We use distorted wave electron scattering calculations to extract the weak charge form factor F W (q), the weak charge radius R W , and the point neutron radius R n of 208 Pb from the Lead Radius Experiment (PREX) parity-violating asymmetry measurement. The form factor is the Fourier transform of the weak charge density at the average momentum transferq = 0.475 fm −1 . We find F W (q) = 0.204 ± 0.028 (exp) ± 0.001 (model). We use the Helm model to infer the weak radius from F W (q). We find R W = 5.826 ± 0.181 (exp) ± 0.027 (model) fm. Here the experimental error includes PREX statistical and systematic errors, while the model error describes the uncertainty in R W from uncertainties in the surface thickness σ of the weak charge density. The weak radius is larger than the charge radius, implying a "weak charge skin" where the surface region is relatively enriched in weak charges compared to (electromagnetic) charges. We extract the point neutron radius R n = 5.751 ± 0.175 (exp) ± 0.026 (model) ± 0.005 (strange) fm from R W . Here there is only a very small error (strange) from possible strange quark contributions. We find R n to be slightly smaller than R W because of the nucleon's size. Finally, we find a neutron skin thickness of R n − R p = 0.302 ± 0.175 (exp) ± 0.026 (model) ± 0.005 (strange) fm, where R p is the point proton radius.

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Large experimental programmes in the fields of nuclear and particle physics search for evidence of physics beyond that explained by current theories. The observation of the Higgs boson completed the set of particles predicted by the standard model, which currently provides the best description of fundamental particles and forces. However, this theory's limitations include a failure to predict fundamental parameters, such as the mass of the Higgs boson, and the inability to account for dark matter and energy, gravity, and the matter-antimatter asymmetry in the Universe, among other phenomena. These limitations have inspired searches for physics beyond the standard model in the post-Higgs era through the direct production of additional particles at high-energy accelerators, which have so far been unsuccessful. Examples include searches for supersymmetric particles, which connect bosons (integer-spin particles) with fermions (half-integer-spin particles), and for leptoquarks, which mix the fundamental quarks with leptons. Alternatively, indirect searches using precise measurements of well predicted standard-model observables allow highly targeted alternative tests for physics beyond the standard model because they can reach mass and energy scales beyond those directly accessible by today's high-energy accelerators. Such an indirect search aims to determine the weak charge of the proton, which defines the strength of the proton's interaction with other particles via the well known neutral electroweak force. Because parity symmetry (invariance under the spatial inversion (x, y, z) → (-x, -y, -z)) is violated only in the weak interaction, it provides a tool with which to isolate the weak interaction and thus to measure the proton's weak charge . Here we report the value 0.0719 ± 0.0045, where the uncertainty is one standard deviation, derived from our measured parity-violating asymmetry in the scattering of polarized electrons on protons, which is -226.5 ± 9.3 parts per billion (the uncertainty is one standard deviation). Our value for the proton's weak charge is in excellent agreement with the standard model and sets multi-teraelectronvolt-scale constraints on any semi-leptonic parity-violating physics not described within the standard model. Our results show that precision parity-violating measurements enable searches for physics beyond the standard model that can compete with direct searches at high-energy accelerators and, together with astronomical observations, can provide fertile approaches to probing higher mass scales.

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%.

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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.

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The ⌳ 13 C hypernucleus was studied by measuring ␥ rays in coincidence with the 13 C(K Ϫ , Ϫ ) reaction. ␥ rays from the 1/2 Ϫ and 3/2 Ϫ states, which are the partners of the spin-orbit doublet states with a predominant configuration of ͓ 12 C g.s. (0 ϩ ) p ⌳ ͔, to the ground state were measured. The splitting of the states was found to be ⌬E(1/2 Ϫ Ϫ3/2 Ϫ )ϭϩ152Ϯ54(stat)Ϯ36(syst) keV. This value is 20-30 times smaller than that of single particle states in nuclei around this mass region. The j ⌳ ϭl ⌳ Ϫ1/2͓(p 1/2 ) ⌳ ͔ state appeared higher in energy, as in normal nuclei. The value gives new insight into the Y N interaction. The excitation energies of the 1/2 Ϫ and 3/2 Ϫ states were obtained as 10.982Ϯ0.031(stat)Ϯ0.056(syst) and 10.830Ϯ0.031(stat)Ϯ0.056(syst) MeV, respectively. We also observed ␥ rays from the 3/2 ϩ state, which has a ͓ 12 C(2 ϩ ) s ⌳ ͔ configuration, to the ground state in ⌳ 13 C. The excitation energy of the 3/2 ϩ state was obtained as 4.880Ϯ0.010(stat) Ϯ0.017(syst) MeV. Nuclear ␥ rays with energies of 4.438 and 15.100 MeV had similar yields, which suggests that a quasifree knockout of a ⌳ particle is dominant in highly excited regions.