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.
No description provided.
No description provided.
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.
No description provided.
No description provided.
No description provided.
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.
No description provided.
No description provided.
No description provided.
Fermilab Experiment-665 measured deep-inelastic scattering of 490 GeV muons off deuterium and xenon targets. Events were selected with a range of energy exchange ν from 100 GeV to 500 GeV and with large ranges of Q2 and xBj: 0.1 GeV2/c2<Q2<150 GeV2/c2 and 0.001<xBj<0.5. The fractional energy (z) distributions of forward-produced hadrons from the two targets have been compared as a function of the kinematics of the scattering; specifically, the kinematic region of ‘‘shadowing’’ has been compared to that of nonshadowing. The dependence of the distributions upon the order of the hadrons, determined by the fractional energies, has been examined as well; a strong degree of similarity has been observed in the shapes of the distributions of the different order hadrons. These z distributions, however, show no nuclear dependence, even in the kinematic region of shadowing.
Z distributions for the second fastest hadron rescaled to the energy available to it.
Z distributions for the second fastest hadron rescaled to the energy available to it.
Z distributions for the second fastest hadron rescaled to the energy available to it.
We report results of the first measurements of Lambda and Antilambda polarization produced in deep inelastic polarized muon scattering on the nucleon. The results are consistent with an expected trend towards positive polarization with increasing x_F. The polarizations of Lambda and Antilambda appear to have opposite signs. A large negative polarization for Lambda at low positive x_F is observed and is not explained by existing models.A possible interpretation is presented.
The measured and corrected (undiluted) polarizations.
The measured and corrected (undiluted) polarizations.
Measurements were made at SLAC of the cross section for scattering 29 GeV electrons from carbon at a laboratory angle of 4.5 degrees, corresponding to 0.03<x<0.1 and 1.3<Q^2<2.7 GeV^2. Values of R=sigma_L/sigma_T were extracted in this kinematic range by comparing these data to cross sections measured at a higher beam energy by the NMC collaboration. The results are in reasonable agreement with pQCD calculations and with extrapolations of the R1990 parameterization of previous data. A new fit is made including these data and other recent results.
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.
No description provided.
Extrapolarity to full x range.
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.
Integrals of G2 from x = 0.03 to 1.0.
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.
Extrapolation to the full x range was made using E154 data (see PL 405B, 180 and PRL 79, 26).
The diffractive production of ρ0(770 @#@) mesons in muon-proton interactions is studied in the kinematic region 0.15 GeV2< Q2< 20 GeV2 and 20 GeV < ? < 420 GeV. The data were obtained in the Fermilab fixed-target experiment E665 with primary muons of 470 GeV energy. Results are presented on the Q2, x and ? dependence of the cross section, on the shape of the ρ+ρt - mass spectrum, on the slope of the diffraction peak and on the production and decay angular distributions of the ρ0(770). The cross section for diffractive production of ρ0 by virtual photons on protons depends mainly on Q2. At fixed Q2, no significant dependence on x or ? is observed. The extrapolation to Q2 = 0 yields a photoproduction cross section of (10.30 ± 0.33) μb. The slope of the t′ distribution has a value of (7.0 ± 0.2) GeV−2, with a tendency to decrease as Q2 increases. The production and decay angular distributions of the ρ0 depend strongly on Q2 and are consistent with s-channel helicity conservation. The ratio R = σl/σt deduced from the decay angular distributions rises strongly with Q2, passing the value of 1 at Q2≈ 2 GeV2.
Statistical errors only.
Statistical errors only.
Cross section extrapolated to Q**2 = 0.
We have measured the proton and deuteron spin structure functions g_1^p and g_1^d in the region of the nucleon resonances for W^2 < 5 GeV^2 and $Q^2\simeq 0.5$ and $Q^2\simeq 1.2$ GeV^2 by inelastically scattering 9.7 GeV polarized electrons off polarized $^{15}NH_3$ and $^{15}ND_3$ targets. We observe significant structure in g_1^p in the resonance region. We have used the present results, together with the deep-inelastic data at higher W^2, to extract $\Gamma(Q^2)\equiv\int_0^1 g_1(x,Q^2) dx$. This is the first information on the low-Q^2 evolution of Gamma toward the Gerasimov-Drell-Hearn limit at Q^2 = 0.
The integral of the structure functions g1 for the resonance region W**2 < 4 GeV**2.
The integral of the structure functions g1 for the resonance region W**2 < 4 GeV**2.
The integral of the structure functions g1 for the full W region including the deep-inelastic region as given by fits to the world's data.
Using data from the Fermilab fixed target experiment E665, general properties of forward produced charged hadrons in μp interactions at a primary muon energy of 470 GeV are investigated. The normalized inclusive singleparticle distributions for Feynman-x D(xF ) and for the transverse momentum D(p2t , xF ) are measured as a function of W and Q2. The dependence of the average transverse momentum squared 〈p2t〉 on xF , W and Q2 is studied. The increasing contribution from diffractive production as Q2 decreases leads to a reduction of the average charged hadron multiplicities at low (positive) xF and an enhancement at large xF , for Q2 ≲ 10 GeV2. It also reduces 〈p2t〉 for Q2 ≲ 5 GeV2 and 0.4 ≲ xF < 1.0.
Normalised inclusive single particle distributions of charged hadrons for all events in W intervals. Additional systematic uncertainty of 4 PCT.
Normalised inclusive single particle distributions of charged hadrons for all events in Q**2 intervals. Additional systematic uncertainty of 4 PCT.
Normalised inclusive single particle distributions of charged hadrons for all events in X (Bjorken) intervals. Additional systematic uncertainty of 4 PCT.
We have measured the neutron structure function g$_{2}^{n}$ and the virtual photon-nucleon asymmetry A$_{2}^{n}$ over the kinematic range $0.014\leq x \leq 0.7$ and $1.0 \leq Q^{2} \leq 17.0$ by scattering 48.3 GeV longitudinally polarized electrons from polarized $^{3}$He. Results for A$_{2}^{n}$ are significantly smaller than the $\sqrt{R}$ positivity limit over most of the measured range and data for g$_2^{n}$ are generally consistent with the twist-2 Wandzura-Wilczek prediction. Using our measured g$_{2}^{n}$ we obtain results for the twist-3 reduced matrix element $d_{2}^{n}$, and the integral $\int$g$_{2}^{n}(x)dx$ in the range $0.014\leq x \leq 1.0$. Data from this experiment are combined with existing data for g$_{2}^{n}$ to obtain an average for $d_{2}^{n}$ and the integral $\int$g$_{2}^{n}(x)dx$.
Data measured using the 2.75 degree spectrometer.
Data measured using the 5.5 degree spectrometer.
Measured value of the twist-3 reduced matrix element D2.
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.
Longitudinal and transverse momentum spectra of final state hadrons produced in deep-inelastic muon-deuterium scattering at incident muon energy of 490 GeV have been measured up to a hadronic center of mass energy of 30 GeV. The longitudinal distributions agree well with data from earlier muon-nucleon scattering experiments; these distributions tend to increase in steepness as the center of mass energy increases. Comparisons with e + e − data at comparable center of mass energies indicate slight differences. The transverse momentum distributions show an increase in mean p T 2 with an increase in the center of mass energy.
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 $\alpha_s = 0.32\pm 0.05$.
No description provided.
No description provided.
G1 evaluated at Q**2 = 2GeV**2 assumig A1 does not depend on Q**2.
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.
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.
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.
2.75 degree spectrometer data.
5.5 degree spectrometer data.
10.5 degree spectrometer data.
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