Neutron Valence Structure from Nuclear Deep Inelastic Scattering

Mechanisms of spin-flavor SU(6) symmetry breaking in quantum chromodynamics (QCD) are studied via an extraction of the free neutron structure function from a global analysis of deep inelastic scattering (DIS) data on the proton and on nuclei from $A=2$ (deuterium) to 208 (lead). Modification of the structure function of nucleons bound in atomic nuclei (known as the EMC effect) are consistently accounted for within the framework of a universal modification of nucleons in short-range correlated (SRC) pairs. Our extracted neutron-to-proton structure function ratio $F_2^n/F_2^p$ becomes constant for $x_B\ge 0.6$, equaling $0.47\pm 0.04$ as $x_B\to 1$, in agreement with theoretical predictions of perturbative QCD and the Dyson-Schwinger equation, and in disagreement with predictions of the scalar diquark dominance model. We also predict $F_2^{{}^3\mathrm{He}}/F_2^{{}^3\mathrm{H}}$, recently measured, as yet unpublished, by the MARATHON Collaboration, the nuclear correction function that is needed to extract $F_2^n/F_2^p$ from $F_2^{{}^3\mathrm{He}}/F_2^{{}^3\mathrm{H}}$, and the theoretical uncertainty associated with this extraction.

Figure 1

The extracted global universal modification function (UMF) from the nuclear-EMC effect analysis performed here (red band). The narrow width of the band shows the 68% confidence interval. Data points show the data-driven extractions of Ref. [14], based on individual measurements of $F_2^A/F_2^d$ in a variety of nuclei. Open and closed data points show measurements at $W<\sqrt{2}\mathrm{GeV}$ and $W\ge \sqrt{2}\mathrm{GeV}$, respectively.

Figure 2

Neutron-to-proton structure function ratio $F_2^n/F_2^p$. Data points show the $d(e,e^{\prime }{p}_S)$ tagged-DIS measurement [39]. Our predictions (blue band labeled “nuclear-DIS,” including a 68% confidence interval) are compared with those of CT14 [4] (red band), CJ15 [5] (green band), and Arrington et al. [6] (yellow band), which treat nuclear effects in deuterium DIS data differently (see text for details). The labels show $F_2^n/F_2^p$ predictions at $x_B=1$, such as SU(6) symmetry [40], perturbative QCD (PQCD) [3], Dyson-Schwinger equation (DSE) [2], and scalar diquark models [7, 8]. All predictions are obtained within the parton model framework [28] and all extractions were consistently evolved to the same value of $Q^2$ based on the kinematics of the MARATHON experiment [9], i.e., $Q^2=(14{\mathrm{GeV}}^2)\times x_B$.

Figure 3

Top: Nuclear-DIS analysis result for $F_2^{{}^3\mathrm{He}}/F_2^{{}^3\mathrm{H}}$ (blue band) compared to previous extractions by Tropiano et al. [48] (TEMS [green, purple, orange, assuming different off-shell corrections]) and Kulagin and Petti [49, 50] (KP [red]). Bottom: Nuclear-DIS analysis results for $2F_2^{{}^3\mathrm{He}}/3F_2^d$, $2F_2^{{}^3\mathrm{H}}/3F_2^d$ shown in blue. The width of the bands show the 68% confidence intervals of our analysis. Predictions for $2F_2^{{}^3\mathrm{H}}/3F_2^d$ are based on the assumption $n_{\mathrm{SRC}}^{{}^3\mathrm{H}}=n_{\mathrm{SRC}}^{{}^3\mathrm{He}}$. Symbols show the $2F_2^{{}^3\mathrm{He}}/3F_2^d$ measurement of Ref. [33] rescaled by $\sim 2\%$. TEMS and KP lines do not include uncertainties. See text for details.

Figure 4

Left: Different model predictions for $\mathcal{R}$ as defined in Eq. (7). The present work (blue band, labeled “nuclear-DIS”) includes a 68% confidence interval. The other labeled lines show calculations (not including uncertainties) by Tropiano et al. [48] (TEMS, for different off-shell corrections), Kulagin and Petti [49, 50] (KP), and Afnan et al. [52] (Faddeev PEST). Right: $F_2^n/F_2^p$ extracted from predicted values of $F_2^{{}^3\mathrm{He}}/F_2^{{}^3\mathrm{H}}$ using this work (see blue bands in Fig. 3) in combination with different theoretical predictions for $\mathcal{R}$ [see Eq. (6)]. The blue line here is the central value of the blue band in Fig. 2. See text for details.