Precision measurements of $g_1$ of the proton and of the deuteron with 6 GeV electrons

The inclusive polarized structure functions of the proton and deuteron, $g_1^p$ and $g_1^d$, 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 laboratory angles between 18 and 45 degrees were detected using the CEBAF Large Acceptance Spectrometer (CLAS). For the usual deep inelastic region kinematics, $Q^2>1$ ${\mathrm{GeV}}^2$ and the final-state invariant mass $W>2$ GeV, the ratio of polarized to unpolarized structure functions $g_1/F_1$ 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 quantum chromodynamics, 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.

Figure 1

A schematic of an event in CLAS, with two charged particles passing through three regions of drift chambers (DC), the time of flight (TOF, also known as SC), the Cherenkov counters (CC), and the electromagnetic calorimeter (EC).

Figure 2

Distribution of electron candidates in the EC energy divided by momentum $P$ (with 0.12 GeV offset) plotted vs the number of photoelectrons in the Cherenkov detector. The dashed lines show the cuts applied.

Figure 3

Average raw double-spin count asymmetries vs run number. The black points are for carbon, the green points for the empty cell, the red points for the bottom ${\mathrm{NH}}_3$ target, and the blue points for the top ${\mathrm{NH}}_3$ target (Parts A and B) or the ${\mathrm{ND}}_3$ target (Part C). The vertical dashed lines correspond to changes in beam energy or torus polarity.

Figure 4

Schematic diagram for eg1-dvcs showing the targets used: loosely packed ammonia beads (top), an empty target cell (middle), and a solid carbon target (bottom). Ammonia was the primary experimental target used; carbon and empty targets were used to calculate dilution factors and to make consistency checks. Two ammonia cells were used during the experiment (one is not shown here).

Figure 5

Distribution of $p_T^q$ for exclusive $ep$ elastic scattering from the deuterated ammonia (${\mathrm{ND}}_3$) target.

Figure 6

Dilution factor as a function of $W$ for $Q^2=1$ ${\mathrm{GeV}}^2$ (black, dotted curve), $Q^2=1.6$ ${\mathrm{GeV}}^2$ (red, short-dash curve), $Q^2=3$ ${\mathrm{GeV}}^2$ (blue, long-dash curve), and $Q^2=5$ ${\mathrm{GeV}}^2$ (green, solid curve). The lower set of curves is for the ammonia (${\mathrm{NH}}_3$) target, while the upper set of curves is for the deuterated ammonia (${\mathrm{ND}}_3$) target.

Figure 7

Ratio of positron to electron inclusive rates ($c_s-1$) as a function of momentum for four bins in polar scattering angle $\theta$. The green points are for both particles out-bending in the torus and the red points are for both particles in-bending. The curves are from a simulation (see text for details).

Figure 8

Correction factor $C_{g_2}$ as a function of $Q^2$. The curves are, from top to bottom, $x=0.225$ (black), $x=0.325$ (blue), $x=0.425$ (green), and $x=0.525$ (red). Lower panel is for the proton target, upper panel for the deuteron. Dashed curves use the lowest-twist Wandzura and Wilczeck formula, while the solid curves use a fit to world data.

Figure 9

Results for $g_1/F_1$ as a function of $W$ for the proton in nine bins of $Q^2$. The present results are shown as solid circles, and the published Eg1b results are shown as open circles.

Figure 10

Results for $x{g}_1$ as a function of $W$ for the proton in four bins of $Q^2$. The dashed lines simply connect the results at a particular value of $Q^2$.

Figure 11

Same as Fig. 9 except for the deuteron. For clarity, data from Eg1b are not shown.

Figure 12

Results for $g_1/F_1$ as a function of $Q^2$ for the proton in nine bins of $x$. A bin centering correction was applied to the data points in this plot, of the form $\frac{g_1}{F_1}(x_c,Q^2)/\frac{g_1}{F_1}(x,Q^2)$, where $x_c$ is the value of $x$ at the center of the bin, and $x$ and $Q^2$ are the experimental averages over the size of the bin. The present results are shown as the large black solid points, the JLab Eg1b results [6] are shown as the small blue points, and the results from SLAC [2, 3] are shown as the small green points. The arrows correspond to $W=2$ GeV.

Figure 13

Same as Fig. 12 except for the deuteron. The small green points include results from COMPASS [4], HERMES [5], and SLAC [2, 3]. A bin centering correction was applied to the data points in this plot, of the form $\frac{g_1}{F_1}(x_c,Q^2)/\frac{g_1}{F_1}(x,Q^2)$, where $x_c$ is the value of $x$ at the center of the bin, and $x$ and $Q^2$ are the experimental averages over the size of the bin.