Precision measurements of the nucleon strange form factors at Q2 approximately 0.1 GeV2

Combined Theoretical Analysis of the Parity-Violating Asymmetry for ^{48}Ca and ^{208}Pb

The recent experimental determination of the parity violating asymmetry A_{PV} in ^{48}Ca and ^{208}Pb at Jefferson Lab is important for our understanding on how neutrons and protons arrange themselves inside the atomic nucleus. To better understand the impact of these measurements, we present a rigorous theoretical investigation of A_{PV} in ^{48}Ca and ^{208}Pb and assess the associated uncertainties. We complement our study by inspecting the static electric dipole polarizability in these nuclei. The analysis is carried out within nuclear energy density functional theory with quantified input. We conclude that the simultaneous accurate description of A_{PV} in ^{48}Ca and ^{208}Pb cannot be achieved by our models that accommodate a pool of global nuclear properties, such as masses and charge radii, throughout the nuclear chart, and describe-within one standard deviation-the experimental dipole polarizabilities α_{D} in these nuclei.

Information Content of the Parity-Violating Asymmetry in ^{208}Pb

The parity-violating asymmetry A_{PV} in ^{208}Pb, recently measured by the PREX-2 Collaboration, is studied using modern relativistic (covariant) and nonrelativistic energy density functionals. We first assess the theoretical uncertainty on A_{PV} which is intrinsic to the adopted approach. To this end, we use quantified functionals that are able to accommodate our previous knowledge on nuclear observables such as binding energies, charge radii, and the dipole polarizability α_{D} of ^{208}Pb. We then add the quantified value of A_{PV} together with α_{D} to our calibration dataset to optimize new functionals. Based on these results, we predict a neutron skin thickness in ^{208}Pb r_{skin}=0.19±0.02  fm and the symmetry-energy slope L=54±8  MeV. These values are consistent with other estimates based on astrophysical data and are significantly lower than those recently reported using a particular set of relativistic energy density functionals. We also make a prediction for the A_{PV} value in ^{48}Ca that will be soon available from the CREX measurement.

Strange Quark Magnetic Moment of the Nucleon at the Physical Point

We report a lattice QCD calculation of the strange quark contribution to the nucleon's magnetic moment and charge radius. This analysis presents the first direct determination of strange electromagnetic form factors including at the physical pion mass. We perform a model-independent extraction of the strange magnetic moment and the strange charge radius from the electromagnetic form factors in the momentum transfer range of 0.051  GeV^{2}≲Q^{2}≲1.31  GeV^{2}. The finite lattice spacing and finite volume corrections are included in a global fit with 24 valence quark masses on four lattices with different lattice spacings, different volumes, and four sea quark masses including one at the physical pion mass. We obtain the strange magnetic moment G_{M}^{s}(0)=-0.064(14)(09)μ_{N}. The four-sigma precision in statistics is achieved partly due to low-mode averaging of the quark loop and low-mode substitution to improve the statistics of the nucleon propagator. We also obtain the strange charge radius ⟨r_{s}^{2}⟩_{E}=-0.0043(16)(14)  fm^{2}.

Determination of the strange nucleon form factors

The strange contribution to the electric and magnetic form factors of the nucleon is determined at a range of discrete values of Q^{2} up to 1.4  GeV^{2}. This is done by combining a recent analysis of lattice QCD results for the electromagnetic form factors of the octet baryons with experimental determinations of those quantities. The most precise result is a small negative value for the strange magnetic moment: G_{M}^{s}(Q^{2}=0)=-0.07±0.03μ_{N}. At larger values of Q^{2} both the electric and magnetic form factors are consistent with zero to within 2 standard deviations.

Neutral weak current two-body contributions in inclusive scattering from 12C

An ab initio calculation of the sum rules of the neutral weak response functions in 12C is reported, based on a realistic Hamiltonian, including two- and three-nucleon potentials, and on realistic currents, consisting of one- and two-body terms. We find that the sum rules of the response functions associated with the longitudinal and transverse components of the (spacelike) neutral current are largest and that a significant portion (≃30%) of the calculated strength is due to two-body terms. This fact may have implications for the MiniBooNE and other neutrino quasielastic scattering data on nuclei.

First determination of the weak charge of the proton

The Q(weak) experiment has measured the parity-violating asymmetry in ep elastic scattering at Q(2)=0.025(GeV/c)(2), employing 145 μA of 89% longitudinally polarized electrons on a 34.4 cm long liquid hydrogen target at Jefferson Lab. The results of the experiment's commissioning run, constituting approximately 4% of the data collected in the experiment, are reported here. From these initial results, the measured asymmetry is A(ep)=-279±35 (stat) ± 31 (syst) ppb, which is the smallest and most precise asymmetry ever measured in ep scattering. The small Q(2) of this experiment has made possible the first determination of the weak charge of the proton Q(W)(p) by incorporating earlier parity-violating electron scattering (PVES) data at higher Q(2) to constrain hadronic corrections. The value of Q(W)(p) obtained in this way is Q(W)(p)(PVES)=0.064±0.012, which is in good agreement with the standard model prediction of Q(W)(p)(SM)=0.0710±0.0007. When this result is further combined with the Cs atomic parity violation (APV) measurement, significant constraints on the weak charges of the up and down quarks can also be extracted. That PVES+APV analysis reveals the neutron's weak charge to be Q(W)(n)(PVES+APV)=-0.975±0.010.

Measurements of parity-violating asymmetries in electron-deuteron scattering in the nucleon resonance region

We report on parity-violating asymmetries in the nucleon resonance region measured using inclusive inelastic scattering of 5-6 GeV longitudinally polarized electrons off an unpolarized deuterium target. These results are the first parity-violating asymmetry data in the resonance region beyond the Δ(1232). They provide a verification of quark-hadron duality-the equivalence of the quark- and hadron-based pictures of the nucleon-at the (10-15)% level in this electroweak observable, which is dominated by contributions from the nucleon electroweak γZ interference structure functions. In addition, the results provide constraints on nucleon resonance models relevant for calculating background corrections to elastic parity-violating electron scattering measurements.

Measurement of the neutron radius of 208Pb through parity violation in electron scattering

We report the first measurement of the parity-violating asymmetry A(PV) in the elastic scattering of polarized electrons from 208Pb. A(PV) is sensitive to the radius of the neutron distribution (R(n)). The result A(PV)=0.656±0.060(stat)±0.014(syst) ppm corresponds to a difference between the radii of the neutron and proton distributions R(n)-R(p)=0.33(-0.18)(+0.16) fm and provides the first electroweak observation of the neutron skin which is expected in a heavy, neutron-rich nucleus.

New precision limit on the strange vector form factors of the proton

The parity-violating cross-section asymmetry in the elastic scattering of polarized electrons from unpolarized protons has been measured at a four-momentum transfer squared Q2 = 0.624  GeV2 and beam energy E(b) = 3.48  GeV to be A(PV) = -23.80 ± 0.78(stat) ± 0.36(syst) parts per million. This result is consistent with zero contribution of strange quarks to the combination of electric and magnetic form factors G(E)(s) + 0.517G(M)(s) = 0.003 ± 0.010(stat) ± 0.004(syst) ± 0.009(ff), where the third error is due to the limits of precision on the electromagnetic form factors and radiative corrections. With this measurement, the world data on strange contributions to nucleon form factors are seen to be consistent with zero and not more than a few percent of the proton form factors.

Flavor decomposition of the elastic nucleon electromagnetic form factors

The u- and d-quark contributions to the elastic nucleon electromagnetic form factors have been determined by using experimental data on G(E)(n), G(M)(n), G(E)(p), and G(M)(p). Such a flavor separation of the form factors became possible up to negative four-momentum transfer squared Q(2) = 3.4 GeV(2) with recent data on G(E)(n) from Hall A at Jefferson Lab. For Q(2) above 1 GeV(2), for both the u and the d quark, the ratio of the Pauli and Dirac form factors, F(2)/F(1), was found to be almost constant in sharp contrast to the behavior of F(2)/F(1) for the proton as a whole. Also, again for Q(2)>1 GeV(2), both F(2)(d) and F(1)(d) are roughly proportional to 1/Q(4), whereas the dropoff of F(2)(u) and F(1)(u) is more gradual.

Strange quark contributions to parity-violating asymmetries in the backward angle G0 electron scattering experiment

We have measured parity-violating asymmetries in elastic electron-proton and quasielastic electron-deuteron scattering at Q2=0.22 and 0.63 GeV2. They are sensitive to strange quark contributions to currents in the nucleon and the nucleon axial-vector current. The results indicate strange quark contributions of approximately < 10% of the charge and magnetic nucleon form factors at these four-momentum transfers. We also present the first measurement of anapole moment effects in the axial-vector current at these four-momentum transfers.

Measurement of strange quark contributions to the vector form factors of the proton at Q2 = 0.22 (GeV / c)2

A new measurement of the parity violating asymmetry in elastic electron scattering on hydrogen at backward angles and at a four momentum transfer of Q;{2} = 0.22 (Ge V / c);{2} is reported here. The measured asymmetry is A_{LR} = (-17.23 +/- 0.82_{stat} +/- 0.89_{syst}) x 10;{-6}. The standard model prediction assuming no strangeness is A_{0} = (-15.87 +/- 1.22) x 10;{-6}. In combination with previous results from measurements at forward angles, it is possible to disentangle for the first time the strange form factors at this momentum transfer, G_{E};{s} = 0.050 +/- 0.038 +/- 0.019 and G_{M};{s} = -0.14 +/- 0.11 +/- 0.11.

Effect of two-boson exchange on parity-violating e-p scattering

We compute the corrections from two-photon and gamma-Z exchange in parity-violating elastic electron-proton scattering, used to extract the strange form factors of the proton. We use a hadronic formalism that successfully reconciled the earlier discrepancy in the proton's electron to magnetic form factor ratio, suitably extended to the weak sector. Implementing realistic electroweak form factors, we find effects of the order 2%-3% at Q(2) less, similar0.1 GeV2, which are largest at backward angles and have a strong Q2 dependence at low Q2. Two-boson contributions to the weak axial current are found to be enhanced at low Q2 and for forward angles. We provide corrections at kinematics relevant for recent and upcoming parity-violating experiments.

Two-photon-exchange and gammaZ-exchange corrections to parity-violating elastic electron-proton scattering

Leading electroweak corrections play an important role in precision measurements of the strange form factors. We calculate the two-photon-exchange (TPE) and gammaZ-exchange corrections to the parity-violating asymmetry of the elastic electron-proton scattering in a simple hadronic model including the finite size of the proton. We find both can reach a few percent and are comparable in size with the current experimental measurements of strange-quark effects in the proton neutral weak current. The effect of gammaZ exchange is in general larger than that of TPE, especially at low momentum transfer Q2</=1 GeV2. Their combined effects on the values of G(E)s + beta G(M)s [corrected] extracted in recent experiments can be as large as -40% in certain kinematics.

Measurements of the proton elastic-form-factor ratio mu pG p E/G p M at low momentum transfer

High-precision measurements of the proton elastic form-factor ratio, mu pG p E/G p M, have been made at four-momentum transfer, Q2, values between 0.2 and 0.5 GeV2. The new data, while consistent with previous results, clearly show a ratio less than unity and significant differences from the central values of several recent phenomenological fits. By combining the new form-factor ratio data with an existing cross-section measurement, one finds that in this Q2 range the deviation from unity is primarily due to G p E being smaller than expected.

Testing the standard model by precision measurement of the weak charges of quarks

In a global analysis of the latest parity-violating electron scattering measurements on nuclear targets, we demonstrate a significant improvement in the experimental knowledge of the weak neutral-current lepton-quark interactions at low energy. The precision of this new result, combined with earlier atomic parity-violation measurements, places tight constraints on the size of possible contributions from physics beyond the standard model. Consequently, this result improves the lower-bound on the scale of relevant new physics to approximately 1 TeV.

Charge densities of the neutron and proton

A model-independent analysis of the infinite-momentum-frame charge density of partons in the transverse plane is presented for the nucleon. We find that the neutron-parton charge density is negative at the center, so that the square of the transverse charge radius is positive, in contrast with many expectations. Additionally, the proton's central d quark charge density is larger than that of the u quark by about 30%. The proton (neutron) charge density has a long range positively (negatively) charged component.

Isospin mixing in the nucleon and 4He and the nucleon strange electric form factor

In order to isolate the contribution of the nucleon strange electric form factor to the parity-violating asymmetry measured in 4He(e-->],e')4He experiments, it is crucial to have a reliable estimate of the magnitude of isospin-symmetry-breaking (ISB) corrections in both the nucleon and 4He. We examine this issue in the present Letter. Isospin admixtures in the nucleon are determined in chiral perturbation theory, while those in 4He are derived from nuclear interactions, including explicit ISB terms. A careful analysis of the model dependence in the resulting predictions for the nucleon and nuclear ISB contributions to the asymmetry is carried out. We conclude that, at the low momentum transfers of interest in recent measurements reported by the HAPPEX Collaboration at Jefferson Lab, these contributions are of comparable magnitude to those associated with strangeness components in the nucleon electric form factor.