A measurement of the virtual-photon asymmetry A_2(x,Q^2) and of the spin-structure function g_2(x,Q^2) of the proton are presented for the kinematic range 0.004 < x < 0.9 and 0.18 GeV^2 < Q^2 < 20 GeV^2. The data were collected by the HERMES experiment at the HERA storage ring at DESY while studying inclusive deep-inelastic scattering of 27.6 GeV longitudinally polarized leptons off a transversely polarized hydrogen gas target. The results are consistent with previous experimental data from CERN and SLAC. For the x-range covered, the measured integral of g_2(x) converges to the null result of the Burkhardt-Cottingham sum rule. The x^2 moment of the twist-3 contribution to g_2(x) is found to be compatible with zero.
The spin-structure function $xg_2(x,Q^2)$ and virtual-photon asymmetry $A_2(x,Q^2)$ of the proton in bins of $(x,Q^2)$, see text for details. Statistical and systematic uncertainties are presented separately.
The spin-structure function $xg_2$ and the virtual-photon asymmetry $A_2$ of the proton after evolving to common $Q^2$ and averaging over in each $x$-bin (see text for details). Statistical and systematic uncertainties are presented separately.
Correlation matrix for $xg_2$ in 9 $x$-bins (as in Table 2).
Double-polarization asymmetries for inclusive $ep$ scattering were measured at Jefferson Lab using 2.6 and 4.3 GeV longitudinally polarized electrons incident on a longitudinally polarized NH$_3$ target in the CLAS detector. The polarized structure function $g_1(x,Q^2)$ was extracted throughout the nucleon resonance region and into the deep inelastic regime, for $Q^2 = 0.15 -1.64 $GeV$^2$. The contributions to the first moment $\Gamma_1(Q^2) = \int g_1(x,Q^2)dx$ were determined up to $Q^2=1.2$ GeV$^2$. Using a parametrization for $g_1$ in the unmeasured low $x$ regions, the complete first moment was estimated over this $Q^2$ region. A rapid change in $\Gamma_1$ is observed for $Q^2 < 1 $GeV$^2$, with a sign change near $Q^2 = 0.3 $GeV$^2$, indicating dominant contributions from the resonance region. At $Q^2=1.2$ GeV$^2$ our data are below the pQCD evolved scaling value.
The measured photon asymmetry (A1+ETA*A2) for the Q**2 region 0.15 to 0.22 GeV**2 obtained with a beam energy of 2.6 GeV.
The measured photon asymmetry (A1+ETA*A2) for the Q**2 region 0.6 to 1.10 GeV**2 obtained with a beam energy of 4.3 GeV.
The polarized structure function G1 as a function of Bjorken X for the Q**2range 0.15 to 0.27 GeV.
Precise measurements of the spin structure functions of the proton $g_1^p(x,Q^2)$ and deuteron $g_1^d(x,Q^2)$ are presented over the kinematic range $0.0041 \leq x \leq 0.9$ and $0.18 $ GeV$^2$ $\leq Q^2 \leq 20$ GeV$^2$. The data were collected at the HERMES experiment at DESY, in deep-inelastic scattering of 27.6 GeV longitudinally polarized positrons off longitudinally polarized hydrogen and deuterium gas targets internal to the HERA storage ring. The neutron spin structure function $g_1^n$ is extracted by combining proton and deuteron data. The integrals of $g_1^{p,d}$ at $Q^2=5$ GeV$^2$ are evaluated over the measured $x$ range. Neglecting any possible contribution to the $g_1^d$ integral from the region $x \leq 0.021$, a value of $0.330 \pm 0.011\mathrm{(theo.)}\pm0.025\mathrm{(exp.)}\pm 0.028$(evol.) is obtained for the flavor-singlet axial charge $a_0$ in a leading-twist NNLO analysis.
Integrals of G1 for P, DEUT and N targets.. The second DSYS systematic error is due to the uncertainty in the parameterizations (R, F2, A2, Azz, omegaD).. The third DSYS systematic error is due to the uncertainty in evolving to a common Q**2.
Integrals of G1 for the Non-Singlet contributions.. The second DSYS systematic error is due to the uncertainty in the parameterizations (R, F2, A2, Azz, omegaD).. The third DSYS systematic error is due to the uncertainty in evolving to a common Q**2. Axis error includes +- 5.2/5.2 contribution.
Integrals of G1 over different X ranges for P target at various Q*2 values. The second DSYS systematic error is due to the uncertainty in the parameterizations (R, F2, A2, Azz, omegaD).. The third DSYS systematic error is due to the uncertainty in evolving to a common Q**2. Axis error includes +- 5.2/5.2 contribution.
We report results for the virtual photon asymmetry $A_1$ on the nucleon from new Jefferson Lab measurements. The experiment, which used the CEBAF Large Acceptance Spectrometer and longitudinally polarized proton ($^{15}$NH$_3$) and deuteron ($^{15}$ND$_3$) targets, collected data with a longitudinally polarized electron beam at energies between 1.6 GeV and 5.7 GeV. In the present paper, we concentrate on our results for $A_1(x,Q^2)$ and the related ratio $g_1/F_1(x,Q^2)$ in the resonance and the deep inelastic regions for our lowest and highest beam energies, covering a range in momentum transfer $Q^2$ from 0.05 to 5.0 GeV$^2$ and in final-state invariant mass $W$ up to about 3 GeV. Our data show detailed structure in the resonance region, which leads to a strong $Q^2$--dependence of $A_1(x,Q^2)$ for $W$ below 2 GeV. At higher $W$, a smooth approach to the scaling limit, established by earlier experiments, can be seen, but $A_1(x,Q^2)$ is not strictly $Q^2$--independent. We add significantly to the world data set at high $x$, up to $x = 0.6$. Our data exceed the SU(6)-symmetric quark model expectation for both the proton and the deuteron while being consistent with a negative $d$-quark polarization up to our highest $x$. This data setshould improve next-to-leading order (NLO) pQCD fits of the parton polarization distributions.
A1 and g1/F1 for the P target at incident energy 1.6000 GeV and W = 1.1300 GeV.
A1 and g1/F1 for the P target at incident energy 1.6000 GeV and W = 1.1500 GeV.
A1 and g1/F1 for the P target at incident energy 1.6000 GeV and W = 1.1700 GeV.
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 report the results of a new measurement of spin structure functions of the deuteron in the region of moderate momentum transfer ($Q^2$ = 0.27 -- 1.3 (GeV/c)$^2$) and final hadronic state mass in the nucleon resonance region ($W$ = 1.08 -- 2.0 GeV). We scattered a 2.5 GeV polarized continuous electron beam at Jefferson Lab off a dynamically polarized cryogenic solid state target ($^{15}$ND$_3$) and detected the scattered electrons with the CEBAF Large Acceptance Spectrometer (CLAS). From our data, we extract the longitudinal double spin asymmetry $A_{||}$ and the spin structure function $g_1^d$. Our data are generally in reasonable agreement with existing data from SLAC where they overlap, and they represent a substantial improvement in statistical precision. We compare our results with expectations for resonance asymmetries and extrapolated deep inelastic scaling results. Finally, we evaluate the first moment of the structure function $g_1^d$ and study its approach to both the deep inelastic limit at large $Q^2$ and to the Gerasimov-Drell-Hearn sum rule at the real photon limit ($Q^2 \to 0$). We find that the first moment varies rapidly in the $Q^2$ range of our experiment and crosses zero at $Q^2$ between 0.5 and 0.8 (GeV/c)$^2$, indicating the importance of the $\Delta$ resonance at these momentum transfers.
The measured virtual photon asymmetry (A1D+ETA*A2D) for the Q** region 0.27to 0.39 GeV**2.
The measured virtual photon asymmetry (A1D+ETA*A2D) for the Q** region 0.39to 0.65 GeV**2.
The measured virtual photon asymmetry (A1D+ETA*A2D) for the Q** region 0.65to 1.3 GeV**2.
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.
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.
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