Measurement of the Neutron $F_2$ Structure Function via Spectator Tagging with CLAS

We report on the first measurement of the $F_2$ structure function of the neutron from the semi-inclusive scattering of electrons from deuterium, with low-momentum protons detected in the backward hemisphere. Restricting the momentum of the spectator protons to $\lesssim 100\mathrm{MeV}/c$ and their angles to $\gtrsim 100°$ relative to the momentum transfer allows an interpretation of the process in terms of scattering from nearly on-shell neutrons. The $F_2^n$ data collected cover the nucleon-resonance and deep-inelastic regions over a wide range of Bjorken $x$ for $0.65<Q^2<4.52{\mathrm{GeV}}^2$, with uncertainties from nuclear corrections estimated to be less than a few percent. These measurements provide the first determination of the neutron to proton structure function ratio $F_2^n/F_2^p$ at $0.2\lesssim x\lesssim 0.8$ with little uncertainty due to nuclear effects.

Figure 1

Yield for the semi-inclusive $d(e,e^{\prime }{p}_s)X$ reaction with a backward-moving spectator proton as a function of the invariant mass $W^{*}$ of the neutron debris, compared with the yield for the inclusive $d(e,e^{\prime })X$ reaction as a function of the customary kinematic variable $W$. Yields integrated over $W$ and $W^{*}$ are normalized to be the same. The data are for the 4.223 GeV beam energy and are averaged over the acceptance of CLAS. For backward-moving spectators $W^{*}<W$, which explains the leftward shift of the high $W^{*}$ cutoff in the semi-inclusive spectrum with respect to the inclusive case.

Figure 2

Typical $F_2^n$ spectra from the BoNuS experiment (filled circles) as a function of $W^{*}$ for the various $Q^2$ ranges indicated. The beam energy was 5.262 GeV except for the upper left plot at 4.223 GeV. For comparison the model-dependent extraction from inclusive $F_2^d$ data (open circles) [10] and the phenomenological model from Ref. [23] (solid curve) are also shown. The error bars on the data points are statistical, and the band along the abscissa represents the systematic error without the overall 3% normalization uncertainty or the 3% spectator approximation uncertainty.

Figure 3

Ratio $F_2^n/F_2^p$ versus $x^{*}$ for various lower limits on $W^{*}$. All data are from the 5.262 GeV beam energy. The error bars are statistical, with the total (correlated and uncorrelated) systematic uncertainties indicated by the band along the abscissa. This band does not include the overall 3% normalization uncertainty or the 3% spectator approximation uncertainty. The data are compared with the recent parametrization from the CJ global analysis [5], with the upper and lower uncertainty limits indicated by the solid lines. The inset shows the average $Q^2$ as a function of $x^{*}$ for each $W^{*}$ cut. For these data ${\alpha }_s$ is in the range 1.0–1.2. The arrow indicates the point at which the data are normalized to the CJ value. A single normalization constant $I_{\mathrm{VIP}}$ was used for all data. The resonance region ($W^{*}<2\mathrm{GeV}$) corresponds to $x^{*}\gtrsim 0.4$, 0.5, and 0.6 for square, diamond, and circle points, respectively.