We present a Next-to-Leading order perturbative QCD analysis of world data on the spin dependent structure functions $g_1^p, g_1^n$, and $g_1^d$, including the new experimental information on the $Q^2$ dependence of $g_1^n$. Careful attention is paid to the experimental and theoretical uncertainties. The data constrain the first moments of the polarized valence quark distributions, but only qualitatively constrain the polarized sea quark and gluon distributions. The NLO results are used to determine the $Q^2$ dependence of the ratio $g_1/F_1$ and evolve the experimental data to a constant $Q^2 = 5 GeV^2$. We determine the first moments of the polarized structure functions of the proton and neutron and find agreement with the Bjorken sum rule.
Data from the 2.75 degree spectrometer.
Data from the 2.75 degree spectrometer evolved to a mean Q**2 of 5 GeV**2 using the MSBAR parameterization. The second systematic error is due to the evolution.
Data from the 5.5 degree spectrometer.
The ratio of the deuteron to proton structure functions is measured at very small Bjorken x (down to 10–6) and for Q2>0.001 GeV2 from scattering of 470 GeV muons on liquid hydrogen and deuterium targets. The ratio F2n/F2p extracted from these measurements is found to be constant, at a value of 0.935±0.008±0.034, for x<0.01. This result suggests the presence of nuclear shadowing effects in the deuteron. The dependence of the ratio on Q2 is also examined; no significant variation is found.
F2(N) / F2(P) = 2F2(DEUT)/F2(P) - 1.
F2(N) / F2(P) = 2F2(DEUT)/F2(P) - 1. The systematic uncertainty in the Q**2 dependece is negligible as compared to the statistical uncertainty.
We present results on the cross-section ratio for inelastic muon scattering on neutrons and protons as a function of Bjorken chi;. The data extend to χ values two orders of magnitude smaller than in previous measurements, down to 2×10 −5 , for Q 2 >0.01 GeV 2 . The ratio is consistent with unity throughout this new range.
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The ratio g1/F1 has been measured over the range 0.03<x<0.6 and 0.3<Q2<10 (GeV/c)2 using deep-inelastic scattering of polarized electrons from polarized protons and deuterons. We find g1/F1 to be consistent with no Q2-dependence at fixed x in the deep-inelastic region Q~2>1 (GeV/c)2. A trend is observed for g1/F1 to decrease at lower Q2. Fits to world data with and without a possible Q2-dependence in g1/F1 are in agreement with the Bjorken sum rule, but Delta_q is substantially less than the quark-parton model expectation.
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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%.
Inelastic scattering of 490 GeV μ + from deuterium and xenon nuclei has been studied for x Bj > s .001. The ratio of the xenon/deuterium cross section per nucleon is observed to vary with x Bj , with a depletion in the kinematic range 0.001 < x Bj < 0.025 which exhibits no significant Q 2 dependence. An electromagnetic calorimeter was used to verify the radiative corrections.
Xenon structure function parameterized as being equal to the DEUT structurefunction.
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.
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.
Nuclear shadowing is observed in the per-nucleon cross-sections of positive muons on carbon, calcium and lead as compared to deuterium. The data were taken by Fermilab experiment E665 using inelastically scattered muons of mean incident momentum 470 GeV/c. Cross-section ratios are presented in the kinematic region 0.0001 < XBj <0.56 and 0.1 < Q**2 < 80 GeVc. The data are consistent with no significant nu or Q**2 dependence at fixed XBj. As XBj decreases, the size of the shadowing effect, as well as its A dependence, are found to approach the corresponding measurements in photoproduction.
Per-nucleon cross section ratio for carbon to deuterium.
Per-nucleon cross section ratio for calcium to deuterium.
Per-nucleon cross section ratio for lead to deuterium.
Results on the production of charged hadrons in muon-deuteron and muon-xenon interactions are presented. The data were taken with the E665 spectrometer, which was exposed to the 490 GeV muon beam of the Tevatron at Fermilab. The use of a streamer chamber as vertex detector provides nearly 4π acceptance for charged particles. The μD data are compared with the μXe data in terms of multiplicity distributions, average multiplicities, forward-backward multiplicity correlations, rapidity and transverse momentum distributions and of two-particle rapidity correlations of charged hadrons. The data cover a range of invariant hadronic massesW from 8 to 30 GeV.
Results of negative binomial function fit to the multiplicity distribution of charged hadrons in muon-deuteron scattering. DISPERSION = SQRT(1/MULT + 1/K) is this dispersion of the scaled multiplicity Z = N/MULT.
Results of negative binomial function fit to the multiplicity distribution of charged hadrons in muon-xenon scattering. DISPERSION = SQRT(1/MULT + 1/K) is this dispersion of the scaled multiplicity Z = N/MULT.
Results of negative binomial fits to charged hadron multiplicity distributions in muon-deuteron interactions for backward and forward hemispheres of the hadronic cm.
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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