We present a next-to-leading order QCD analysis of the presently available data on the spin structure function g1 including the final data from the Spin Muon Collaboration. We present results for the first moments of the proton, deuteron, and neutron structure functions, and determine singlet and nonsinglet parton distributions in two factorization schemes. We also test the Bjorken sum rule and find agreement with the theoretical prediction at the level of 10%.
The second systematic (DSYS) error is due to QCD evolution.
First moments of the fitted function G1 evaluated on unmeasured X regions. Total uncertainties due to experimental systematics and theoretical sourc es in the QCD evolution.
Integrals of the nonsinglet (NS) structure function. SMC + E143 data.
Inelastic electron scattering cross sections have been measured for four-momentum transfers between 4.1 GeV 2 and 30.5 GeV 2 . At the large scattering angles of this experiment, the dominant contribution to the cross section comes from the W 1 structure function. In the conventional scaling variables, x and x ′, this structure function does not exhibit scaling behavior, and at fixed x or x ′ it is found to decrease with increasing four-momentum transfer.
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This paper presents the results of the analysis of a single-arm inelastic-electron-scattering experiment at an angle of 4°. We present data on the turnon of scaling in the low-q2 region 0.1<q2<1.8, the neutron-proton comparison at large values of the scaling variable ω, resonance excitation, and the shadowing in scattering from heavy nuclei.
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Measurements of the proton and deuteron $F_2$ structure functions are presented. The data, taken at Jefferson Lab Hall C, span the four-momentum transfer range $0.06 < Q^2 < 2.8$ GeV$^2$, and Bjorken $x$ values from 0.009 to 0.45, thus extending the knowledge of $F_2$ to low values of $Q^2$ at low $x$. Next-to-next-to-leading order calculations using recent parton distribution functions start to deviate from the data for $Q^2<2$ GeV$^2$ at the low and high $x$-values. Down to the lowest value of $Q^2$, the structure function is in good agreement with a parameterization of $F_2$ based on data that have been taken at much higher values of $Q^2$ or much lower values of $x$, and which is constrained by data at the photon point. The ratio of the deuteron and proton structure functions at low $x$ remains well described by a logarithmic dependence on $Q^2$ at low $Q^2$.
The ratios of the Deuteron to Proton cross sections and F2 structure function for an x value of 0.0080. Error is shown without the contribution from radiative corrections of O(alpha**2).
The ratios of the Deuteron to Proton cross sections and F2 structure function for an x value of 0.0125. Error is shown without the contribution from radiative corrections of O(alpha**2).
The ratios of the Deuteron to Proton cross sections and F2 structure function for an x value of 0.0175. Error is shown without the contribution from radiative corrections of O(alpha**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.
The inclusive polarized structure functions of the proton and deuteron, g1p and g1d, were measured with high statistical precision using polarized 6 GeV electrons incident on a polarized ammonia target in Hall B at Jefferson Laboratory. Electrons scattered at lab angles between 18 and 45 degrees were detected using the CEBAF Large Acceptance Spectrometer (CLAS). For the usual DIS kinematics, Q^2>1 GeV^2 and the final-state invariant mass W>2 GeV, the ratio of polarized to unpolarized structure functions g1/F1 is found to be nearly independent of Q^2 at fixed x. Significant resonant structure is apparent at values of W up to 2.3 GeV. In the framework of perturbative QCD, the high-W results can be used to better constrain the polarization of quarks and gluons in the nucleon, as well as high-twist contributions.
Results for G1(P)/F1(P) for the proton in bins of (XB;Q**2), along with average kinematic values and correction factors for each bin. All values are averaged over the event distribution.
Results for G1(DEUT)/F1(DEUT) for the deuteron in bins of (XB;Q**2), along with average kinematic values and correction factors for each bin. All values are averaged over the event distribution.
Results for G1(P)/F1(P) for the proton in bins of (W;Q**2), along with average kinematic values and correction factors for each bin. All values are averaged over the event distribution.
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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Results of inclusive measurements of inelastic electron and positron scattering from unpolarized protons and deuterons at the HERMES experiment are presented. The structure functions $F_2^p$ and $F_2^d$ are determined using a parameterization of existing data for the longitudinal-to-transverse virtual-photon absorption cross-section ratio. The HERMES results provide data in the ranges $0.006\leq x\leq 0.9$ and 0.1 GeV$^2\leq Q^2\leq$ 20 GeV$^2$, covering the transition region between the perturbative and the non-perturbative regimes of QCD in a so-far largely unexplored kinematic region. They are in agreement with existing world data in the region of overlap. The measured cross sections are used, in combination with data from other experiments, to perform fits to the photon-nucleon cross section using the functional form of the ALLM model. The deuteron-to-proton cross-section ratio is also determined.
Results on the differential Born cross section $\frac{d^2\sigma^p}{dx\,dQ^2}$ and $F_2^p$. The statistical uncertainty $\delta_{stat.}$ and the systematic uncertainties $\delta_{PID}$ (particle identification), $\delta_{model}$ (model dependence outside the acceptance), $\delta_{mis.}$ (misalignment), and $\delta_{rad.}$ (Bethe-Heitler efficiencies) are given in percent. Corresponding $x$ bin numbers and $Q^2$ bin numbers and the average values $\langle x \rangle$ and $\langle {Q^2} \rangle$ are listed in the first four columns. The overall normalization uncertainty is 7.6 %. The structure function $F_2^p$ is derived using the parameterization $R=R_{1998}$.
Results on the differential Born cross section $\frac{d^2\sigma^d}{dx\,dQ^2}$ and $F_2^d$. The statistical uncertainty $\delta_{stat.}$ and the systematic uncertainties $\delta_{PID}$ (particle identification), $\delta_{model}$ (model dependence outside the acceptance), $\delta_{mis.}$ (misalignment), and $\delta_{rad.}$ (Bethe-Heitler efficiencies), are given in percent. Corresponding $x$ bin numbers and $Q^2$ bin numbers and the average values $\langle x \rangle$ and $\langle{Q^2}\rangle$ are listed in the first four columns. The overall normalization uncertainty is 7.5 %. The structure function $F_2^d$ is derived using the parameterization $R=R_{1998}$.
Results on the inelastic Born cross-section ratio ${\sigma^d}/{\sigma^p}$. The statistical uncertainty $\delta_{stat.}$, the systematic uncertainty $\delta_{rad.}$ due to radiative corrections and $\delta_{model}$ due to the model dependence outside the acceptance are given in percent. The average values of $x$ and $Q^2$ are listed in the first two columns. The overall normalization uncertainty is 1.4$\%$.
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%.
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.
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