How Well Do We Know the Neutron Structure Function?

We present a detailed analysis of the uncertainty in the neutron $F_{2n}$ structure function extracted from inclusive deuteron and proton deep-inelastic scattering data. The analysis includes experimental uncertainties as well as uncertainties associated with the deuteron wave function, nuclear smearing, and nucleon off-shell corrections. Correctly accounting for the $Q^2$ dependence of the data and calculations and restricting the nuclear corrections to microscopic models of the deuteron, we find a significantly smaller uncertainty in the extracted $F_{2n}/F_{2p}$ ratio than in previous analyses. In addition to yielding an improved extraction of the neutron structure function, this analysis also provides an important baseline that can be compared to future, model-independent extractions of neutron structure to examine nuclear medium effects in the deuteron.

Figure 1

Previous extractions of $F_{2n}/F_{2p}$, using microscopic deuteron calculations (filled symbols) or extrapolations of nuclear effects in heavier nuclei (open symbols): (black) triangles from Ref. 1, (blue) squares from Ref. 2, and (red) circles from Ref. 3. The arrows indicate theoretical predictions for the $x\to 1$ limit (see text).

Figure 2

Neutron to proton structure function ratio $F_{2n}/F_{2p}$ calculated using various deuteron wave functions (see text), within the WBA smearing model [16, 18].

Figure 3

The ratio $F_{2n}/F_{2p}$ calculated using different smearing models, taking the average of the $NN$ potentials from Fig. 2. The solid curves are on-shell calculations: [16, 18] (WBA), relativistic [3, 15] (MST), light-front [4] (ACHL), and a generalized convolution [19] (RT). The dashed curves show the WBA result with off-shell prescriptions from Ref. 15 (MST), and from Ref. 16 (KP) with two different nucleon swelling parameters, 1.5% and 1.8% (see Ref. 32). The ordering of the curves in the legend is based on the value of the extraction at $x=0.9$.

Figure 4

$F_{2n}/F_{2p}$ ratio together with the individual contributions to the systematic uncertainty and the quadrature sum [36]. The red hatched region corresponds to the uncertainty range in Fig. 1.

Figure 5

$F_{2n}/F_{2p}$ ranges for on-shell (solid) and off-shell (dashed) extractions [36].

Figure 6

Ratio $d/u$ extracted from $F_{2n}/F_{2p}$ at $Q^2=16{\mathrm{GeV}}^2$ using Eq. (2), with the gray band indicating the total uncertainties as shown in Fig. 4, with the dashed (solid) curves representing the on-shell (off-shell) nuclear model results. The inset shows the growing fractional uncertainty on $d/u$ as the ratio becomes smaller for $x\to 1$.