Measurement of the $x$- and $Q^2$-Dependence of the Asymmetry $A_1$ on the Nucleon

Abstract

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.

Figures (5)

• Figure 1: Results for the asymmetry $A_{||}/D = A_1 + \eta A_2$ on the proton versus final-state invariant mass $W$, for three bins in $Q^2$. Arrows indicate the masses of several resonances. The first two panels show data obtained with 1.6 GeV beam energy, while the last panel comes from the 5.7 GeV data. The solid line close to the data points is the result for $A_{||}/D$ of our parametrization of previous world data. The dashed line close to zero is the estimated contribution from the unmeasured asymmetry $A_2$ to $A_{||}/D$. Bands at the bottom of all figures indicate systematic errors.
• Figure 2: Measured ratio $g_1/F_1$ as a function of momentum transfer squared $Q^2$ for several bins in $x$ for the proton (left) and the deuteron (right). A few data points from SLAC experiments E143 E143Long (open triangles) and E155 E155Q2 (open squares) are also shown for comparison, as well as data from the first run with CLAS EG1a_pEG1a_d (open circles). The dashed line represents our parametrization of the world data in the DIS region E155Q2. Arrows indicate the conventional limit of the resonance region at $W = 2$ GeV.
• Figure 3: Results for the asymmetry $A_1(x)$ on the proton. Filled circles show our data in the deep inelastic region ($W > 2$ GeV, $Q^2 > 1$ GeV$^2$) while the remaining open symbols are for data from several previous experiments HERMESfinalSMCfinalE155Q2E143Long. The SU(6) expectation for all $x$ is indicated by the arrow. The solid line shows our parametrization of the world data at a fixed $Q^2 = 10$ GeV$^2$. The shaded band covers a range of calculations by Isgur SpinQMIsgur that model the hyperfine--interaction breaking of SU(6) symmetry. The remaining three curves correspond to different scenarios of SU(6) symmetry breaking as presented in the paper by Close and Melnitchouk ClosMeln: helicity-1/2 dominance (dashed), spin-1/2 dominance (dotted) and symmetric wave function suppression (dash-dotted).
• Figure 4: Results for the asymmetry $A_1(x)$ on the deuteron. The lines and symbols have the same meaning as in Fig. \ref{['fig:A1p']}. The data are divided by $(1 - 1.5 w_D) \approx 0.925$ to correct for the deuteron D-state probability $w_D$, while the model predictions are for an isoscalar (proton plus neutron) target.
• Figure 5: Quark polarizations $\Delta u/u$ and $\Delta d/d$ extracted from our data. Included are all data above $W=1.77$ GeV and $Q^2 = 1$ GeV$^2$. Also shown are semi-inclusive results from Hermes HERMESfinal and inclusive results from Hall A data HallA_largex combined with previous data from CLAS EG1a_p . The solid line is from the NLO fit to the world data by GRV GRV, the dashed line is from the AAC fit AAC, the dash-dotted line is from Gehrmann and Stirling Gehrmann and the dotted line indicates the latest fit from LSS LSS .