted (removed) at a beam energy of 45 (48) GeV are shown as solid (open) circles (triangles). The solid line represents the grand average, with the expected modulation of the asymmetry sign for each beam energy and half-wave plate state. Only statistical uncertainties are shown.

Figure 2

Predicted variation [18] of ${sin}^2{\theta }_{\mathrm{W}}^{\mathrm{eff}}$ as a function of momentum transfer $Q$ (solid line) and its estimated theoretical uncertainty (shaded area). Results of prior low-energy experiments [6, 16] (closed triangle, shown at an arbitrarily higher $Q$) and [7] (open triangle) are overlaid together with the $Z^0$ pole value [16] (square) and this measurement (circle).