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.
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.
The spin asymmetry in deep inelastic scattering of longitudinally polarised muons by longitudinally polarised protons has been measured over a large x range (0.01< x <0.7). The spin-dependent structure function g 1 ( x ) for the proton has been determined and its integral over x found to be 0.114±0.012±0.026, in disagreement with the Ellis-Jaffe sum rule. Assuming the validity of the Bjorken sum rule, this result implies a significant negative value for the integral of g 1 for the neutron. These values for the integrals of g 1 lead to the conclusion that the total quark spin constitutes a rather small fraction of the spin of the nucleon.
THE AVERAGE VALUES OF Q**2 IN EACH X-BIN ARE AS FOLLOWS: X=0.015,Q2=3.5: X=0.025,Q2=4.5: X=0.035,Q2=6.0: X=0.050,Q2=8.0: X=0.078,Q2=10.3: X=0.124,Q2=12.9: X=0.175,Q2=15.2: X=0.248,Q2=18.0: X=0.344,Q2=22.5: X=0.466,Q2=29.5.
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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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.
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Extrapolarity to full x range.
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The photoabsorption asymmetry A1 for exclusive RHO0 production.
The photoabsorption asymmetry A1 for exclusive RHO0 production as a function of Q**2.
The photoabsorption asymmetry A1 for exclusive RHO0 production as a function of W.
Double-spin asymmetries in the cross section of electroproduction of $\rho^0$ and $\phi$ mesons on the proton and deuteron are measured at the HERMES experiment. The photoabsorption asymmetry in exclusive $\rho^0$ electroproduction on the proton exhibits a positive tendency. This is consistent with theoretical predictions that the exchange of an object with unnatural parity contributes to exclusive $\rho^0$ electroproduction by transverse photons. The photoabsorption asymmetry on the deuteron is found to be consistent with zero. Double-spin asymmetries in $\rho^0$ and $\phi $ meson electroproduction by quasi-real photons were also found to be consistent with zero: the asymmetry in the case of the $\phi$ meson is compatible with a theoretical prediction which involves $s\bar{s}$ knockout from the nucleon.
The photoabsorption asymmetry A1 for exclusive RHO0 production.
The photoabsorption asymmetry A1 for exclusive PHI electroproduction.
The photoabsorption asymmetry A1 for electroproduction of RHO0 mesons by quasi-real photons.
Final results are presented from the inclusive measurement of deep-inelastic polarised-muon scattering on longitudinally polarised deuterons using a $^6$LiD target. The data were taken at $160~{\rm GeV}$ beam energy and the results are shown for the kinematic range $1~({\rm GeV}/c)^2 < Q^2 < 100~({\rm GeV}/c)^2$ in photon virtuality, $0.004<x<0.7$ in the Bjorken scaling variable and $W > 4~{\rm GeV}/c^2$ in the mass of the hadronic final state. The deuteron double-spin asymmetry $A_1^{\rm d}$ and the deuteron longitudinal-spin structure function $g_1^{\rm d}$ are presented in bins of $x$ and $Q^2$. Towards lowest accessible values of $x$, $g_1^{\rm d}$ decreases and becomes consistent with zero within uncertainties. The presented final $g_1^{\rm d}$ values together with the recently published final $g_1^{\rm p}$ values of COMPASS are used to again evaluate the Bjorken sum rule and perform the QCD fit to the $g_1$ world data at next-to-leading order of the strong coupling constant. In both cases, changes in central values of the resulting numbers are well within statistical uncertainties. The flavour-singlet axial charge $a_0$, {which is identified in the $\overline{\rm MS}$ renormalisation scheme with the total contribution of quark helicities to the nucleon spin}, is extracted from only the COMPASS deuteron data with negligible extrapolation uncertainty: $a_0 (Q^2 = 3~({\rm GeV}/c)^2) = 0.32 \pm 0.02_{\rm stat} \pm0.04_{\rm syst} \pm 0.05_{\rm evol}$. Together with the recent results on the proton spin structure function $g_1^{\rm p}$, the results on $g_1^{\rm d}$ constitute the COMPASS legacy on the measurements of $g_1$ through inclusive spin-dependent deep inelastic scattering.
Values of $A_1^d$ and $g_1^d$ for the COMPASS deuteron data at 160 GeV in $x$ bins averaged over $Q^2$.
Values of $A_1^d$ and $g_1^d$ for the COMPASS deuteron data at 160 GeV in (x, $Q^2$) bins.
Values of $g_1^{NS}$ for the COMPASS data in $x$ bins averaged over $Q^2$.
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 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.
Results are reported from the HERMES experiment at HERA on a measurement of the neutron spin structure function $g_1~n(x,Q~2)$ in deep inelastic scattering using 27.5 GeV longitudinally polarized positrons incident on a polarized $~3$He internal gas target. The data cover the kinematic range $0.023<x<0.6$ and $1 (GeV/c)~2 < Q~2 <15 (GeV/c)~2$. The integral $\int_{0.023}~{0.6} g_1~n(x) dx$ evaluated at a fixed $Q~2$ of $2.5 (GeV/c)~2$ is $-0.034\pm 0.013(stat.)\pm 0.005(syst.)$. Assuming Regge behavior at low $x$, the first moment $\Gamma_1~n=\int_0~1 g_1~n(x) dx$ is $-0.037\pm 0.013(stat.)\pm 0.005(syst.)\pm 0.006(extrapol.)$.
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Data extrapolated to full x region. Second systematic error is the error on this extrapolation.
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