Measurement of the $x$- and $Q^2$-Dependence of the Asymmetry $A_1$ on the Nucleon

The CLAS collaboration Dharmawardane, K.V. ; Kuhn, S.E. ; Bosted, Peter E. ; et al.
Phys.Lett.B 641 (2006) 11-17, 2006.
Inspire Record 717523 DOI 10.17182/hepdata.6726

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.

306 data tables

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.

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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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Measurements of the Q**2 dependence of the proton and neutron spin structure functions g1(p) and g1(n).

The E155 collaboration Anthony, P.L ; Arnold, R.G ; Averett, T ; et al.
Phys.Lett.B 493 (2000) 19-28, 2000.
Inspire Record 530798 DOI 10.17182/hepdata.27035

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.

12 data tables

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.

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Measurement of the deuteron spin structure function g1(d)(x) for 1-(GeV/c)**2 < Q**2 < 40-(GeV/c)**2.

The E155 collaboration Anthony, P.L. ; Arnold, R.G. ; Averett, T. ; et al.
Phys.Lett.B 463 (1999) 339-345, 1999.
Inspire Record 496268 DOI 10.17182/hepdata.41630

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.

4 data tables

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.

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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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Spin structure of the proton from polarized inclusive deep-inelastic muon proton scattering.

The Spin Muon (SMC) collaboration Adams, D. ; Adeva, B. ; Arik, E. ; et al.
Phys.Rev.D 56 (1997) 5330-5358, 1997.
Inspire Record 440355 DOI 10.17182/hepdata.47485

We have measured the spin-dependent structure function $g_1~p$ in inclusive deep-inelastic scattering of polarized muons off polarized protons, in the kinematic range $0.003 < x < 0.7$ and $1 GeV~2 < Q~2 < 60 GeV~2$. A next-to-leading order QCD analysis is used to evolve the measured $g_1~p(x,Q~2)$ to a fixed $Q~2_0$. The first moment of $g_1~p$ at $Q~2_0 = 10 GeV~2$ is $\Gamma~p = 0.136\pm 0.013(stat.) \pm 0.009(syst.)\pm 0.005(evol.)$. This result is below the prediction of the Ellis-Jaffe sum rule by more than two standard deviations. The singlet axial charge $a_0$ is found to be $0.28 \pm 0.16$. In the Adler-Bardeen factorization scheme, $\Delta g \simeq 2$ is required to bring $\Delta \Sigma$ in agreement with the Quark-Parton Model. A combined analysis of all available proton and deuteron data confirms the Bjorken sum rule.

11 data tables

Data for Q**2 > 1 GeV**2.

Data for Q**2 > 0.2 GeV**2.

Statistical errors only.

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The spin-dependent structure function g1(x) of the deuteron from polarized deep-inelastic muon scattering.

The Spin Muon (SMC) collaboration Adams, D. ; Adeva, B. ; Akdogan, T. ; et al.
Phys.Lett.B 396 (1997) 338-348, 1997.
Inspire Record 440053 DOI 10.17182/hepdata.47513

We present a new measurement of the spin-dependent structure function g 1 d of the deuteron from deep inelastic scattering of 190 GeV polarized muons on polarized deuterons. The results are combined with our previous measurements of g 1 d . A perturbative QCD evolution in next-to-leading order is used to compute g 1 d ( x ) at a constant Q 2 . At Q 2 = 10 GeV 2 , we obtain a first moment Γ 1 d =∫ 1 d g 1 d d x =0.041±0.008, a flavour-singlet axial charge of the nucleon a 0 = 0.30 ± 0.08, and an axial charge of the strange quark a s = −0.09 ± 0.03. Using our earlier determination of Γ 1 p , we obtain Γ 1 p − Γ 1 m = 0.183 ± 0.035 at Q 2 = 10GeV 2 . This result is in agreement with the Bjorken sum rule which predicts Γ 1 p − Γ 1 n = 0.186 ± 0.002 at the same Q 2 .

6 data tables

Measurements of the transverse virtual photon asymmetry A2. Statistical errors only.

The virtual-photon deuteron cross section asymmetry A1 from the combined SMC data. Statistical errors only.

The spin dependent structure function G1(D).

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A New measurement of the spin dependent structure function g1(x) of the deuteron

The Spin Muon collaboration Adams, D. ; Adeva, B. ; Arik, E. ; et al.
Phys.Lett.B 357 (1995) 248-254, 1995.
Inspire Record 397392 DOI 10.17182/hepdata.47847

We present a new measurement of the spin-dependent structure function g 1 d of the deuteron in deep inelastic scattering of 190 GeV polarised muons on polarised deuterons, in the kinematic range 0.003 < x < 0.7 and 1 GeV 2 < Q 2 < 60 GeV 2 . This structure function is found to be negative at small x . The first moment Γ 1 d =∫ 0 1 g 1 d d x evaluated at Q 0 2 = 10 GeV 2 is 0.034 ± 0.009 (stat.) ± 0.006 (syst.). This value is below the Ellis-Jaffe sum rule prediction by three standard deviations. Using our earlier determination of Γ 1 p , we obtain Γ 1 p − Γ 1 n = 0.199 ± 0.038 which agrees with the Bjorken sum rule.

4 data tables

Results on the virtual photon deuteron asymmetry.

Results on the spin structure function of the deuteron.

Results on the spin structure function of the neutron.

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