Measurement of the structure function of the nearly free neutron using spectator tagging in inelastic ${}^2\mathrm{H}$($e$,$e^{\prime }{p}_s$)$X$ scattering with CLAS

Background: Much less is known about neutron structure than that of the proton due to the absence of free neutron targets. Neutron information is usually extracted from data on nuclear targets such as deuterium, requiring corrections for nuclear binding and nucleon off-shell effects. These corrections are model dependent and have significant uncertainties, especially for large values of the Bjorken scaling variable $x$. As a consequence, the same data can lead to different conclusions, for example, about the behavior of the $d$ quark distribution in the proton at large $x$.

Purpose: The Barely Off-shell Nucleon Structure experiment at Jefferson Lab measured the inelastic electron-deuteron scattering cross section, tagging spectator protons in coincidence with the scattered electrons. This method reduces nuclear binding uncertainties significantly and has allowed for the first time a (nearly) model-independent extraction of the neutron structure function $F_2(x,Q^2)$ in the resonance and deep-inelastic regions.

Method: A novel compact radial time projection chamber was built to detect protons with momentum between 70 and 150 MeV$/c$ and over a nearly $4\pi$ angular range. For the extraction of the free-neutron structure function $F_2^n$, spectator protons at backward angles ($>{100}^{\circ }$ relative to the momentum transfer) and with momenta below 100 MeV$/c$ were selected, ensuring that the scattering took place on a nearly free neutron. The scattered electrons were detected with Jefferson Lab's CLAS spectrometer, with data taken at beam energies near 2, 4, and 5 GeV.

Results: The extracted neutron structure function $F_2^n$ and its ratio to the inclusive deuteron structure function $F_2^d$ are presented in both the resonance and the deep-inelastic regions for momentum transfer squared $Q^2$ between 0.7 and 5 GeV${}^2/c^2$, invariant mass $W$ between 1 and 2.7 GeV$/c^2$, and Bjorken $x$ between 0.25 and 0.6 (in the deep-inelastic scattering region). The dependence of the semi-inclusive cross section on the spectator proton momentum and angle is investigated, and tests of the spectator mechanism for different kinematics are performed.

Conclusions: Our data set on the structure function ratio $F_2^n/F_2^d$ can be used to study neutron resonance excitations, test quark-hadron duality in the neutron, develop more precise parametrizations of structure functions, and investigate binding effects (including possible mechanisms for the nuclear EMC effect) and provide a first glimpse of the asymptotic behavior of $d/u$ at $x\to 1$.

Figure 1

Ratio of inclusive neutron-to-proton structure functions $F_2^n/F_2^p$ from the CJ global PDF analysis [13]. The shaded bands illustrate the range of possible values for the ratio from nuclear corrections and experimental uncertainties. The vertical arrow indicates the edge of the region in $x$ where the ratio is constrained by data ($x\lesssim 0.8$).

Figure 2

Semi-inclusive scattering from a deuteron with detection of a spectator proton, $p_s$, within the framework of (a) the nuclear IA and (b) including the effects of final-state interactions.

Figure 3

Schematics of the BONuS RTPC. See text for details.

Figure 4

BONuS data readout scheme.

Figure 5

An RTPC event in several views (top row, two-dimensional projections on end cap and center plane; bottom row, two different three-dimensional views, the second rotated by ${90}^{\circ }$). Black blobs indicate ionized charge traced back to the spot of the ionization; solid lines going through them indicate fitted tracks. An outline of the RTPC is overlaid.

Figure 6

Comparison of electron-scattering angles, as reported by the RTPC and CLAS, before (a) and after (b) calibration. The comparison is shown for the left half of the RTPC; the right half results are similar. Both experimental distributions (thin colored lines) and Gaussian fits to them (thick lines) are shown.

Figure 7

The ionization density distribution of particles registered by the RTPC after the RTPC gain calibration. The solid curves are calculated based on the Bethe-Bloch formula for $dE/dx$ for various particles, in order from bottom to top: proton, deuteron, triton, helion (${}^3\mathrm{He}$), $\alpha$ (${}^4\mathrm{He}$). The target was filled with ${}^4\mathrm{He}$ gas and the electron energy was 2 GeV for this measurement.

Figure 8

Representative plot of the $\Delta z$ distribution for coincidences (solid histogram) between electrons (in CLAS) and spectator protons (in the RTPC) from the 5-GeV data set. Inner vertical lines indicate the region selected for data analysis ($-1.5,...,+1.5$ cm). The dashed line indicates the corresponding distribution for accidental coincidences obtained by matching tracks from different events (see text), cross-normalized to the data outside the outer vertical lines ($-2.0,...,+2.0$ cm). The good agreement in the “wings” outside those lines indicates that the shape of the background is well represented by this method. See text for more details.

Figure 9

$W^{*}$ distributions (for 1.10 GeV${}^2/c^2<Q^2<2.23$ GeV${}^2/c^2$) of measured counts for the 5.3-GeV beam energy with spectator protons detected at angles greater than about 100${}^{\circ }$ and momenta between 70 and 85 MeV$/c$. The data are shown before (upper black squares) and after subtraction of accidental coincidences and other backgrounds (lower blue triangles). Also shown are the normalized simulated counts for elastic scattering off a neutron inside the deuteron, including the radiative tail (open red circles, bottom). Note the good agreement between this simulation and the data in the quasielastic region, $W^{*}<1$ GeV.

Figure 10

Ratio $R_{D/S}$ of experimental data (with subtracted background and elastic tail) to the simulation as a function of $cos{\theta }_{pq}$ for a selected bin in $Q^2$ (from 1.10 to 2.23 GeV${}^2/c^2$) and $W^{*}$ (from 1.35 to 1.6 GeV$/c^2$), for a beam energy of 5.25 GeV. Each panel corresponds to one of our four bins in the spectator momentum $p_s$: (a) 70–85 MeV$/c$, (b) 85–100 MeV$/c$, (c) 100–120 MeV$/c$, (d) 120–150 MeV$/c$. The error bars are statistical only, with systematic uncertainties shown as a band at the bottom.

Figure 11

The same ratio as in Fig. 10, but for a higher bin in $W^{*}$ (from 1.85 to 2.20 GeV$/c^2$).

Figure 12

The same ratio as in Fig. 11 for a beam energy of 4.23 GeV.

Figure 13

Ratio of experimental data (after subtraction of accidental background and elastic tail) to the full simulation with the spectator model as a function of $W^{*}$. The data are for $Q^2$ from 1.10 to 2.23 GeV${}^2/c^2$ and $cos{\theta }_{pq}$ from $-1.0$ to $-0.2$. Again, they are shown in four bins in the spectator momentum $p_s$: (a) 70–85 MeV$/c$, (b) 85–100 MeV$/c$, (c) 100–120 MeV$/c$, (d) 120–150 MeV$/c$. The beam energy is 5.3 GeV. Error bars are statistical only, with systematic uncertainties shown as bands.

Figure 14

Same ratio as in Fig. 13 except for sideways spectator angles, $-0.2\le cos{\theta }_{pq}\le 0.2$.

Figure 15

Ratios of $F_2^{n,\mathrm{eff}}(x^{*},Q^2,p_s)$ for backward spectator momenta in each of the three higher $p_s$ bins [(a) = 85–100 MeV$/c$, (b) =100–120 MeV$/c$, (c) =120–150 MeV$/c$] to $F_2^{n,\mathrm{eff}}(x^{*},Q^2,p_s)$ for the lowest $p_s$ bin. Data are for $Q^2=1.1$–2.2 GeV${}^2/c^2$, $cos{\theta }_{pq}$ from $-$1.0 to $-$0.2, and 5.3-GeV beam energy. Error bars are statistical only. The arrows indicate the approximate location of the edge of the DIS region, $W^{*}=2$ GeV.

Figure 16

Same as Fig. 15, but for a higher $Q^2$ bin, $2.2–4.5$ GeV${}^2/c^2$.

Figure 17

$F_2^n/F_2^d$ vs $W^{*2}$ for 4.2-GeV beam energy. The data are from the VIP region $p_s\le 100$ MeV$/c$ and ${\theta }_{pq}\ge {100}^{\circ }$. Error bars indicate statistical uncertainties, while the bands show the point-to-point systematic uncertainties. The data have been normalized to the preliminary new fit of the world data by Christy et al. [69] (see text), which is shown as a solid line. We estimate that there is an overall normalization uncertainty of up to 10%.

Figure 18

Same as Fig. 17, for 5-GeV beam energy.

Figure 19

Extracted structure function $F_2^n$ as a function of squared final-state invariant mass $W^{*2}$ for six bins in $Q^2$. Results are shown for two beam energies, 4.2 GeV (green circles) and 5.3 GeV (red squares). Error bars are statistical only, with systematic uncertainties for the 5.3-GeV data shown as a band. (Systematic uncertainties of 4.2-GeV are very similar in magnitude to the shown ones). The solid line indicates a new fit to the world data on deuteron and proton targets that does not include BONuS data (see text).

Figure 20

Results for the neutron structure function $F_2^n\left(x\right)$ (integrated over $Q^2>1$ GeV${}^2/c^2$ while requiring $W^{*}>1.8$ GeV$/c^2$) from the Monte Carlo method (labeled “Analysis 1”) and ratio method (labeled “Analysis 2”). The range of $F_2^n$ from the CJ fit [13] is shown by the two solid lines. Systematic uncertainties for the Monte Carlo method are shown as the shaded band. The two analysis results are cross normalized to the average of the CJ fit at $x=0.32$.

Figure 21

Results for the ratio of the neutron to proton structure functions $F_2^n/F_2^p\left(x\right)$ (integrated over $Q^2>1$ GeV${}^2/c^2$ and three different minimum values for $W^{*}$) from the ratio method. The uncertainty range from the CJ fit [13] is shown by the (yellow) shaded band. Systematic uncertainties are shown as the (red) shaded band at the bottom. Our data are cross normalized to the average of the CJ fit at $x=0.32$. The inset shows the average $Q^2$ for each data point, separately for the three lower $W^{*}$ limits.