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 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 measured the spin structure functions g2p and g2d and the virtual photon asymmetries A2p and A2d over the kinematic range 0.02 < x < 0.8 and 0.7 < Q^2 < 20 GeV^2 by scattering 29.1 and 32.3 GeV longitudinally polarized electrons from transversely polarized NH3 and 6LiD targets. Our measured g2 approximately follows the twist-2 Wandzura-Wilczek calculation. The twist-3 reduced matrix elements d2p and d2n are less than two standard deviations from zero. The data are inconsistent with the Burkhardt-Cottingham sum rule if there is no pathological behavior as x->0. The Efremov-Leader-Teryaev integral is consistent with zero within our measured kinematic range. The absolute value of A2 is significantly smaller than the sqrt[R(1+A1)/2] limit.
Values of A2 and X*G2 from proton and deuterium target data at mean electron scattering angle of 2.75 degrees and incident energy 29.1 GeV. Errors shown are statistical only.
Values of A2 and X*G2 from proton and deuterium target data at mean electron scattering angle of 5.5 degrees and incident energy 29.1 GeV. Errors shown are statistical only.
Values of A2 and X*G2 from proton and deuterium target data at mean electron scattering angle of 10.5 degrees and incident energy 29.1 GeV. Errors shown are statistical only.
The structure functions g1p and g1n have been measured over the range 0.014 < x < 0.9 and 1 < Q2 < 40 GeV2 using deep-inelastic scattering of 48 GeV longitudinally polarized electrons from polarized protons and deuterons. We find that the Q2 dependence of g1p (g1n) at fixed x is very similar to that of the spin-averaged structure function F1p (F1n). From a NLO QCD fit to all available data we find $\Gamma_1^p - \Gamma_1^n =0.176 \pm 0.003 \pm 0.007$ at Q2=5 GeV2, in agreement with the Bjorken sum rule prediction of 0.182 \pm 0.005.
Results for G1/F1 for the proton and neutron.
Results for G1/F1 for the proton and neutron.
Results for G1/F1 for the proton and neutron.
New measurements are reported on the deuteron spin structure function g_1^d. These results were obtained from deep inelastic scattering of 48.3 GeV electrons on polarized deuterons in the kinematic range 0.01 < x < 0.9 and 1 < Q^2 < 40 (GeV/c)^2. These are the first high dose electron scattering data obtained using lithium deuteride (6Li2H) as the target material. Extrapolations of the data were performed to obtain moments of g_1^d, including Gamma_1^d, and the net quark polarization Delta Sigma.
Extrapolation to the full x range was made using E154 data (see PL 405B, 180 and PRL 79, 26).
Measurments of g1/F1 and g1 using the 2.75 degree spectrometer.
Measurments of g1/F1 and g1 using the 5.5 degree spectrometer.
We have measured the spin structure functions g2p and g2d and the virtual photon asymmetries A2p and A2d over the kinematic range 0.02 < x < 0.8 and 1.0 < Q^2 < 30(GeV/c)^2 by scattering 38.8 GeV longitudinally polarized electrons from transversely polarized NH3 and 6LiD targets.The absolute value of A2 is significantly smaller than the sqrt{R} positivity limit over the measured range, while g2 is consistent with the twist-2 Wandzura-Wilczek calculation. We obtain results for the twist-3 reduced matrix elements d2p, d2d and d2n. The Burkhardt-Cottingham sum rule integral - int(g2(x)dx) is reported for the range 0.02 < x < 0.8.
2.75 degree spectrometer data.
5.5 degree spectrometer data.
10.5 degree spectrometer data.
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%.
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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