Measurement of strange-quark contributions to the nucleon's form factors at Q(2) = 0.230 (GeV/c)(2)

Study of Two-Photon Exchange via the Beam Transverse Single Spin Asymmetry in Electron-Proton Elastic Scattering at Forward Angles over a Wide Energy Range

We report on a new measurement of the beam transverse single spin asymmetry in electron-proton elastic scattering, A_{⊥}^{ep}, at five beam energies from 315.1 to 1508.4 MeV and at a scattering angle of 30°<θ<40°. The covered Q^{2} values are 0.032, 0.057, 0.082, 0.218, 0.613 (GeV/c)^{2}. The measurement clearly indicates significant inelastic contributions to the two-photon-exchange (TPE) amplitude in the low-Q^{2} kinematic region. No theoretical calculation is able to reproduce our result. Comparison with a calculation based on unitarity, which only takes into account elastic and πN inelastic intermediate states, suggests that there are other inelastic intermediate states such as ππN, KΛ, and ηN. Covering a wide energy range, our new high-precision data provide a benchmark to study those intermediate states.

First Measurement of the Q^{2} Dependence of the Beam-Normal Single Spin Asymmetry for Elastic Scattering off Carbon

We report on the first Q^{2}-dependent measurement of the beam-normal single spin asymmetry A_{n} in the elastic scattering of 570 MeV vertically polarized electrons off ^{12}C. We cover the Q^{2} range between 0.02 and 0.05  GeV^{2}/c^{2} and determine A_{n} at four different Q^{2} values. The experimental results are compared to a theoretical calculation that relates A_{n} to the imaginary part of the two-photon exchange amplitude. The result emphasizes that the Q^{2} behavior of A_{n} given by the ratio of the Compton to charge form factors cannot be treated independently of the target nucleus.

New Measurements of the Beam Normal Spin Asymmetries at Large Backward Angles with Hydrogen and Deuterium Targets

New measurements of the beam normal single spin asymmetry in the electron elastic and quasielastic scattering on the proton and deuteron, respectively, at large backward angles and at ⟨Q^{2}⟩=0.22  (GeV/c)^{2} and ⟨Q^{2}⟩=0.35  ( GeV/c)^{2} are reported. The experimentally observed asymmetries are compared with the theoretical calculation of Pasquini and Vanderhaeghen [Phys. Rev. C 70, 045206 (2004).PRVCAN0556-281310.1103/PhysRevC.70.045206]. The agreement of the measurements with the theoretical calculations shows a dominance of the inelastic intermediate excited states of the nucleon, πN and the Δ resonance. The measurements explore a new, important parameter region of the exchanged virtual photon virtualities.

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.

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.

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.

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.

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.

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.

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

We report new measurements of the parity-violating asymmetry A(PV) in elastic scattering of 3 GeV electrons off hydrogen and 4He targets with <theta(lab)> 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 <Q(2)>=0.077 GeV2, and G(E)(s)+0.09G(M)(s)=0.007+/-0.011+/-0.006 at <Q(2)>=0.109 GeV2, providing new limits on the role of strange quarks in the nucleon charge and magnetization distributions.

Extracting nucleon strange and anapole form factors from world data

The complete world set of parity-violating electron scattering data up to Q2 approximately 0.3 GeV2 is analyzed. We extract the current experimental determination of the strange electric and magnetic form factors of the proton, as well as the weak axial form factors of the proton and neutron, at Q2=0.1 GeV2. Within experimental uncertainties, we find that the strange form factors are consistent with zero, as are the anapole contributions to the axial form factors. Nevertheless, the correlation between the strange and anapole contributions suggest that there is only a small probability that these form factors all vanish simultaneously.

Strange electric form factor of the proton

By combining the constraints of charge symmetry with new chiral extrapolation techniques and recent low-mass quenched lattice QCD simulations of the individual quark contributions to the electric charge radii of the baryon octet, we obtain an accurate determination of the strange electric charge radius of the proton. While this analysis provides a value for G(E)(s)(Q(2) = 0.1 GeV(2)) in agreement with the best current data, the theoretical error is comparable with that expected from future HAPPEX results from JLab. Together with the earlier determination of G(M)(s), this result considerably constrains the role of hidden flavor in the structure of the nucleon.

Parity-violating electron scattering from 4He and the strange electric form factor of the nucleon

We have measured the parity-violating electroweak asymmetry in the elastic scattering of polarized electrons from 4He at an average scattering angle <theta(lab)> = 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.

Strange-quark contributions to parity-violating asymmetries in the forward g0 electron-proton scattering experiment

We have measured parity-violating asymmetries in elastic electron-proton scattering over the range of momentum transfers 0.12 < or =Q2 < or =1.0 GeV2. These asymmetries, arising from interference of the electromagnetic and neutral weak interactions, are sensitive to strange-quark contributions to the currents of the proton. The measurements were made at Jefferson Laboratory using a toroidal spectrometer to detect the recoiling protons from a liquid hydrogen target. The results indicate nonzero, Q2 dependent, strange-quark contributions and provide new information beyond that obtained in previous experiments.

Two-photon-exchange correction to parity-violating elastic electron-proton scattering

Higher-order QED effects play an important role in precision measurements of nucleon elastic form factors in electron scattering. Here we introduce a two-photon-exchange QED correction to the parity-violating polarization asymmetry of elastic electron-proton scattering. We calculate this correction in the parton model using the formalism of generalized parton distributions, and demonstrate that it can reach several percent in certain kinematics, becoming comparable in size with existing experimental measurements of strange-quark effects in the proton neutral weak current.

Evidence for strange-quark contributions to the nucleon's form factors at Q2=0.108 (GeV/c)2

We report on a measurement of the parity violating asymmetry in the elastic scattering of polarized electrons off unpolarized protons with the A4 apparatus at MAMI in Mainz at a four momentum transfer value of Q(2)=0.108 (GeV/c)(2) and at a forward electron scattering angle of 30 degrees <theta(e)<40 degrees . The measured asymmetry is A(LR)(e-->p)=[-1.36+/-0.29(stat)+/-0.13(syst)]x10(-6). The expectation from the standard model assuming no strangeness contribution to the vector current is A(0)=(-2.06+/-0.14)x10(-6). We have improved the statistical accuracy by a factor of 3 as compared to our previous measurements at a higher Q2. We have extracted the strangeness contribution to the electromagnetic form factors from our data to be G(s)(E)+0.106G(s)(M)=0.071+/-0.036 at Q(2)=0.108 (GeV/c)(2). We again find the value for G(s)(E)+0.106G(s)(M) to be positive, this time at an improved significance level of two sigma.

Measurement of the transverse beam spin asymmetry in elastic electron-proton scattering and the inelastic contribution to the imaginary part of the two-photon exchange amplitude

We report on a measurement of the asymmetry in the scattering of transversely polarized electrons off unpolarized protons, A( perpendicular), at two Q2 values of 0.106 and 0.230 (GeV/c)(2) and a scattering angle of 30 degrees <theta(e)<40 degrees . The measured transverse asymmetries are A( perpendicular)(Q(2)=0.106 (GeV/c)(2))=(-8.59+/-0.89(stat)+/-0.75(syst))x10(-6) and A( perpendicular)(Q(2)=0.230 (GeV/c)(2))=(-8.52+/-2.31(stat)+/-0.87(syst))x10(-6). The first errors denote the statistical error and the second the systematic uncertainties. From comparison with theoretical estimates of A( perpendicular) we conclude that piN-intermediate states give a substantial contribution to the imaginary part of the two-photon amplitude. There is no obvious reason why this should be different for the real part of the two-photon amplitude, which enters into the radiative corrections for the Rosenbluth separation measurements of the electric form factor of the proton.