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).
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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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%.
New results for the double spin asymmetry $A_1^{\rm p}$ and the proton longitudinal spin structure function $g_1^{\rm p}$ are presented. They were obtained by the COMPASS collaboration using polarised 200 GeV muons scattered off a longitudinally polarised NH$_3$ target. The data were collected in 2011 and complement those recorded in 2007 at 160\,GeV, in particular at lower values of $x$. They improve the statistical precision of $g_1^{\rm p}(x)$ by about a factor of two in the region $x\lesssim 0.02$. A next-to-leading order QCD fit to the $g_1$ world data is performed. It leads to a new determination of the quark spin contribution to the nucleon spin, $\Delta \Sigma$ ranging from 0.26 to 0.36, and to a re-evaluation of the first moment of $g_1^{\rm p}$. The uncertainty of $\Delta \Sigma$ is mostly due to the large uncertainty in the present determinations of the gluon helicity distribution. A new evaluation of the Bjorken sum rule based on the COMPASS results for the non-singlet structure function $g_1^{\rm NS}(x,Q^2)$ yields as ratio of the axial and vector coupling constants $|g_{\rm A}/g_{\rm V}| = 1.22 \pm 0.05~({\rm stat.}) \pm 0.10~({\rm syst.})$, which validates the sum rule to an accuracy of about 9\%.
Values of $A_1^{\rm p}$ and $g_1^{\rm p}$ for the 2011 COMPASS data at 200 GeV in ($x$, $Q^2$) bins.
Values of $A_1^{\rm p}$ and $g_1^{\rm p}$ for the 2011 COMPASS data at 200 GeV in $x$ bins averaged over $Q^2$.
Values of $A_1^{\rm p}$ for the 2007 COMPASS data at 160 GeV in ($x$, $Q^2$) bins.
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.
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.
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.
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.
No description provided.
Extrapolarity to full x range.
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 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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