Neutron valence structure from nuclear deep inelastic scattering

TL;DR

This paper extracts the neutron structure function from DIS data, accounting for nuclear effects, and finds the neutron-to-proton ratio approaches 0.47 at high x, aligning with QCD predictions.

Contribution

It provides a novel extraction of the neutron structure function from global DIS data, incorporating nuclear modifications within a universal SRC framework.

Findings

Neutron-to-proton structure function ratio approaches 0.47 at high x.

Results agree with perturbative QCD and Dyson-Schwinger predictions.

Provides predictions for $F_2^{^3He}/F_2^{^3H}$ and associated uncertainties.

Abstract

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 $x_B \ge 0.6$, equalling $0.47 \pm 0.04$ as $x_B \rightarrow 1$, 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 We also predict $F_2^{^3\mathrm{He}}/F_2^{^3\mathrm{H}}$, recently measured, yet unpublished, by the MARATHON collaboration, the nuclear correction function that is needed to extract $F_2^n/F_2^p$ from $F_2^{^3\mathrm{He}}/F_2^{^3\mathrm{H}}$, and the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.

Equations

$$\begin{array}{r}{F}_2^A=Z{F}_2^p+N{F}_2^n+n_{SRC}^A(\Delta F_2^p+\Delta F_2^n),\end{array}$$

$$\displaystyle\begin{split}\frac{F_{2}^{A}}{F_{2}^{d}}=&&\frac{\Delta F_{2}^{p}+\Delta F_{2}^{n}}{F_{2}^{d}/n_{SRC}^{d}}&\times(\frac{n_{SRC}^{A}}{n_{SRC}^{d}}-N)+(Z-N)\frac{F_{2}^{p}}{F_{2}^{d}}+N\\ =&&f_{\text{univ}}(x_{B})&\times(\frac{n_{SRC}^{A}}{n_{SRC}^{d}}-N)+(Z-N)\frac{F_{2}^{p}}{F_{2}^{d}}+N,\end{split}$$

$$\begin{array}{r}{f}_{\text{univ}}=n_{SRC}^d\frac{\Delta F_2^p+\Delta F_2^n}{F_2^d}.\end{array}$$

$$\begin{array}{r}{f}_{\text{univ}}=\alpha +\beta x_B+\gamma e^{\delta (1-x_B)}\end{array}$$

$$\begin{array}{r}\frac{F_2^n}{F_2^p}=\frac{1-f_{\text{univ}}}{F_2^p/F_2^d}-1.\end{array}$$

$$\begin{array}{r}\frac{F_2^n}{F_2^p}=\frac{2\mathcal{R}-F_2^{{}^3\mathrm{He}}/F_2^{{}^3\mathrm{H}}}{2F_2^{{}^3\mathrm{He}}/F_2^{{}^3\mathrm{H}}-\mathcal{R}},\end{array}$$

$$\begin{array}{r}\mathcal{R}\equiv \frac{F_2^{{}^3\mathrm{He}}}{2F_2^p+F_2^n}\times \frac{F_2^p+2F_2^n}{F_2^{{}^3\mathrm{H}}}.\end{array}$$

Full text

I Introduction

Almost all the visible mass in the universe comes from the mass of protons and neutrons, and is dynamically generated by the strong interactions of quarks and gluons Bashir et al. (2012). These interactions are described by the theory of strong interactions, Quantum Chromodynamics (QCD). While the structure of low-energy QCD largely follows spin-flavor SU(6) symmetry, this symmetry is broken, as evident by the mass difference between the proton and its first excited state, the Delta resonance. The exact symmetry-breaking mechanism is still an open question. This affects our understanding of emergent QCD phenomena such as baryon structure, masses, and magnetic moments Roberts et al. (2013). Answering this question is thus one of the main motivations for the ongoing international effort to measure the quark-gluon structure of hadrons.

Different symmetry-breaking mechanisms can be discriminated among experimentally by measuring nucleon structure functions, which are sensitive to the distributions of quarks inside nucleons. Specifically, realistic models of QCD make very different predictions for the relative probability for a single quark to carry all of the momentum of a neutron compared to that of a proton, i.e., the proton to neutron structure function ratio, $F_{2}^{n}(x_{B},Q^{2})/F_{2}^{p}(x_{B},Q^{2})$, as $x_{B}\rightarrow 1$ (where $x_{B}=Q^{2}/2m\nu$ is the fractional quark momenta in the collinear reference frame where the nucleon is fast, $Q^{2}$ is the four-momentum transfer squared, $m$ is the nucleon mass, and $\nu$ is the energy transfer).

While the proton structure function has been extensively measured, the lack of a free neutron target prevents equivalent measurements of the neutron structure function, thereby preventing a direct test of QCD symmetry breaking mechanisms.

Here we use measurements of all available structure functions of nuclei (ranging from deuterium to lead) to extract the free neutron structure function, while consistently accounting for the nuclear-medium induced modification of the quark distributions in atomic nuclei. Using data on such a wide span of nuclei provides a large lever arm that allows us to precisely constrain $F_{2}^{n}(x_{B},Q^{2})/F_{2}^{p}(x_{B},Q^{2})$, obtaining new insight into the fundamental structure of QCD.

We find that as $x_{B}$ approaches unity, $F_{2}^{n}(x_{B},Q^{2})/F_{2}^{p}(x_{B},Q^{2})$ saturates at a value of $0.47\pm 0.04$, giving credence to modern predictions of QCD such as those based on the Dyson Schwinger Equation ($0.41-0.49$) Roberts et al. (2013) and Perturbative QCD ($3/7$) Farrar and Jackson (1975). This contrasts with previous extractions that did not include DIS measurements of nuclei heavier than deuterium Dulat et al. (2016); Accardi et al. (2016); Arrington et al. (2012) and claimed to support the scalar di-quark ($1/4$) Close (1973); Carlitz (1975) view of the nucleon.

The large differences between previous extractions of $F_{2}^{n}(x_{B},Q^{2})/F_{2}^{p}(x_{B},Q^{2})$ and those of this work emphasize the need for direct experimental verification. The MARATHON Experiment Petratos et al. (2010) recently measured $F_{2}^{{}^{3}\mathrm{He}}(x_{B},Q^{2})/F_{2}^{{}^{3}\mathrm{H}}(x_{B},Q^{2})$ with the goal of providing an independent determination of $F_{2}^{n}(x_{B},Q^{2})/F_{2}^{p}(x_{B},Q^{2})$ with minimal sensitivity to nuclear medium effects. This extraction is based on the assumption that such effects should be very similar for ${{}^{3}\mathrm{He}}$ and ${{}^{3}\mathrm{H}}$, thereby cancelling in their ratio. Using the results of our global analysis, we present predictions for the $F_{2}^{{}^{3}\mathrm{He}}(x_{B},Q^{2})/F_{2}^{{}^{3}\mathrm{H}}(x_{B},Q^{2})$ ratio and the nuclear correction function required to extract $F_{2}^{n}(x_{B},Q^{2})/F_{2}^{p}(x_{B},Q^{2})$ from it. By comparing our correction function with those of earlier works we quantify the model uncertainty associated with this extraction, which can be as high as $\sim 25\%$ for current realistic models.

II Universal Nucleon Modification and the EMC Effect

Given the lack of a free neutron target, the modification of the quark-gluon structure of nucleons bound in atomic nuclei, known as the EMC effect, is the main issue preventing a direct extraction of the free neutron structure function from lepton Deep Inelastic Scattering (DIS) measurements of atomic nuclei, see Ref. Hen et al. (2017) for a recent review.

We account for the EMC effect in nuclear DIS data by exploiting recent insight to its origin, gained from observations of a correlation between the magnitude of the EMC effect in different nuclei and the relative amount of short-range correlated (SRC) nucleon pairs in those nuclei Weinstein et al. (2011); Hen et al. (2012, 2013, 2017); Schmookler et al. (2019); Frankfurt and Strikman (1988).

SRC pairs are predominantly proton-neutron ($pn$) pairs Piasetzky et al. (2006); Subedi et al. (2008); Korover et al. (2014); Hen et al. (2014); Duer et al. (2018, 2019). They have large relative and individual momenta, smaller center-of-mass momenta, and account for 60-70% of the kinetic energy carried by nucleons in the nucleus Tang et al. (2003); Shneor et al. (2007); Korover et al. (2014); Cohen et al. (2018). Therefore, nucleons in such pairs have significant spatial overlap and are far off their mass-shell ($E^{2}-p^{2}-m^{2}<0$).

These extreme conditions, and the observed correlation between SRC pair abundances and the magnitude of the EMC effect, imply that the EMC effect could be driven primarily by the modification of the structure functions of nucleons in SRC pairs Weinstein et al. (2011); Hen et al. (2012, 2017).

Utilizing scale separation between SRC and uncorrelated (mean-field) nucleons, Ref. Schmookler et al. (2019) modeled the nuclear structure function as having contributions from unmodified uncorrelated nucleons and from modified correlated nucleons in $np$-SRC pairs:

[TABLE]

where $N$ and $Z$ are the number of neutrons and protons in the nucleus ($N+Z=A$), $n_{SRC}^{A}$ is the average number of nucleons in $np$-SRC pairs, $\Delta F_{2}^{p}$ and $\Delta F_{2}^{n}$ are the average differences between the structure functions of free nucleons and nucleons in SRC pairs, and we omitted the explicit $x_{B}$ and $Q^{2}$ dependence of the $F_{2}$ structure functions for brevity. This model assumes that both the EMC effect at $0.3\leq x_{B}\leq 0.7$ and nucleon-motion effects (which are important at $x_{B}>0.7$) are dominated by short-range correlations Frankfurt and Strikman (1988); Sargsian et al. (2003); Melnitchouk et al. (1997). Therefore both are approximately proportional to SRC pair abundances and captured by Eq. 1. This model neglects the contribution of $pp$- and $nn$-SRC pairs that, due to the predominance of the Tensor interaction at short-distance, are only $\approx 10\%$ of all $NN$-SRC pairs in both light and heavy nuclei  Piasetzky et al. (2006); Subedi et al. (2008); Korover et al. (2014); Hen et al. (2014); Duer et al. (2018, 2019), and have little impact on our results. See supplementary materials for details.

To reduce sensitivity to isospin, target-mass, and higher twist effects Virchaux and Milsztajn (1992), DIS data are traditionally given in the form of $F_{2}^{A}/F_{2}^{d}$ ratios. We use Eq. 1 to express this ratio as:

[TABLE]

where we defined a nucleus independent universal modification function (UMF)

[TABLE]

Consistent UMFs were previously extracted for nuclei from 3He to 208Pb, pointing to the existence of a global UMF for SRC pairs in any nucleus (see Fig. 1) Schmookler et al. (2019). Here we extract the global UMF using Bayesian inference by means of a Hamiltonian Markov Chain Monte Carlo (HMCMC) Carpenter et al. (2017); Team (2018), referred to herein as Nuclear-DIS analysis.

We parametrized the UMF for all nuclei as

[TABLE]

and estimated its parameters ($\alpha$, $\beta$, $\gamma$, and $\delta$) using HMCMC-based inference from $F_{2}^{A}/F_{2}^{d}$ data Schmookler et al. (2019); Gomez et al. (1994); Seely et al. (2009) for $0.08\leq x_{B}\leq 0.95$ in 3He, 4He, 9Be, 12C, 27Al, 56Fe, 197Au, and 208Pb, via Eq. 2. Here, and throughout this work, we consistently removed all isoscalar corrections previously applied to asymmetric nuclei data. We assumed $\frac{n_{SRC}^{A}/A}{n_{SRC}^{d}/2}=a_{2}(A/d)$, the average per-nucleon cross-section ratio for quasi-elastic electron scattering in nucleus $A$ relative to deuterium at $1.5<x_{B}<2$ Frankfurt et al. (1993); Egiyan et al. (2003, 2006); Fomin et al. (2012); Hen et al. (2012); Schmookler et al. (2019). $F_{2}^{p}/F_{2}^{d}$ is taken from Table 2 of Ref. Arrington et al. (2009). As consistent parameterizations of $F_{2}^{p}/F_{2}^{d}$ as a function of $x_{B}$ are needed for the UMF extraction, we parametrized it as $F_{2}^{p}/F_{2}^{d}=\alpha_{d}+\beta_{d}x_{B}+\gamma_{d}e^{\delta_{d}(1-x_{B})}$. We determine all parameters, including those of the UMF and $F_{2}^{p}/F_{2}^{d}$ simultaneously from data as part of the Nuclear-DIS analysis. See online supplementary materials for details on the inference procedure, posterior distributions of the parameters, and discussion of the kinematical coverage of the fitted data.

The Nuclear-DIS analysis reproduced all the $F_{2}^{A}/F_{2}^{d}$ data over the entire measured $x_{B}$ range, see online supplementary materials Fig. 1. The resulting global UMF (red band in Fig. 1) extends up to $x_{B}\sim 0.95$ and agrees well with the individual nuclear UMFs extracted in Ref Schmookler et al. (2019).

III $F_{2}^{n}/F_{2}^{p}$ Extraction

Using Eq. 1 to model nuclear effects in $F_{2}^{d}$ we express $F_{2}^{n}/F_{2}^{p}$ as:

[TABLE]

We extract $F_{2}^{n}/F_{2}^{p}$ using $f_{\text{univ}}$ and $F_{2}^{p}/F_{2}^{d}$ determined by our Nuclear-DIS analysis discussed above (see Fig. 2). Our results are consistent with the experimental extraction using tagged $d(e,e^{\prime}p_{S})$ DIS measurements on the deuteron Baillie et al. (2012). $F_{2}^{n}/F_{2}^{p}$ decreases steadily for $0.2\leq x_{B}<0.6$, and becomes approximately constant starting at $x_{B}\approx 0.6$. The $x_{B}\rightarrow 1$ limit of $F_{2}^{n}/F_{2}^{p}$ equals $0.47\pm 0.04$.

Removing low-$W$ DIS data ($W<\sqrt{2}$ GeV) from our analysis limits our extraction to $x_{B}\sim 0.8$ but does not change its conclusions since $F_{2}^{n}/F_{2}^{p}$ still saturates starting at $x_{B}\approx 0.6$. The hatched region of the blue band in Fig. 2 corresponds to our model extraction using the low-$W$ DIS data to reach up to $x_{B}\sim 0.95$. Similarly, we verified that evolving $F_{2}^{p}/F_{2}^{d}$ from $Q_{0}^{2}=12$ GeV2 to $Q^{2}=5$ GeV2 does not significantly change our extraction up to $x_{B}\sim 0.8$. See online supplementary materials for details.

Our Nuclear-DIS analysis gives significantly larger values of $F_{2}^{n}/F_{2}^{p}$ than several previous extractions which do not use $A>2$ nuclear-DIS data, including: (A) CTEQ global analysis (CT14) Dulat et al. (2016), which uses $W$ ($>3.5$ GeV) and $Q^{2}$ ($>2$ GeV2) DIS data for $A\leq 2$ (with no corrections for any nuclear effects in the deuteron) combined with various other reactions such as jet production and $W^{\pm},Z$ production, (B) CTEQ-JLab global analysis (CJ15) Accardi et al. (2016), which uses $A\leq 2$ DIS data with looser cuts of $W>1.7$ GeV and $Q^{2}>1.3$ GeV2, together with recently published $W^{\pm}$-boson charge asymmetries from D0 Abazov et al. (2015) and additional corrections for deuterium off-shell, higher-twist, and target-mass effects, and (C) Arrington et al. Arrington et al. (2012), which includes only $A\leq 2$ DIS data with only corrections for Fermi motion and binding (see Fig. 2).

CT14 and CJ15 extracted parton distribution functions rather than nucleon structure functions. In order to compare their results with our $F_{2}^{n}/F_{2}^{p}$ extraction, we constructed the corresponding nucleon structure functions from their individual parton distribution functions, accounting for valence region corrections (higher-twist, target-mass) according to Refs. Accardi et al. (2016); Accardi (private communication). These corrections largely cancel in the $F_{2}^{n}/F_{2}^{p}$ ratio.

The comparison with CJ15 is particularly interesting as that extraction of $d(x_{B})$ is predominantly constrained by the D0  $W^{\pm}$ boson asymmetry data Abazov et al. (2015); Accardi et al. (2016), corresponding to $Q^{2}=m_{W}^{2}$. This may indicate a tension between our low $Q^{2}$ results and results of the CJ15 analysis of the D0 dataset at $x_{B}\geq 0.6$.

We find that the $x_{B}\rightarrow 1$ limit of $F_{2}^{n}/F_{2}^{p}$ equals $0.47\pm 0.04$ for our Nuclear-DIS extraction. Our results agree with predictions based on perturbative QCD Farrar and Jackson (1975) and the Dyson-Schwinger Equation (DSE) Roberts et al. (2013) and disagree with the Scalar Diquark model prediction Close (1973); Carlitz (1975). This disagrees with the previous extractions (that apply nuclear corrections to the deuteron but do not consistently use data from heavier nuclei) that either could not discriminate among predictions, or preferred the scalar diquark prediction. Our result is consistent with the upper edge of the CT14 extraction, which does not rely on nuclear corrections. However, our $F_{2}^{n}/F_{2}^{p}$ has much smaller uncertainties which allow us to discriminate among models.

Thus, accounting for the modification of nucleons bound in deuterium increases $F_{2}^{n}$ at high-$x_{B}$. This was seen previously, see e.g. Ref. Melnitchouk and Thomas (1996); Yang and Bodek (1999); Frankfurt and Strikman (1988); Hen et al. (2011). However, the magnitude of this increase at $x_{B}>0.6$ is larger in our analysis as compared with those analyses that only use deuterium data. The high-$x_{B}$ disagreement between our nuclear DIS analysis and the analyses of Refs. Dulat et al. (2016); Accardi et al. (2016); Arrington et al. (2012) underscores the need for the forthcoming independent extraction by the MARATHON collaboration. Below we present our predictions for their observables and quantify the model uncertainty associated with their $F_{2}^{n}/F_{2}^{p}$ extraction.

IV $F_{2}^{n}/F_{2}^{p}$: Extraction from $A=3$ Mirror-Nuclei Data

The MARATHON experiment recently measured DIS on 2H, 3H and 3He. They plan to independently extract $F_{2}^{n}/F_{2}^{p}$ from $F_{2}^{{}^{3}\mathrm{He}}/F_{2}^{{}^{3}\mathrm{H}}$ using Petratos et al. (2010):

[TABLE]

where $\mathcal{R}$ is a theoretical correction factor which measures the cancellation of nuclear effects in $F_{2}^{{}^{3}\mathrm{He}}/F_{2}^{{}^{3}\mathrm{H}}$,

[TABLE]

Since 3He and 3H should have similar nuclear effects $\mathcal{R}$ should be close to 1.

We use our UMF to predict the expected DIS ratios for $[F_{2}^{{}^{3}\mathrm{He}}/3]/[F_{2}^{d}/2]$, $[F_{2}^{{}^{3}\mathrm{H}}/3]/[F_{2}^{d}/2]$, and $F_{2}^{{}^{3}\mathrm{He}}/F_{2}^{{}^{3}\mathrm{H}}$ (see Fig. 3). Since the $n_{SRC}^{{}^{3}\mathrm{H}}/n_{SRC}^{d}$ data are not yet published, we assumed $n_{SRC}^{{}^{3}\mathrm{H}}=n_{SRC}^{{}^{3}\mathrm{He}}$. Varying this by $\pm 20\%$ changed our results by less than $5\%$ at moderate and high-$x$, see online supplementary materials.

We compare our predictions for $[F_{2}^{{}^{3}\mathrm{He}}/3]/[F_{2}^{d}/2]$, $[F_{2}^{{}^{3}\mathrm{H}}/3]/[F_{2}^{d}/2]$, and $F_{2}^{{}^{3}\mathrm{He}}/F_{2}^{{}^{3}\mathrm{H}}$ with other models, shown as colored lines in Fig. 3. Our prediction is overall similar to that of Kulagin and Petti (KP) Kulagin and Petti (private communication, 2010), though there are differences at high $x_{B}$ in the $[F_{2}^{{}^{3}\mathrm{He}}/3]/[F_{2}^{d}/2]$, and $F_{2}^{{}^{3}\mathrm{He}}/F_{2}^{{}^{3}\mathrm{H}}$ ratios. The Tropiano et al. (TEMS) analysis Tropiano et al. (2019) combine the CJ15 global PDF fits Accardi et al. (2016) and their off-shell correction in deuterium, with additional fits to $[F_{2}^{{}^{3}\mathrm{He}}/3]/[F_{2}^{d}/2]$ data Seely et al. (2009), to extract off-shell corrections in $A=3$ nuclei. TEMS-CJ assumes fully isoscalar off-shell corrections. In Tropiano et al. (2019), fits allowing non-isoscalar off-shell corrections were also performed, which required an isoscalar correction as input. TEMS-CJ${}_{\textrm{non-iso}}$ uses the isoscalar correction from CJ15, while TEMS-KP${}_{\textrm{non-iso}}$ uses a different isoscalar correction, developed by Kulagin and Petti Kulagin and Petti (private communication, 2010). For $x_{B}>0.6$, TEMS-CJ${}_{\textrm{non-iso}}$ and TEMS-KP${}_{\textrm{non-iso}}$ predictions Tropiano et al. (2019) individually disagree with our prediction of $F_{2}^{{}^{3}\mathrm{He}}/F_{2}^{{}^{3}\mathrm{H}}$. However, the spread of the two curves at $x_{B}>0.6$ highlights the minimal sensitivity that $[F_{2}^{{}^{3}\mathrm{He}}/3]/[F_{2}^{d}/2]$ alone can provide to constraining non-isoscalar off-shell effects. We agree with the isoscalar off-shell predictions of TEMS-CJ up to $x_{B}\sim 0.5$. For $x_{B}<0.5$, even including uncertainty of TEMS-CJ${}_{\textrm{non-iso}}$ and TEMS-KP${}_{\textrm{non-iso}}$ (see supplementary materials), we predict a slightly higher ratio as compared to these two predictions.

We also studied the effect of different models of $\mathcal{R}$ on the extractions of $F_{2}^{n}/F_{2}^{p}$ from $F_{2}^{{}^{3}\mathrm{He}}/F_{2}^{{}^{3}\mathrm{H}}$. Fig. 4 (left panel) shows several theoretical predictions of $\mathcal{R}$. While individual models vary by only a few percent, the choice of model can lead to significant, differences in the extracted $F_{2}^{n}/F_{2}^{p}$, especially at large $x_{B}$. Fig. 4 (right panel) shows $F_{2}^{n}/F_{2}^{p}$ extracted using Eq. 6. Here we assume $F_{2}^{{}^{3}\mathrm{He}}/F_{2}^{{}^{3}\mathrm{H}}$ from our Nuclear-DIS analysis and then use various models of $\mathcal{R}$ to extract $F_{2}^{n}/F_{2}^{p}$, similar to the extraction MARATHON will perform with their measured $F_{2}^{{}^{3}\mathrm{He}}/F_{2}^{{}^{3}\mathrm{H}}$. While our prediction for $F_{2}^{{}^{3}\mathrm{He}}/F_{2}^{{}^{3}\mathrm{H}}$ is similar to that of KP (see Fig. 3), the differences at $x_{B}>0.7$ create large differences in $\mathcal{R}$, which cause a $\sim 10\%$ difference in the extracted $F_{2}^{n}/F_{2}^{p}$. The predictions of TEMS Tropiano et al. (2019) lead to larger differences in $F_{2}^{n}/F_{2}^{p}$ and therefore even larger model uncertainties at large-$x_{B}$ Sargsian et al. (2002). Performing the extraction of $F_{2}^{n}/F_{2}^{p}$ with different models for $F_{2}^{{}^{3}\mathrm{He}}/F_{2}^{{}^{3}\mathrm{H}}$ give similar uncertainty in $F_{2}^{n}/F_{2}^{p}$; see supplementary materials Fig 7.

Once the MARATHON $F_{2}^{{}^{3}\mathrm{He}}/F_{2}^{{}^{3}\mathrm{H}}$ data is published, this model uncertainty could be reduced by iteratively improving the extracted $F_{2}^{n}$ using Eqs. 6 and 7 Petratos et al. (2010). However, in this procedure, care must be taken to ensure consistency with global nuclear DIS data, as was done in our analysis.

V Conclusions

Using Bayesian inference by means of a Hamiltonian Markov Chain Monte Carlo, we extracted a nucleon universal modification function (UMF) that is consistent with DIS measurements of nuclei from $A=2$ to 208. We used it to correct Deuteron DIS data for bound-nucleon structure-modification effects and to extract $F_{2}^{n}/F_{2}^{p}$ up to $x_{B}\approx 0.9$.

The extracted $F_{2}^{n}/F_{2}^{p}$ ratio saturates at high-$x_{B}$ at a value of $0.47\pm 0.04$, which is consistent with perturbative QCD and DSE predictions Farrar and Jackson (1975); Roberts et al. (2013), is lower than the SU(6) symmetry prediction of 2/3 Close (1979), and is significantly greater than the Scalar Diquark model prediction of 1/4 Close (1973); Carlitz (1975). Our Nuclear-DIS analysis prediction also agrees with the most recent experimental extraction by the BONuS experiment Baillie et al. (2012). The BONuS experiment will take more data soon at higher energies and provide a more stringent test of our predictions. The forthcoming parity-violating DIS program using SoLID at Jefferson Lab will further probe $d/u$ directly using a proton target SoLID Collaboration (2014).

We also used the UMF to predict the Tritium and 3He DIS cross section ratios, recently measured by the MARATHON experiment Petratos et al. (2010), and to estimate the nuclear correction function $\mathcal{R}$ that they plan to use to extract $F_{2}^{n}/F_{2}^{p}$ from their data. We showed that different models of $\mathcal{R}$ lead to non-negligible model uncertainty in the planned extraction of $F_{2}^{n}/F_{2}^{p}$.

Acknowledgements.

We thank C. Keppel, W. Melnitchouk, and N. Sato for useful discussions. This work was supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under Award Numbers DE-FG02-94ER40818, DE-FG02-96ER-40960, DE-FG02-93ER40771, and DE-AC05-06OR23177 under which Jefferson Science Associates operates the Thomas Jefferson National Accelerator Facility, the Pazy foundation, and the Israeli Science Foundation (Israel) under Grants Nos. 136/12 and 1334/16.