The response function of nuclei in the quasielastic region at large momentum transfer (q≤10 fm−1) is measured for a series of nuclei, He4, C12, Al27, Fe56, and Au197, up to large values of the Bjorken scaling variables x<2.5.
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The parity-violating asymmetries between a longitudinally-polarized electron beam and an unpolarized deuterium target have been measured recently. The measurement covered two kinematic points in the deep inelastic scattering region and five in the nucleon resonance region. We provide here details of the experimental setup, data analysis, and results on all asymmetry measurements including parity-violating electron asymmetries and those of inclusive pion production and beam-normal asymmetries. The parity-violating deep-inelastic asymmetries were used to extract the electron-quark weak effective couplings, and the resonance asymmetries provided the first evidence for quark-hadron duality in electroweak observables. These electron asymmetries and their interpretation were published earlier, but are presented here in more detail.
Asymmetry results on $\vec e-^2$H parity-violating scattering from the PVDIS experiment at JLab.
Asymmetry results on $\vec e-^2$H parity-violating scattering from the PVDIS experiment at JLab, for RES I settings.
Asymmetry results on $\vec e-^2$H parity-violating scattering from the PVDIS experiment at JLab, for RES II settings.
Exclusive electroproduction of pi0 mesons on protons in the backward hemisphere has been studied at Q**2 = 1.0 GeV**2 by detecting protons in the forward direction in coincidence with scattered electrons from the 4 GeV electron beam in Jefferson Lab's Hall A. The data span the range of the total (gamma* p) center-of-mass energy W from the pion production threshold to W = 2.0 GeV. The differential cross sections sigma_T+epsilon*sigma_L, sigma_TL, and sigma_TT were separated from the azimuthal distribution and are presented together with the MAID and SAID parametrizations.
Cross section SIG(T) + EPSILON*SIG(L) for COS(THETA*) = -0.975.
Cross section SIG(T) + EPSILON*SIG(L) for COS(THETA*) = -0.925.
Cross section SIG(T) + EPSILON*SIG(L) for COS(THETA*) = -0.875.
We present the first measurement of the Q^2-dependence of the neutron spin structure function g_2^n at five kinematic points covering 0.57 (GeV/c)^2 <= Q^2 <= 1.34 (GeV/c)^2 at x~0.2. Though the naive quark-parton model predicts g_2=0, non-zero values for g_2 occur in more realistic models of the nucleon which include quark-gluon correlations, finite quark masses or orbital angular momentum. When scattering from a non-interacting quark, $g_2^n$ can be predicted using next-to-leading order fits to world data for g_1^n. Deviations from this prediction provide an opportunity to examine QCD dynamics in nucleon structure. Our results show a positive deviation from this prediction at lower Q^2, indicating that contributions such as quark-gluon interactions may be important. Precision data obtained for g_1^n are consistent with next-to-leading order fits to world data.
Measured values of G1N ang G2N.
We report on measurements of the neutron spin asymmetries $A_{1,2}^n$ and polarized structure functions $g_{1,2}^n$ at three kinematics in the deep inelastic region, with $x=0.33$, 0.47 and 0.60 and $Q^2=2.7$, 3.5 and 4.8 (GeV/c)$^2$, respectively. These measurements were performed using a 5.7 GeV longitudinally-polarized electron beam and a polarized $^3$He target. The results for $A_1^n$ and $g_1^n$ at $x=0.33$ are consistent with previous world data and, at the two higher $x$ points, have improved the precision of the world data by about an order of magnitude. The new $A_1^n$ data show a zero crossing around $x=0.47$ and the value at $x=0.60$ is significantly positive. These results agree with a next-to-leading order QCD analysis of previous world data. The trend of data at high $x$ agrees with constituent quark model predictions but disagrees with that from leading-order perturbative QCD (pQCD) assuming hadron helicity conservation. Results for $A_2^n$ and $g_2^n$ have a precision comparable to the best world data in this kinematic region. Combined with previous world data, the moment $d_2^n$ was evaluated and the new result has improved the precision of this quantity by about a factor of two. When combined with the world proton data, polarized quark distribution functions were extracted from the new $g_1^n/F_1^n$ values based on the quark parton model. While results for $\Delta u/u$ agree well with predictions from various models, results for $\Delta d/d$ disagree with the leading-order pQCD prediction when hadron helicity conservation is imposed.
Measurements of the HE3 asymmetries.
Measurements of the HE3 spin structure functions.
Measurements of the HE3 spin structure functions.
We have measured the neutron spin asymmetry $A_1^n$ with high precision at three kinematics in the deep inelastic region at $x=0.33$, 0.47 and 0.60, and $Q^2=2.7$, 3.5 and 4.8 (GeV/c)$^2$, respectively. Our results unambiguously show, for the first time, that $A_1^n$ crosses zero around $x=0.47$ and becomes significantly positive at $x=0.60$. Combined with the world proton data, polarized quark distributions were extracted. Our results, in general, agree with relativistic constituent quark models and with perturbative quantum chromodynamics (pQCD) analyses based on the earlier data. However they deviate from pQCD predictions based on hadron helicity conservation.
Measured values of A1 and G1/F1.
We have made the first measurements of the virtual Compton scattering process via the e p -> e p gamma exclusive reaction at Q**2 = 1 GeV**2 in the nucleon resonance region. The cross section is obtained at center of mass (CM) backward angle, theta_gamma_gamma*, in a range of total (gamma* p) CM energy W from the proton mass up to W = 1.91 GeV. The data show resonant structures in the first and second resonance regions, and are well reproduced at higher W by the Bethe-Heitler+Born cross section, including t-channel pi0-exchange. At high W, our data, together with existing real photon data, show a striking Q**2 independence. Our measurement of the ratio of H(e,e'p)gamma to H(e,e'p)pi0 cross sections is presented and compared to model predictions.
Cross section for the reaction E P --> E P GAMMA at a polar angle given by COS(THETA) = -0.975 and azimuthal angle PHI = 15 degrees both in the centre-of-mass frame of the GAMMA* P --> GAMMA* P reaction.
Cross section for the reaction E P --> E P GAMMA at a polar angle given by COS(THETA) = -0.975 and azimuthal angle PHI = 45 degrees both in the centre-of-mass frame of the GAMMA* P --> GAMMA* P reaction.
Cross section for the reaction E P --> E P GAMMA at a polar angle given by COS(THETA) = -0.975 and azimuthal angle PHI = 75 degrees both in the centre-of-mass frame of the GAMMA* P --> GAMMA* P reaction.
We have measured the transverse asymmetry from inclusive scattering of longitudinally polarized electrons from polarized 3He nuclei at quasi-elastic kinematics in Hall A at Jefferson Lab with high statistical and systematic precision. The neutron magnetic form factor was extracted based on Faddeev calculations with an experimental uncertainty of less than 2 %.
Ratio of neutron magnetic form-factor to dipole value.
We have measured the parity-violating electroweak asymmetry in the elastic scattering of polarized electrons from the proton. The kinematic point (theta_lab = 12.3 degrees and Q^2=0.48 (GeV/c)^2) is chosen to provide sensitivity, at a level that is of theoretical interest, to the strange electric form factor G_E^s. The result, A=-14.5 +- 2.2 ppm, is consistent with the electroweak Standard Model and no additional contributions from strange quarks. In particular, the measurement implies G_E^s + 0.39G_M^s = 0.023 +- 0.034 (stat) +- 0.022 (syst) +- 0.026 (delta G_E^n), where the last uncertainty arises from the estimated uncertainty in the neutron electric form factor.
Longitudinally polarized beam. C=L and C=R means left- and right polarization. The second systematic uncertainty arises from the estimated uncertainty inthe neutron electromagnetic from factor.
Measurements are reported of the proton and deuteron spin structure functions g1 at beam energies of 29.1, 16.2, and 9.7 GeV and g2 at a beam energy of 29.1 GeV. The integrals of g1 over x have been evaluated at fixed Q**2 = 3 (GeV/c)**2 using the full data set. The Q**2 dependence of the ratio g1/F1 was studied and found to be small for Q**2 > 1 (GeV/c)**2. Within experimental precision the g2 data are well-described by the Wandzura-Wilczek twist-2 contribution. Twist-3 matrix elements were extracted and compared to theoretical predictions. The asymmetry A2 was measured and found to be significantly smaller than the positivity limit for both proton and deuteron targets. A2 for the proton is found to be positive and inconsistent with zero. Measurements of g1 in the resonance region show strong variations with x and Q**2, consistent with resonant amplitudes extracted from unpolarized data. These data allow us to study the Q**2 dependence of the first moments of g1 below the scaling region.
Averaged A1(P) for the DIS (W**2 > 4 GeV) region. Additional normalization uncertainty 3.7%.
Detailed A1(P) for the DIS (W**2 > 4 GeV) region. Additional normalization uncertainty 3.7%.
Detailed A1(P) for the DIS (W**2 > 4 GeV) region. Additional normalization uncertainty 3.7%.
Measurements were made at SLAC of the cross section for scattering 29 GeV electrons from carbon at a laboratory angle of 4.5 degrees, corresponding to 0.03<x<0.1 and 1.3<Q^2<2.7 GeV^2. Values of R=sigma_L/sigma_T were extracted in this kinematic range by comparing these data to cross sections measured at a higher beam energy by the NMC collaboration. The results are in reasonable agreement with pQCD calculations and with extrapolations of the R1990 parameterization of previous data. A new fit is made including these data and other recent results.
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The neutron longitudinal and transverse asymmetries $A^n_1$ and $A^n_2$ have been extracted from deep inelastic scattering of polarized electrons by a polarized $^3$He target at incident energies of 19.42, 22.66 and 25.51 GeV. The measurement allows for the determination of the neutron spin structure functions $g^n_1 (x,Q^2)$ and $g^n_2(x,Q^2)$ over the range $0.03 < x < 0.6$ at an average $Q^2$ of 2 (GeV$/c)^2$. The data are used for the evaluation of the Ellis-Jaffe and Bjorken sum rules. The neutron spin structure function $g^n_1 (x,Q^2)$ is small and negative within the range of our measurement, yielding an integral ${\int_{0.03}^{0.6} g_1^n(x) dx}= -0.028 \pm 0.006 (stat) \pm 0.006 (syst) $. Assuming Regge behavior at low $x$, we extract $\Gamma_1^n=\int^1_0 g^n_1(x)dx = -0.031 \pm 0.006 (stat)\pm 0.009 (syst) $. Combined with previous proton integral results from SLAC experiment E143, we find $\Gamma_1^p - \Gamma_1^n = 0.160 \pm 0.015$ in agreement with the Bjorken sum rule prediction $\Gamma^p_1 - \Gamma ^n_1 = 0.176 \pm 0.008$ at a $Q^2$ value of 3 (GeV$/c)^2$ evaluated using $\alpha_s = 0.32\pm 0.05$.
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We have measured proton and deuteron virtual photon-nucleon asymmetries A2p and A2d and structure functions g2p and g2d over the range 0.03<x<0.8 and 1.3<Q2<10 (GeV/c)2 by inelastically scattering polarized electrons off polarized ammonia targets. Results for A2 are significantly smaller than the positivity limit sqrt(R) for both targets. Within experimental precision, the g2 data are well-described by the twist-2 contribution g2WW. Twist-3 matrix elements have been extracted and are compared to theorectical predictions.
Proton data measured in the 4.5 degree spectrometer.
Proton data measured in the 7.0 degree spectrometer.
Deuteron data measured in the 4.5 degree spectrometer.
We have measured the neutron structure function g$_{2}^{n}$ and the virtual photon-nucleon asymmetry A$_{2}^{n}$ over the kinematic range $0.014\leq x \leq 0.7$ and $1.0 \leq Q^{2} \leq 17.0$ by scattering 48.3 GeV longitudinally polarized electrons from polarized $^{3}$He. Results for A$_{2}^{n}$ are significantly smaller than the $\sqrt{R}$ positivity limit over most of the measured range and data for g$_2^{n}$ are generally consistent with the twist-2 Wandzura-Wilczek prediction. Using our measured g$_{2}^{n}$ we obtain results for the twist-3 reduced matrix element $d_{2}^{n}$, and the integral $\int$g$_{2}^{n}(x)dx$ in the range $0.014\leq x \leq 1.0$. Data from this experiment are combined with existing data for g$_{2}^{n}$ to obtain an average for $d_{2}^{n}$ and the integral $\int$g$_{2}^{n}(x)dx$.
Data measured using the 2.75 degree spectrometer.
Data measured using the 5.5 degree spectrometer.
Measured value of the twist-3 reduced matrix element D2.
We present a Next-to-Leading order perturbative QCD analysis of world data on the spin dependent structure functions $g_1^p, g_1^n$, and $g_1^d$, including the new experimental information on the $Q^2$ dependence of $g_1^n$. Careful attention is paid to the experimental and theoretical uncertainties. The data constrain the first moments of the polarized valence quark distributions, but only qualitatively constrain the polarized sea quark and gluon distributions. The NLO results are used to determine the $Q^2$ dependence of the ratio $g_1/F_1$ and evolve the experimental data to a constant $Q^2 = 5 GeV^2$. We determine the first moments of the polarized structure functions of the proton and neutron and find agreement with the Bjorken sum rule.
Data from the 2.75 degree spectrometer.
Data from the 2.75 degree spectrometer evolved to a mean Q**2 of 5 GeV**2 using the MSBAR parameterization. The second systematic error is due to the evolution.
Data from the 5.5 degree spectrometer.
We report on a precision measurement of the neutron spin structure function $g^n_1$ using deep inelastic scattering of polarized electrons by polarized ^3He. For the kinematic range 0.014<x<0.7 and 1 (GeV/c)^2< Q^2< 17 (GeV/c)^2, we obtain $\int^{0.7}_{0.014} g^n_1(x)dx = -0.036 \pm 0.004 (stat) \pm 0.005 (syst)$ at an average $Q^2=5 (GeV/c)^2$. We find relatively large negative values for $g^n_1$ at low $x$. The results call into question the usual Regge theory method for extrapolating to x=0 to find the full neutron integral $\int^1_0 g^n_1(x)dx$, needed for testing quark-parton model and QCD sum rules.
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We have measured the proton and deuteron spin structure functions g_1^p and g_1^d in the region of the nucleon resonances for W^2 < 5 GeV^2 and $Q^2\simeq 0.5$ and $Q^2\simeq 1.2$ GeV^2 by inelastically scattering 9.7 GeV polarized electrons off polarized $^{15}NH_3$ and $^{15}ND_3$ targets. We observe significant structure in g_1^p in the resonance region. We have used the present results, together with the deep-inelastic data at higher W^2, to extract $\Gamma(Q^2)\equiv\int_0^1 g_1(x,Q^2) dx$. This is the first information on the low-Q^2 evolution of Gamma toward the Gerasimov-Drell-Hearn limit at Q^2 = 0.
The integral of the structure functions g1 for the resonance region W**2 < 4 GeV**2.
The integral of the structure functions g1 for the resonance region W**2 < 4 GeV**2.
The integral of the structure functions g1 for the full W region including the deep-inelastic region as given by fits to the world's data.
The ratio g1/F1 has been measured over the range 0.03<x<0.6 and 0.3<Q2<10 (GeV/c)2 using deep-inelastic scattering of polarized electrons from polarized protons and deuterons. We find g1/F1 to be consistent with no Q2-dependence at fixed x in the deep-inelastic region Q~2>1 (GeV/c)2. A trend is observed for g1/F1 to decrease at lower Q2. Fits to world data with and without a possible Q2-dependence in g1/F1 are in agreement with the Bjorken sum rule, but Delta_q is substantially less than the quark-parton model expectation.
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We have measured the ratio g1pF1p over the range 0.029<x<0.8 and 1.3<Q2<10 (GeV/c)2 using deep-inelastic scattering of polarized electrons from polarized ammonia. An evaluation of the integral ∫01g1p(x, Q2)dx at fixed Q2=3 (GeV/c)2 yields 0.127±0.004(stat)±0.010(syst), in agreement with previous experiments, but well below the Ellis-Jaffe sum rule prediction of 0.160±0.006. In the quark-parton model, this implies Δq=0.27±0.10.
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Values of G1 computed assuming G1/F1 is independent of Q**2 and using a fixed Q**2 of 3 GeV**2.
We report on a high-statistics measurement of the deuteron spin structure function g1d at a beam energy of 29 GeV in the kinematic range 0.029<x<0.8 and 1<Q2<10 (GeV /c)2. The integral γ1d=∫1g1ddx evaluated at fixed Q2=3 (GeV /c)2 gives 0.042±0.003(stat)±0.004(syst). Combining this result with our earlier measurement of g1p, we find γ1p−γ1n=0.163±0.010(stat)±0.016(syst), which agrees with the prediction of the Bjorken sum rule with O(αs3) corrections, γ1p−γ1n=0.171±0.008. We find the quark contribution to the proton helicity to be Δq=0.30±0.06.
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Values of G1 computed assuming G1/F1 is independent of Q**2 and evaluated at Q**2 = 3 GeV**2.
The spin structure function of the neutron g1n has been determined over the range 0.03<x<0.6 at an average Q2 of 2 (GeV/c)2 by measuring the asymmetry in deep inelastic scattering of polarized electrons from a polarized He3 target at energies between 19 and 26 GeV. The integral of the neutron spin structure function is found to be F01g1n(x)dx=-0.022±0.011. Earlier reported proton results together with the Bjorken sum rule predict F01g1n(x)dx=-0.059±0.019.
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Extrapolarity to full x range.
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