We report on a precision measurement of the parity-violating asymmetry in fixed target electronelectron (Møller) scattering: AP V = (−131 ± 14 (stat.) ± 10 (syst.)) × 10 −9 , leading to the determination of the weak mixing angle sin 2 θ eff W = 0.2397 ± 0.0010 (stat.) ± 0.0008 (syst.), evaluated at Q 2 = 0.026 GeV 2 . Combining this result with the measurements of sin 2 θ eff W at the Z 0 pole, the running of the weak mixing angle is observed with over 6σ significance. The measurement sets constraints on new physics effects at the TeV scale.PACS numbers: 11.30. Er, 12.15.Lk, 12.15.Mm, 13.66.Lm, 13.88.+e, 14.60.Cd Precision measurements of weak neutral current processes at low energies rigorously test the Standard Model of electroweak interactions. Such measurements are sensitive to new physics effects at TeV energies, and are complementary to searches at high energy colliders.One class of low-energy electroweak measurements involves scattering of longitudinally polarized electrons from unpolarized targets, allowing for the determination of a parity-violating asymmetry Z is due to higher order amplitudes involving virtual weak vector bosons and fermions in quantum loops, referred to as electroweak radiative corrections [4,5].To date, the most precise low-energy determinations of the weak mixing angle come from studies of parity violation in atomic transitions [6] and measurements of the neutral current to charge current cross section ratios in neutrino-nucleon deep inelastic scattering [7]. In this Letter, we present a measurement of the weak mixing angle in electron-electron (Møller) scattering, a purely leptonic reaction with little theoretical uncertainty. We have previously reported the first observation of A P V in Møller scattering [8]. Here, we report on a significantly improved measurement of A P V resulting in a precision determination of sin 2 θ eff W at low momentum transfer. At a beam energy of ≃ 50 GeV available at End Station A at SLAC and a center-of-mass scattering angle of 90• , A P V in Møller scattering is predicted to be ≃ 320 parts per billion (ppb) at tree level [9]. Electroweak radiative corrections [4,5] and the experimental acceptance reduce the measured asymmetry by more than 50%.

We report new measurements of the parity-violating asymmetry A(PV) in elastic scattering of 3 GeV electrons off hydrogen and 4He targets with approximately 6.0 degrees . The 4He result is A(PV)=(+6.40+/-0.23(stat)+/-0.12(syst))x10(-6). The hydrogen result is A(PV)=(-1.58+/-0.12(stat)+/-0.04(syst))x10(-6). These results significantly improve constraints on the electric and magnetic strange form factors G(E)(s) and G(M)(s). We extract G(E)(s)=0.002+/-0.014+/-0.007 at =0.077 GeV2, and G(E)(s)+0.09G(M)(s)=0.007+/-0.011+/-0.006 at =0.109 GeV2, providing new limits on the role of strange quarks in the nucleon charge and magnetization distributions.

We have measured the beam-normal single-spin asymmetry An in the elastic scattering of 1-3 GeV transversely polarized electrons from 1 H and for the first time from 4 He, 12 C, and 208 Pb. For 1 H, 4 He and 12 C, the measurements are in agreement with calculations that relate An to the imaginary part of the two-photon exchange amplitude including inelastic intermediate states. Surprisingly, the 208 Pb result is significantly smaller than the corresponding prediction using the same formalism. These results suggest that a systematic set of new An measurements might emerge as a new and sensitive probe of the structure of heavy nuclei.

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We have measured the parity-violating electroweak asymmetry in the elastic scattering of polarized electrons from 4He at an average scattering angle = 5.7 degrees and a four-momentum transfer Q2 = 0.091 GeV2 . From these data, for the first time, the strange electric form factor of the nucleon G(E)s can be isolated. The measured asymmetry of A(PV) = (6.72 +/- 0.84(stat) +/- 0.21(syst) x 10(-6) yields a value of G(E)s = -0.038 +/- 0.042(stat) +/- 0.010(syst), consistent with zero.