Precision measurement of the neutron spin asymmetries and spin-dependent structure functions in the valence quark region

We report on measurements of the neutron spin asymmetries $A_{1,2}^n$ and polarized structure functions $g_{1,2}^n$ at three kinematics in the deep inelastic region, with $x=0.33$, 0.47, and 0.60 and $Q^2=2.7$, 3.5, and $4.8{(\mathrm{GeV}∕c)}^2$, respectively. These measurements were performed using a $5.7\mathrm{GeV}$ longitudinally polarized electron beam and a polarized ${}^3\mathrm{He}$ target. The results for $A_1^n$ and $g_1^n$ at $x=0.33$ are consistent with previous world data and, at the two higher-$x$ points, have improved the precision of the world data by about an order of magnitude. The new $A_1^n$ data show a zero crossing around $x=0.47$ and the value at $x=0.60$ is significantly positive. These results agree with a next-to-leading-order QCD analysis of previous world data. The trend of data at high $x$ agrees with constituent quark model predictions but disagrees with that from leading-order perturbative QCD (PQCD) assuming hadron helicity conservation. Results for $A_2^n$ and $g_2^n$ have a precision comparable to the best world data in this kinematic region. Combined with previous world data, the moment $d_2^n$ was evaluated and the new result has improved the precision of this quantity by about a factor of 2. When combined with the world proton data, polarized quark distribution functions were extracted from the new $g_1^n∕F_1^n$ values based on the quark-parton model. While results for $\Delta u∕u$ agree well with predictions from various models, results for $\Delta d∕d$ disagree with the leading-order PQCD prediction when hadron helicity conservation is imposed.

Figure 1

Previous data on $A_1^n$ [25, 49, 50, 51, 52, 53] and various theoretical predictions: $A_1^n$ from SU(6) symmetry (solid line at zero) [17], hyperfine-perturbed RCQM (shaded band) [28], BBS parametrization at $Q^2=4{(\mathrm{GeV}∕c)}^2$ (higher solid) [30], LSS(BBS) parametrization at $Q^2=4{(\mathrm{GeV}∕c)}^2$ (dashed) [31], statistical model at $Q^2=4{(\mathrm{GeV}∕c)}^2$ (long-dashed) [42], quark-hadron duality using two different SU(6)-breaking mechanisms (dash-dot-dotted and dash-dot-dot-dotted) [47], and nonmeson cloudy bag model (dash-dotted) [48]; $g_1^n∕F_1^n$ from LSS2001 parametrization at $Q^2=5{(\mathrm{GeV}∕c)}^2$ (lower solid) [41] and from chiral soliton models [43] at $Q^2=3{(\mathrm{GeV}∕c)}^2$ (long-dash–dotted) and [44] at $Q^2=4.8{(\mathrm{GeV}∕c)}^2$ (dotted).

Figure 2

World data on $A_1^p$ [23, 24, 25, 53, 54] and predictions for $g_1^p∕F_1^p$ at $Q^2=5{(\mathrm{GeV}∕c)}^2$ from the E155 experimental fit (long-dash–dot–dotted) [53] and a new fit as described in Sec. 6B (long-dash–dot–dot–dotted). The solid curve corresponds to the prediction for $g_1^n∕F_1^n$ from LSS(2001) parametrization at $Q^2=5{(\mathrm{GeV}∕c)}^2$. Other curves are the same as in Fig. 1 except that there is no prediction for the proton from BBS and LSS(BBS) parametrizations.

Figure 3

An illustration of the ${}^3\mathrm{He}$ wave function. The $S$, $S^{\prime }$, and $D$ state contributions are from calculations using the AV18 two-nucleon interaction and the Tucson-Melbourne three-nucleon force, as given in Ref. [56].

Figure 4

(Color online) Top view of the experimental Hall A (not to scale).

Figure 5

Helicity signal and the helicity status of DAQ in toggle (top) and pseudorandom (bottom) modes.

Figure 6

(Color online) Schematic layout of the left HRS and detector package (not to scale).

Figure 7

(Color online) Summed ADC signal of the left HRS gas Čerenkov detector without cuts, after lead glass counters electron cut, and after pion cut. The vertical line shows a cut of ADC sum higher than 400 channels applied to select electrons.

Figure 8

(Color online) Energy deposited in the first layer (preshower) vs that in the second layer (shower) of lead glass counters in the right HRS. The two blobs correspond to the spectrum with a tight gas Čerenkov ADC electron cut and with a pion cut applied. The lines show the boundary of the two-dimensional cut used to select electrons in the data analysis.

Figure 9

(Color online) JLab target cell; geometries are given in millimeters for cell 2 used in this experiment.

Figure 10

(Color online) Target setup overview (schematic).

Figure 11

(Color online) Laser polarizing optics setup (schematic) for the Hall A polarized ${}^3\mathrm{He}$ target.

Figure 12

Target polarization, starting June 1 of 2001, as measured by EPR and NMR polarimetries.

Figure 13

Procedure for asymmetry analysis.

Figure 14

Procedure for cross section analysis.

Figure 15

(Color online) Elastic parallel asymmetry results for the two HRS’s. The kinematics are $E=1.2\mathrm{GeV}$ and $\theta =20°$. A cut in the invariant mass $\mid W-M_{{}^3\mathrm{He}}\mid <6\mathrm{MeV}$ was used to select elastic events. Data from runs with beam half-wave plate inserted are shown as triangles. The error bars shown are total errors including a 4.5% systematic uncertainty, which is dominated by the error of the beam and target polarizations. The combined asymmetry and its total error from $\approx 20$ runs are shown by the horizontal solid and dashed lines, respectively, as well as the solid circle as labeled [58].

Figure 16

(Color online) Elastic cross section results for the two HRS’s. The kinematics were $E=1.2\mathrm{GeV}$ and $\theta =20°$. A systematic error of 67% was assigned to each data point, which was dominated by the uncertainty in the target density and the HRS transport functions [58].

Figure 17

(Color online) Measured raw $\Delta \left(1232\right)$ transverse asymmetry, with beam half-wave plate inserted and target spin pointing to the left side of the beamline. The kinematics are $E=1.2\mathrm{MeV}$, $\theta =20°$, and $E^{\prime }=0.8\mathrm{GeV}∕c$. The dashed lines show the expected value obtained from previous ${}^3\mathrm{He}$ data extrapolated in $Q^2$.

Figure 18

Results for the ${}^3\mathrm{He}$ asymmetry $A_1^{{}^3\mathrm{He}}$ and the structure functions $g_1^{{}^3\mathrm{He}}$ as a function of $x$, along with previous data from SLAC [51, 100] and HERMES [101]. Error bars of the results from this work include both statistical and systematic uncertainties.

Figure 19

Our $A_1^n$ results along with theoretical predictions and previous world data obtained from polarized ${}^3\mathrm{He}$ targets [50, 51, 52]. Curves: predictions of $A_1^n$ from SU(6) symmetry ($x$ axis at zero) [17], constituent quark model (shaded band) [28], statistical model at $Q^2=4{(\mathrm{GeV}∕c)}^2$ (long-dashed) [42], quark-hadron duality using two different SU(6)-breaking mechanisms (dash-dot-dotted and dash-dot-dot-dotted), and nonmeson cloudy bag model (dash-dotted) [48]; predictions of $g_1^n∕F_1^n$ from PQCD HHC-based BBS parametrization at $Q^2=4{(\mathrm{GeV}∕c)}^2$ (higher solid) [30] andLSS(BBS) parametrization at $Q^2=4{(\mathrm{GeV}∕c)}^2$ (dashed) [31], LSS 2001 NLO polarized parton densities at $Q^2=5{(\mathrm{GeV}∕c)}^2$ (lower solid) [41], and chiral soliton models [43] at $Q^2=3{(\mathrm{GeV}∕c)}^2$ (long-dash–dotted) and [44] at $Q^2=4.8{(\mathrm{GeV}∕c)}^2$ (dotted).

Figure 20

Results for $g_1^n∕F_1^n$ along with previous world data from SLAC [25, 53]. The curves are the prediction for $g_1^n∕F_1^n$ from the LSS 2001 NLO polarized parton densities at $Q^2=5{(\mathrm{GeV}∕c)}^2$ [41], the E155 experimental fit at $Q^2=5{(\mathrm{GeV}∕c)}^2$ (long-dash–dot–dotted) [53], and the new fit as described in the text (long-dash–dot–dot–dotted).

Figure 21

Results for $g_1^n$ along with previous world data from SLAC [51, 52, 53] and HERMES [50].

Figure 22

Results for $A_2^n$ along with the best previous world data [102]. The curve gives the twist-2 contribution at $Q^2=4{(\mathrm{GeV}∕c)}^2$ calculated using the E155 experimental fit [53] and $g_2^{\mathrm{WW}}$ of Eq. (5).

Figure 23

Results for $x{g}_2^n$ along with the best previous world data [102]. The curve gives the twist-2 contribution at $Q^2=4{(\mathrm{GeV}∕c)}^2$ calculated using the E155 experimental fit [53] and $g_2^{\mathrm{WW}}$ of Eq. (5).

Figure 24

Results for $(\Delta u+\Delta \overline{u})∕(u+\overline{u})$ and $(\Delta d+\Delta \overline{d})∕(d+\overline{d})$ in the quark-parton model, compared with semi-inclusive data from HERMES [106] and CTEQ unpolarized PDF [107] as described in the text, the RCQM predictions (dash-dotted) [28], predictions from LSS 2001 NLO polarized parton densities at $Q^2=5{(\mathrm{GeV}∕c)}^2$ (solid) [41], the statistical model at $Q^2=4{(\mathrm{GeV}∕c)}^2$ (long-dashed) [42], the PQCD-based predictions with the HHC constraint (dashed) [31], the duality model using two different SU(6)-breaking mechanisms (dash-dot-dotted and dash-dot-dot-dotted) [47], and predictions from chiral soliton model at $Q^2=4.8{(\mathrm{GeV}∕c)}^2$ (dotted) [44]. The error bars of our data include the uncertainties given in Table 13. The shaded band near the horizontal axis shows the difference between $\Delta q_V∕q_V$ and $(\Delta q+\Delta \overline{q})∕(q+\overline{q})$ that needs to be added to the data when comparing with the RCQM calculation.

Figure 25

(Color online) Electron scattering in the one-photon exchange approximation.

Figure 26

(Color online) Polar and azimuthal angles of the target spin.