Global Study of Nuclear Structure Functions

R. Petti; S.A. Kulagin

REVIEW

Global Study of Nuclear Structure Functions

S.A. Kulagin, R. Petti

High Energy Physics - Phenomenology · Submitted 31 Dec 2004 · 95 references

Pith's verdict: A solid global fit to nuclear F2 ratios with a genuinely useful decomposition; the soft spots sit in the interpretation and the high-Q2 extrapolation, not in the headline chi-squared.

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arXiv IDhep-ph/0412425 (version 3)

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CitationR. Petti, S.A. Kulagin. "Global Study of Nuclear Structure Functions." arXiv:hep-ph/0412425 (2004). https://pith.science/paper/HLOCA5VF

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Editor's note

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Bottom line: the fit is real and the effect-by-effect decomposition is useful. The parts to discount are the swelling claim and the high-Q2 effective cross section, both of which rest on assumptions the data do not test. The stress-test note gets this roughly right, and it also gets right that the universality assumption does not touch the headline fit — Eq. 91 fits delta f2 directly, so the chi-squared of 458.9 for 556 does not depend on it. Worth saying that plainly rather than letting the concern spread to the whole paper. What is actually new: three nucleus-independent parameters, per-nucleus fits in Table II that agree within uncertainties, and Fig. 3, which is the physics message — Fermi motion and binding alone miss the large-x data and an off-shell correction is required. The factor-of-2 enhancement of shadowing in the F3 asymmetry from the combinatorial structure of double scattering (Sec. IV B 1) is a nice piece of reasoning. Soft spots, in order of weight. First, Sec. VI B inverts the logic: the high-Q2 cross section is fixed by imposing delta N_OS + delta N_NS = 0, and Fig. 5 then shows the cancellation as though it were a check. The paper says outright that x1 = 0.050 was chosen because it makes that cancellation work. Honest circularity is still circularity, and the neutrino predictions at Q2 = 20 inherit it. Second, the delta f_q = delta f_qbar universality is assumed, not tested; footnote 11's divergence argument is an artifact of extrapolating the sea to x to 0, not a disproof of the alternative. Fine to assume, but it should be labelled as an assumption. Third, Fig. 11 is not clean out-of-sample: footnote 2 states the PDFs were extracted including the deuterium nuclear corrections from this paper, so the D/p agreement is partly by construction. Fourth, the PDF baseline is unpublished, which hurts reproduction. Fifth, the swelling estimate in Sec. VI C is a two-parameter fit to the large-x shape of delta f2 converted into a 9% radius increase — suggestive, not a measurement, and the framing is a bit stronger than the evidence. Who should read it: anyone doing neutrino oscillation systematics, the NuTeV angle, or neutron extraction from deuterium. It deserves a serious referee.

Referee report

Significance

The paper's central result is a genuinely useful one: a single parameter set, common to all nuclei, reproduces the measured ratios over the full available kinematic range with χ2/d.o.f. ≈ 0.83, and the per-nucleus fits in Table II are mutually consistent within uncertainties, which is real evidence for the universality hypothesis. The tabulation of systematic uncertainties (Table IV) and the small parameter correlation matrix (Table III) are done properly, and the fit is restricted to Q2 ≥ 1 GeV2 with lower-Q2 points retained only as validation, which is the right protocol. The predictions for neutrino structure functions (Figs. 16–18) are falsifiable with existing NOMAD, NuTeV and CHORUS samples (Table V), and the observation that nuclear shadowing of xF3 is enhanced relative to F2 by the combinatorial factor of Eq. (60) is a concrete, testable statement. The comparison with deuterium data excluded from the fit (Fig. 11) is a meaningful out-of-sample check, subject to the caveat noted below.

Major objections (4)

[Sec. VI B, Figs. 5 and 6] The high-Q2 behaviour of the effective cross section is fixed by imposing δN_OS_val + δN_NS_val = 0 and solving for σ̄T, and the same cancellation is then displayed in Fig. 5 as a consistency check of the model. As written, the logic runs in the wrong direction: the condition is used as an equation to determine the cross section (as the text indeed states) and then the resulting cancellation is presented as evidence that off-shell and shadowing effects balance. The cancellation at Q2 ≈ 15 GeV2 in Fig. 5 is therefore a consequence of the construction, not an independent verification. This matters because the spliced cross section of Fig. 6 feeds directly into the neutrino predictions of Sec. VII B. Please state explicitly in the text and in the Fig. 5 caption that the high-Q2 branch is defined by the normalization condition, and either provide an independent argument for the matching point or restrict the neutrino predictions to the Q2 range where σ̄T is data-constrained.
[Sec. V G 2, and Sec. VI A] The parameter x1 is not determined by the fit: the text states that among fits with comparable χ2 the value x1 = 0.050 was chosen 'since this value provides a good cancellation between off-shell and shadowing corrections in the normalization for all nuclei.' The subsequent demonstration of that cancellation in Fig. 5 and the valence-number discussion of Sec. VI A therefore use a parameter tuned to the very quantity they are meant to validate. The scan over 0.030 ≤ x1 ≤ 0.065 is mentioned but the corresponding χ2 values are not reported, so the reader cannot judge how strongly, if at all, the data constrain x1. Please tabulate χ2 versus x1 for the scan, and state plainly that the cancellation is imposed rather than predicted.
[Footnote 2 and Sec. VI E, Fig. 11] Section VI E presents the D/p comparison as a test of the model on data 'not used in the fits,' but footnote 2 states that the parton distributions employed were obtained from fits that already 'take into account the nuclear corrections to D data described in the present paper.' The deuterium prediction is therefore not independent of the model it is testing: the D nuclear correction has entered through the PDF extraction. This does not undermine the heavy-nucleus fit, but it does weaken one of the results advertised in the abstract. Please either repeat the comparison with PDFs extracted without the deuterium nuclear correction, or reword Sec. VI E and the abstract to describe Fig. 11 as a consistency check rather than an out-of-sample test.
[Sec. VI C, Eqs. (99)–(100)] The interpretation of the off-shell function in terms of nucleon 'swelling' rests on a two-parameter model (c and λ) whose values are fixed by matching two features of the phenomenological δf2, namely the position of the large-x zero x0 and the slope δf2'(x0). A two-parameter model adjusted to two numbers is not a prediction, so the quoted ≈9% increase in the core radius should be presented as a re-expression of the fit rather than as an independent determination. The model also neglects the sea by construction, as the authors note. Please soften the language accordingly, and state what independent observable (for example, the Coulomb sum rule constraint of Ref. [78], which the text cites) would discriminate this interpretation from, say, a change in the off-shell spectral density with no change in confinement scale.

Minor objections (10)

[Table I] The E665 entry reads '207Ca/12C'; this should presumably be 40Ca/12C, and the same typographical error appears in the reference list entry [12]. Please correct both.
[Table II caption] The caption reads 'Uncertainties are startistical only'; correct to 'statistical'.
[Sec. I and Table I] The introduction cites the recent JLab measurements [13, 23] as part of the motivation, but no JLab data appear in Table I or in the fits. Please explain the omission, or add the data if they fall in the covered kinematic range.
[Sec. V D, Eq. (91)] With h = 1 + x0 the parameterization gives δf2(1) = CN x0(1 − x0)(1 − x1) ≈ 1.9 for the fitted parameters, i.e. the off-shell correction does not vanish at threshold. Since the available data constrain δf2 only up to x ≈ 0.8, the behaviour of the extrapolation at x → 1 propagates into the large-x deuterium and neutrino predictions. Please comment on this and, if possible, show the sensitivity of Figs. 11–13 and 16–17 to the large-x form of δf2.
[Sec. V G, Eq. (93)] The model is averaged over the x bin but evaluated at the single average Q̄2, and the text acknowledges that the Q2 distribution within a bin is unknown. Given the strong Q2 dependence shown in Fig. 8 at x > 0.65 and x < 0.05, it would strengthen the paper to quantify the bias induced by this approximation for at least one representative data set.
[Sec. V G 3 and Fig. 4] The uncertainty band on δf2(x) in Fig. 4 should be annotated with the x range over which it is data-constrained, so that readers do not mistake the extrapolated region for a determined one.
[Sec. IV A 6, Eq. (44)] The off-shell correction is treated to first order in v = (p2 − M2)/M2, and the text notes that the correction reaches 25% at x > 0.7 for heavy nuclei. An estimate of the neglected second-order term, using the spectral function already at hand, would help bound this systematic; the current discussion leaves it entirely open.
[Fig. 3 caption] The abbreviations FMB, OS, PI and NS used in the legend are defined only in the body text. Please spell them out in the caption.
[Sec. VII B] The neutrino predictions assume that coherent axial-vector interactions at high Q2 resemble the vector ones, with the effective amplitude taken from the electromagnetic fit. This is a significant assumption for Figs. 16–18 and should be stated in the figure captions, not only in the surrounding text.
[Sec. VI D, Fig. 10] The statement that at x ≈ 0.3 the ratio R2 depends on neither A nor Q2 is interesting and worth quantifying: please give the residual spread across the nuclei and Q2 values shown.

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The paper

The paper claims

A single set of three nucleus-independent numbers reproduces measured nuclear structure-function ratios from deuterium to lead, once an off-shell correction to the bound nucleon is included.

The reading

The paper asks whether the whole body of measured ratios $R_2(A'/A) = F_2^{A'}/F_2^{A}$ — the shadowing dip at small $x$, the antishadowing bump near $x=0.1$, and the EMC dip and rise at large $x$ — can be described by one model whose nuclear parameters are the same for every nucleus. The authors build that model from four ingredients: a nuclear spectral function for Fermi motion and binding, a pion-excess distribution constrained by light-cone momentum balance, a Glauber multiple-scattering treatment of shadowing with an effective hadron-nucleon amplitude, and a phenomenological off-shell function $f_2(x)$ that lets a bound nucleon's structure differ from a free one. Fitting only to the ratios, so that the nucleon parton distributions largely cancel, they extract three shared parameters and report $458.9$ for $556$ degrees of freedom across the assembled world data. The result matters because it turns the assorted nuclear effects into a small, portable parameter set that can be transported to deuterium, to nuclear parton distributions, and to neutrino scattering on the heavy targets those experiments require.

What carries the argument

The machinery is a convolution: the nuclear structure function is written as an integral of a nuclear spectral function $P(ε,p)$ — the joint distribution of bound-nucleon momentum and separation energy — against the structure function of an off-shell nucleon, with a separate pion-excess convolution added and a coherent multiple-scattering correction subtracted. The spectral function is modelled as a mean-field part plus a correlated two-nucleon part whose high-momentum tail is taken proportional to the deuteron wave function. The pion distribution $f_{π/A}(y) = C y (1-y)^n$ is not free: its first and inverse-first moments are fixed by the light-cone momentum sum rule and by a pion-field equation-of-motion relation $m_π^2 ⟨φ^2⟩ = ε_B + ⟨T⟩$, so the meson sector is pinned by nuclear binding energies rather than fitted. Shadowing enters through a Glauber-type double- and higher-scattering series with a two-parameter effective amplitude $a_T = (i+α_T)σ̄_T/2$, where $σ̄_T(Q^2)$ interpolates between a low-$Q^2$ vector-meson value of $27$ mb and a high-$Q^2$ limit. The load-bearing new object is $f_2(x)$, the logarithmic derivative of the bound-nucleon structure function with respect to virtuality, which the authors treat as a third structure function of the nucleon, inaccessible in free-proton scattering but measurable in nuclei.

Extended reading notes

Core claim

The central claim is that nuclear deep-inelastic data are quantitatively describable by one model with three parameters common to all nuclei: $C_N = 8.10$, $x_0 = 0.448$, $Q_0^2 = 1.43$ GeV$^2$, with a fourth parameter $x_1 = 0.050$ fixed by a separate normalization requirement. The off-shell function takes the form $f_2(x) = C_N (x-x_1)(x-x_0)(h-x)$ with $h = 1+x_0$, so it changes sign twice: positive at small $x$, where the bound nucleon's negative virtuality turns it into an effective leading-twist shadowing correction, and negative between $x_1$ and $x_0$, where it enhances the bound-nucleon structure function and supplies the antishadowing bump. The authors verify universality by fitting independent subsets of nuclei from $^4$He to $^{207}$Pb and finding compatible parameters (Table II), and they report that the same parameters, extracted from heavy nuclei, describe the deuterium-to-proton ratio $R_2(D/p)$, which was not used in the fits (Fig. 11). A further claim ties the two coherent pieces together: nuclear shadowing gives a negative correction to the valence quark number while the off-shell effect gives a positive one, and the two cancel over a wide range of $Q^2$, exactly at $Q^2$ near $15$ GeV$^2$ (Fig. 5).

Load-bearing premise

The whole fit rests on one off-shell function applying equally to quarks and antiquarks in a bound nucleon, so that the measured $f_2(x)$ can be read as a single universal modification rather than two different ones.

Editorial extensions

If this is right

Nuclear effects in charged-lepton DIS can be transported to any target with the same three numbers, removing the need for a per-nucleus fit when predicting $F_2$ ratios.
Deuterium corrections become a prediction rather than an input, which changes the systematic error budget in extracting the neutron structure function from deuterium and proton data.
Nuclear valence and sea quark distributions can be computed with the same machinery, with the sea showing little or no enhancement for $0.02 < x < 0.2$, consistent with the Drell-Yan result of no observed nuclear sea enhancement.
Neutrino charged-current structure functions $F_2^{ν}$ and $xF_3^{ν}$ on carbon, iron, argon and lead can be predicted at $Q^2 > 5$ GeV$^2$, with $xF_3$ shadowing systematically stronger than $F_2$ shadowing at small $x$.
The sign and size of the off-shell function at large $x$ translate into roughly a 9% increase of the bound nucleon's core radius, a quantitative statement about nucleon swelling in nuclear matter.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the universal off-shell function holds, then a Drell-Yan measurement on a heavy target versus deuterium at $x \sim 0.3$-$0.6$ should track the same $f_2(x)$ shape as the DIS fit; a mismatch would separate quark from antiquark off-shellness, which this analysis cannot do.
The claim that shadowing and off-shell corrections cancel in the valence number is used both as a consistency check and, at high $Q^2$, as the equation that fixes the effective cross-section where no shadowing data exist. That makes the high-$Q^2$ prediction a consequence of the assumption rather than an independent test, so a direct measurement of $R_2$ in the shadowing region at $Q^2 \gtrsim 20$
Because the pion distribution is fixed by nuclear binding energies rather than by data, the pion excess is the least adjustable and simultaneously the least directly verified ingredient; a semi-inclusive measurement sensitive to the nuclear pion field would test it independently of the DIS ratios.
The same parameter set could be applied to the parity-violating and axial channels, where the paper assumes the axial effective amplitude resembles the vector one at high $Q^2$; a neutrino/antineutrino comparison of $xF_3$ on two targets would probe that assumption directly.

Original abstract

We present the results of a phenomenological study of unpolarized nuclear structure functions for a wide kinematical region of x and Q^2. As a basis of our phenomenology we develop a model which takes into account a number of different nuclear effects including nuclear shadowing, Fermi motion and binding, nuclear pion excess and off-shell correction to bound nucleon structure functions. Within this approach we perform a statistical analysis of available data on the ratio of the nuclear structure functions F_2 for different nuclei in the range from the deuteron to the lead. We express the off-shell effect and the effective scattering amplitude describing nuclear shadowing in terms of few parameters which are common to all nuclei and have a clear physical interpretation. The parameters are then extracted from statistical analysis of data. As a result, we obtain an excellent overall agreement between our calculations and data in the entire kinematical region of x and Q^2. We discuss a number of applications of our model which include the calculation of the deuteron structure functions, nuclear valence and sea quark distributions and nuclear structure functions for neutrino charged-current scattering.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.22 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We present the results of a phenomenological study of unpolarized nuclear structure functions for a wide kinematical region of x and Q^2. As a basis of our phenomenology we develop a model which takes into account a number of different nuclear effects including nuclear shadowing, Fermi motion and binding, nuclear pion excess and off-shell correction to bound nucleon structure functions. Within this approach we perform a statistical analysis of available data on the ratio of the nuclear structure functions F_2 for different nuclei in the range from the deuteron to the lead. We express the off-shell effect and the effective scattering amplitude describing nuclear shadowing in terms of few parameters which are common to all nuclei and have a clear physical interpretation. The parameters are then extracted from statistical analysis of data. As a result, we obtain an excellent overall agreement between our calculations and data in the entire kinematical region of x and Q^2. We discuss a number of applications of our model which include the calculation of the deuteron structure functions, nuclear valence and sea quark distributions and nuclear structure functions for neutrino charged-current scattering.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We present the results of a phenomenological study of unpolarized nuclear structure functions for a wide kinematical region of x and Q^2.	contribution 1.00	0.94	0.06	asserted 0.95
s1	As a basis of our phenomenology we develop a model which takes into account a number of different nuclear effects including nuclear shadowing, Fermi motion and binding, nuclear pion excess and off-shell correction to bound nucleon structure functions.	method 0.98	0.92	0.03	asserted 1.00
s2	Within this approach we perform a statistical analysis of available data on the ratio of the nuclear structure functions F_2 for different nuclei in the range from the deuteron to the lead.	method 0.92	0.95	0.04	asserted 0.98
s3	We express the off-shell effect and the effective scattering amplitude describing nuclear shadowing in terms of few parameters which are common to all nuclei and have a clear physical interpretation.	method 0.92	0.92	0.06	asserted 1.00
s4	The parameters are then extracted from statistical analysis of data.	method 0.96	0.93	0.04	asserted 0.97
s5	As a result, we obtain an excellent overall agreement between our calculations and data in the entire kinematical region of x and Q^2.	result 1.00	0.95	0.83	asserted 1.00
s6	We discuss a number of applications of our model which include the calculation of the deuteron structure functions, nuclear valence and sea quark distributions and nuclear structure functions for neutrino charged-current scattering.	contribution 0.80	0.85	0.05	asserted 0.91

What kind of paper the classifier reports this is: theoretical result 0.78 · evidence from analysis of existing data 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 3.** FIG. 3: Different nuclear effects on the ratio of

**Figure 4.** FIG. 4: Off-shell function

**Figure 5.** FIG. 5: Relative off-shell (

**Figure 6.** FIG. 6: Phenomenological cross section ¯σ

**Figure 7.** FIG. 7: Phenomenological off-shell function

**Figure 8.** FIG. 8: Our predictions for the ratio of

**Figure 11.** FIG. 11: Comparison of E665 and NMC data to our calculations (

**Figure 12.** FIG. 12: Comparison of the extrapolations of E139 nuclear da

**Figure 13.** FIG. 13: Our predictions for the ratio

**Figure 14.** FIG. 14: Nuclear effects for the isoscalar and the isovector q

**Figure 15.** FIG. 15: Nuclear effects for isoscalar valence and sea quark d

**Figure 16.** FIG. 16: Our predictions for ratios of

**Figure 17.** FIG. 17: Our predictions for ratios of

**Figure 18.** FIG. 18: Comparison of different nuclear effects calculated fo

Showing 17 of the paper's 18 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-ph/0412425 by the authors.

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How later papers used it

60 later papers cite it

Evidence: substantial. 43 of the citing papers share no author with it, and 14 of those carry a confident label from Pith's citation classifier.

Pith read 18 of the 230 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 used its method or tool. 2 more papers by the same authors are listed: 1 used its method or tool and 1 used its data or values.

Uses its method or tool 2 of 17 papers with this label · 1 by the same authors

Followed this paper's approach, which assumes that S_1(p,E) at high momentum and high separation energy is dominated by ground state configurations with a correlated nucleon-nucleon pair and the remaining (A - 2) nucleons moving with low center-of-mass momentum.

Nucleon momentum distribution extracted from the experimental scaling function (2020) · 0.97 · paraphrased: the licence does not allow quoting

By the same authors

Following Ref. [ref] , we address nuclear corrections in the DIS process at large $x$ by treating it as an incoherent scattering off bound nucleons in the target rest frame.

On the Interplay of Nuclear and Higher-Twist Corrections in Nuclear Structure Functions (2024) (same authors) · Theory and Analysis Framework · 1.00

Uses its data or values 1 of 5 papers with this label · 1 by the same authors

By the same authors

Using the results of Ref. [ref] we have $δf∼1$ at large $x>0.6$.

Nuclear effects in the deuteron and global QCD analyses (2022) (same authors) · Nucleon structure functions · 0.81

How the literature uses it

50 arXiv papers cite this in 209 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 107 sentences without a confident label

Contests it 2 papers

It should be noted, that TMC procedure of Ref. [ref] violates the $x→1$ behavior leading to nonzero $F_2$ at and below the inelastic threshold (see, e.g., discussion in [ref] ).

Nuclear effects in the deuteron in the resonance and deep-inelastic scattering region · The proton and the neutron structure functions · contest 0.76
It should be remarked that the TMC procedure of Ref. [ref] violates the inelastic threshold behavior of the SFs, leading to nonzero values at $x≥1$ (see, e.g., the discussion in Ref. [ref] ).

Hybrid model of proton structure functions · Deep inelastic scattering · contest 0.81

Builds on it 1 paper

In order to further study the sensitivity to the nuclear smearing in eq:IA, we repeat the standalone extraction of $δf(x)$ in Ref [ref] after rescaling the nuclear spectral function describing the properties of heavy nuclei [ref] by the ratios of the various deuteron wave functions shown in Fig. [ref].

Nuclear Effects in the Deuteron and Constraints on the d/u Ratio · Off-shell Function $δf$ · 0.80

Uses its method or tool 14 papers

In order to achieve an accurate description of data, we implement a re-weighting procedure for the charm cross-section: [equation] where $σ^^_μμ$ is the original LEPTO cross-section used to generate the MC events and $σ^^_μμ$ is the new cross-section obtained from an analytical calculation [ref] .

A Precision Measurement of Charm Dimuon Production in Neutrino Interactions from the NOMAD Experiment · Cross-section weights · 0.99
We apply nuclear corrections to Eq. ([ref]) using the calculation of Ref. [ref] .

Determination of Strange Sea Distributions from Neutrino-Nucleon Deep Inelastic Scattering · Theoretical Framework · 1.00
Our results indicate that the accuracy in the determination of the $d/u$ ratio can be further substantially improved by including the DIS data off a deuterium target corrected for nuclear effects using the model of Ref. [ref] with the universal off-shell function $δf$.

Nuclear Effects in the Deuteron and Constraints on the d/u Ratio · Summary · 0.81

Uses its data or values 5 papers

In turn, this OS correction is controlled by the universal off-shell function $δf$ in SF:OS, which was determined from DIS data with the corresponding uncertainty [ref] .

Nuclear Effects in the Deuteron and Constraints on the d/u Ratio · Model Predictions and Phenomenology · 0.89
The corresponding function $δf$ was determined for the isoscalar nucleon from an analysis of nuclear DIS data on the cross-section ratios $σ^A/σ^d$ [ref] .

Nuclear effects in the deuteron and global QCD analyses · Introduction · 0.89
Similarly, we take the value of $A=0.31$ and $B=0.98$ from the global fit analysis of [ref] using the identical assumption for the free-neutron structure function. * The result of Kulagin and Petti [ref] (KP), who assumed a third-order polynomial of the form [equation] with parameters $C$, $x_0$, and $x_1$.

Studying the Impact of Virtuality-Dependent Nucleon Structure Modification on Spectator-Tagged Deep Inelastic Scattering · Formalism · 0.99

Compares with it 11 papers

The largest deviations between the CJ15 and MMHT14 analyses and the model of Ref. [ref] are observed in the intermediate region $x∼0.15$ and at large $x>0.6$ (cf. Fig. [ref]), although their significance is limited by the current uncertainties.

Nuclear Effects in the Deuteron and Constraints on the d/u Ratio · Constraints on $d/u$ and $F_2^n/F_2^p$ · 0.97
Moreover, in Fig. [ref], our $r(x)$ is compared with i) the data extracted by MARATHON [ref] through Eq. [ref] with the theoretical quantity $R^ht(x)$ evaluated following Refs. [ref] , and ii) the SMC $r(x)$ ratio [ref] .

The European Muon Collaboration effect in Light-Front Hamiltonian Dynamics · Introduction · 0.95
The results of Ref. [ref] on $δf$ are consistent with the previous determination from nuclei with $A≥4$ [ref] .

Nuclear effects in the deuteron and global QCD analyses · Introduction · 0.92

Cites it as support 7 papers

However, the study of nuclear DIS and DY data [ref] supports the hypothesis of the OS function universality, with no significant $Q^2$ dependence suggested by the data, i.e. $δf(x,Q^2)=δf(x)$.

Nuclear Effects in the Deuteron and Constraints on the d/u Ratio · Off-shell Correction · 1.00
We assume equal functions $δf_T=δf_2=δf$ for $F_T$ and $F_2$, motivated by the observation that $F_T≈F_2$ in the region for which the OS effect is numerically important [ref] .

On the Interplay of Nuclear and Higher-Twist Corrections in Nuclear Structure Functions · Theory and Analysis Framework · 1.00
We also comment that the proton and the neutron SFs of Ref. [ref] show a very good performance in analysis of the nuclear EMC effect in Refs. [ref] as well as in the interpretation of a recent measurement of $F_2^n/F_2^p$ [ref] .

Hybrid model of proton structure functions · Deep inelastic scattering · 0.97

Cites it as background 15 papers

In this case the nuclear $F_2^A$ structure function can be written in convolution form as a sum of on-shell and off-shell nucleon contributions [ref] ,

Isospin dependence of nuclear EMC effect from global QCD analysis · Nuclear structure functions · 0.81
There are several theoretical approaches in describing inclusive DIS from a deeply bound nucleon in the nucleus [ref] , ranging from models in which the deuteron is treated non-relativistically with off-shell effects included in the leading twist approximation, to models in which the scattering process is described in the light-front reference frame which allows to suppress the negative energy contributions in the bound nucleon propagator (referred to as $Z$-graphs).

Nuclear final-state interactions in deep inelastic scattering off the lightest nuclei · Virtual nucleon approximation · 0.99
The off-shell correction in nuclear DIS has been the subject of detailed phenomenological studies [ref] .

On the Cancellation of Nuclear Effects in the Valence Region · Results and discussion · 0.95

Discussion

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