Precision Measurement of the Weak Mixing Angle in Mller Scattering

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