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.
We report on the first measurement of the spin-dependent structure function g 1 d of the deuteron in the deep inelastic scattering of polarised muons off polarised deuterons, in the kinematical range 0.006< x <0.6, 1 GeV 2 < Q 2 <30 GeV 2 . The first moment, Γ 1 d =ʃ 0 1 g 1 d d x=0.023±0.020 ( stat. ) ± 0.015 ( syst. ) , is smaller than the prediction of the Ellis-Jaffe sum rules. Using earlier measurements of g 1 p , we infer the first moment of the spin-dependent neutron structure function g 1 n . The difference Γ 1 p − Γ 1 n =0.20±0.05 (stat.) ± 0.04 (syst.) agrees with the prediction of the Bjorken sum rule, Γ 1 p − Γ 1 n =0.191±0.002.
Virtual photon asymmetry A1.
Spin-dependent structure function G1.
: We have measured the spin-dependent structure function $g_1~p$ of the proton in deep inelastic scattering of polarized muons off polarized protons, in the kinematic range $0.003<x<0.7$ and $1\,\mbox{GeV}~2<Q~2<60\,\mbox{GeV}~2$. Its first moment, $\int_0~1 g_1~p(x) dx $, is found to be $0.136 \pm 0.011\,(\mbox{stat.})\pm 0.011\,(\mbox{syst.})$ at $Q~2=10\,\mbox{GeV}~2$. This value is smaller than the prediction of the Ellis--Jaffe sum rule by two standard deviations, and is consistent with previous measurements. A combined analysis of all available proton, deuteron and neutron data confirms the Bjorken sum rule to within $10\%$ of the theoretical value.
Results on the virtual photon proton asymmetry.
Results on the spin structure function of the proton.
Data for g1 at fixed Q**2 = 10 GeV (assuming no Q**2 dependence of A1).
We measured the spin asymmetry in the scattering of 100 GeV longitudinally-polarized muons on transversely polarized protons. The asymmetry was found to be compatible with zero in the kinematic range $0.006<x<0.6$, $1<Q~2<30\,\mbox{GeV}~2$. {}From this result we derive the upper limits for the virtual photon--proton asymmetry $A_2$, and for the spin structure function $g_2$. For $x<0.15$, $A_2$ is significantly smaller than its positivity limit $\sqrt{R}$.
No description provided.
Nucleon spin structure function g2.
We report on a high-statistics measurement of the deuteron spin structure function g1d at a beam energy of 29 GeV in the kinematic range 0.029<x<0.8 and 1<Q2<10 (GeV /c)2. The integral γ1d=∫1g1ddx evaluated at fixed Q2=3 (GeV /c)2 gives 0.042±0.003(stat)±0.004(syst). Combining this result with our earlier measurement of g1p, we find γ1p−γ1n=0.163±0.010(stat)±0.016(syst), which agrees with the prediction of the Bjorken sum rule with O(αs3) corrections, γ1p−γ1n=0.171±0.008. We find the quark contribution to the proton helicity to be Δq=0.30±0.06.
No description provided.
Values of G1 computed assuming G1/F1 is independent of Q**2 and evaluated at Q**2 = 3 GeV**2.
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.
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 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 .
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).
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.
Data for Q**2 > 1 GeV**2.
Data for Q**2 > 0.2 GeV**2.
Statistical errors only.
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 $-0.037\pm 0.013(stat.)\pm 0.005(syst.)\pm 0.006(extrapol.)$.
No description provided.
Data extrapolated to full x region. Second systematic error is the error on this extrapolation.