Neutron Structure Function

Measurements of nuclear structure functions are also important for the understanding of the structure of the neutron. As free neutron targets are not available and neutron beams are too low in energy or intensity, information on the neutron structure is generally taken from measurements on nuclear targets. Current data for the neutron structure function come from measurements on deuterium and hydrogen, using models of the nuclear effects to remove the proton contribution to the deuterium measurements [15,16]. The ability to extract the neutron structure from measurements on deuterium depends on our knowledge of the proton structure function, the deuteron momentum distribution, and the procedure used to extract the neutron component. The extraction must include a model of nuclear effects beyond the nucleon momentum distribution, and this model must be tested in order to be confident that it adequately describes all of the necessary nuclear effects.

Measurements of the neutron structure function are important for understanding the quark structure of nucleons. The difference between the structure of the neutron and the proton is sensitive to the u-quark and d-quark distributions in the proton. In particular, the ratio of the neutron to proton structure function as x approaches unity is sensitive to the high-x u-quark and d-quark valence distributions. Several predictions exist for this ratio at x=1. SU(6) spin-flavor symmetry predicts u^p_v(x) = 2 d^p_v(x), and dⁿ_v(x) = 2 uⁿ_v(x), where u_v(d_v) is the up(down) valence distribution in the proton or neutron. This leads to a value of F₂ⁿ(x)/F₂^p(x) = 2/3 for large values of x (where the valence quarks dominate). DIS measurements indicate that SU(6) symmetry is broken, and that the proton d-quark distribution is softer than the u-quark distribution. If u-quark dominance is assumed (i.e. only u-quarks contribute in the limit $x \approx 1$), the prediction is $F_2^n(x)/F_2^p(x) \rightarrow 1/4$ as $x \rightarrow 1$. Other assumptions lead to a prediction that the ratio of d/u at large x is non-zero. Models by Farrar and Jackson [17], and Brodsky et al. [18] predict that $u/d \rightarrow 5$ as $x \rightarrow 1$,and thus $F_2^n/F_2^p \rightarrow 3/7$. The initial analysis of SLAC and EMC experiments [15,19] indicated a value close to 1/4, but the extraction of the neutron structure function only included corrections for the momentum distribution in the deuteron and did not include binding effects. A later reanalysis [20], including binding effects, found a value closer to the 3/7 prediction. Figure 3 shows the extracted F₂ⁿ/F₂^p ratio using both an on-shell prescription that only includes the momentum distribution and an off-shell prescription that includes binding. Clearly the off-shell effects are very important, and additional data that can be used to check these models is needed to determine how accurately we can extract the neutron structure from measurements on the deuteron.

  

Figure: Ratio of F₂ⁿ/F₂^p extracted from the SLAC measurements [3,21] using an on-shell prescription (hollow circles) and an off-shell prescription (filled circles) to extract the neutron structure function [20].

We propose to measure structure functions for hydrogen, deuterium, ³He, and ⁴He for x > 0.3 and $Q^2 \geq 1.0$ (GeV/c)². The maximum Q² value measured will vary between $Q^2 \approx 3$ (GeV/c)² for the lowest value of x, to $Q^2 \approx 8$ (GeV/c)² for $x \sim 1$.The proposed measurement will extend the kinematic coverage to larger values of x then previous measurements. While the extraction of the neutron structure function at large values of x will still be limited by the uncertainties in modeling the nuclear effects, this data will allow us to refine these models. The EMC ratios for ³He and ⁴He will improve our ability to determine the nuclear effects in deuterium. These measurements of the EMC effect in light nuclei will help determine the appropriate way to model nuclear effects for deuterium.

In addition to looking at the nuclear dependence of the EMC effect for light nuclei, we can also use these data to directly test the extraction of nucleon structure from measurements on nuclei. We can use the ³He and ²H measurements to extract the proton structure function to test the model of the nuclear effects used in the extraction of the nucleon structure. This procedure depends on modeling the nuclear effects in both deuterium and ³He. Similarly, one can compare the neutron structure extracted from ²H and ¹H to the structure function extracted by comparing ³He and ¹H, or ⁴He and ³He. The nuclear effects are larger in these cases, and comparisons of the extracted neutron structure function will provide a strong test of the extraction procedure, especially for larger values of x where the nuclear effects are largest and the model dependence of the extraction is difficult to determine.