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.