Measurement of the virtual-photon asymmetry A2 and the spin-structure function g2 of the proton

The HERMES collaboration Airapetian, A. ; Akopov, N. ; Akopov, Z. ; et al.
Eur.Phys.J.C 72 (2012) 1921, 2012.
Inspire Record 1082840 DOI 10.17182/hepdata.66230

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.

4 data tables

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).

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Measurement of the proton spin structure function g1(x,Q**2) for Q**2 from 0.15-GeV**2 to 1.6-GeV**2 with CLAS.

The CLAS collaboration Fatemi, R. ; Skabelin, A.V. ; Burkert, V.D. ; et al.
Phys.Rev.Lett. 91 (2003) 222002, 2003.
Inspire Record 621221 DOI 10.17182/hepdata.41917

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.

8 data tables

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.

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Measurement of inclusive spin structure functions of the deuteron with CLAS.

The CLAS collaboration Yun, J. ; Kuhn, S.E. ; Dodge, G.E. ; et al.
Phys.Rev.C 67 (2003) 055204, 2003.
Inspire Record 604799 DOI 10.17182/hepdata.41972

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.

7 data tables

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.

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Precision measurement of the proton and deuteron spin structure functions g2 and asymmetries A(2).

The E155 collaboration Anthony, P.L. ; Arnold, R.G. ; Averett, T. ; et al.
Phys.Lett.B 553 (2003) 18-24, 2003.
Inspire Record 585675 DOI 10.17182/hepdata.27033

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.

7 data tables

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.

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Measurement of the proton and deuteron spin structure functions g2 and asymmetry A(2).

The E155 collaboration Anthony, P.L. ; Arnold, R.G. ; Averett, T. ; et al.
Phys.Lett.B 458 (1999) 529-535, 1999.
Inspire Record 493768 DOI 10.17182/hepdata.27072

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.

4 data tables

2.75 degree spectrometer data.

5.5 degree spectrometer data.

10.5 degree spectrometer data.

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Measurements of the proton and deuteron spin structure functions g1 and g2.

The E143 collaboration Abe, K. ; Akagi, T. ; Anthony, P.L. ; et al.
Phys.Rev.D 58 (1998) 112003, 1998.
Inspire Record 467140 DOI 10.17182/hepdata.22265

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.

33 data tables

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%.

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Measurement of the proton and deuteron spin structure function g2 and asymmetry A2.

The E143 collaboration Abe, K. ; Akagi, T. ; Anthony, P.L. ; et al.
Phys.Rev.Lett. 76 (1996) 587-591, 1996.
Inspire Record 400029 DOI 10.17182/hepdata.19584

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.

8 data tables

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.

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