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REVIEW 4 major objections 5 minor 3 cited by

Deep-inelastic scattering off helium-3 and tritium cannot be described by free-nucleon quark distributions alone; nucleon off-shell corrections with both isoscalar and isovector components are required.

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2026-08-02 22:27 UTC pith:U7YRDQCU

load-bearing objection Core result survives scrutiny: A<=3 DIS demands off-shell corrections and MARATHON's KP normalization looks biased; the isovector signal is suggestive but model-dependent. the 4 major comments →

arxiv 2602.16589 v2 pith:U7YRDQCU submitted 2026-02-18 hep-ph hep-exnucl-th

Isospin dependence of nuclear EMC effect from global QCD analysis

C. Cocuzza , T. J. Hague , W. Melnitchouk , N. Sato , A.W. Thomas This is my paper
classification hep-ph hep-exnucl-th
keywords EMC effectoff-shell nucleon correctionsisospin dependenceglobal QCD analysisparton distribution functionsdeep inelastic scatteringlight nucleiMARATHON data
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper reports a global QCD analysis of deep-inelastic scattering data on protons, deuterons, helium-3, and tritium, including the new MARATHON measurements of the 3He/D and 3H/D ratios. It finds that the 3He/D data are completely unexplained without nucleon off-shell corrections: the reduced chi-squared drops from 5.10 to 1.04 when these corrections are added. The analysis also yields EMC ratios for the deuteron, helium-3, and tritium at x_B = 0.31 that sit about 2.3–3.0 sigma below the values imposed by the heavy-nucleus-based normalization model used in the experimental analysis. A sympathetic reader would take this as the strongest current evidence that the nuclear EMC effect is present and isospin dependent even in the lightest nuclei, and that the experimental data should not be normalized to a model tuned to heavy nuclei.

Core claim

The central claim is that nucleon off-shell corrections—the modification of the bound nucleon's quark distributions relative to its free-nucleon counterpart—are required to describe inclusive deep-inelastic scattering from A=2 and A=3 nuclei. In the global fit, the 3He/D ratio data rule out the on-shell-only description (chi2_red = 5.10) and are well described once off-shell corrections are introduced (chi2_red = 1.04). The analysis further suggests a nonzero isovector component, visible in the difference of the off-shell u and d distributions at large x, alongside a large isoscalar component. Consequently, the extracted EMC ratios R_D, R_3He, and R_3H at x_B = 0.31 disagree with the values

What carries the argument

The central object is the nuclear structure function expressed as a convolution of on-shell and off-shell nucleon contributions: F2^A = sum_N [ f^on_{N/A} ⊗ F2^N + f^off_{N/A} ⊗ δF2^{N/A} ]. The unknown off-shell correction δF2 is parametrized through off-shell PDFs δq_{N/A}, which are decomposed into an isoscalar part δq0 and isovector parts δu1, δd1 with a prescribed combinatorics (the isovector part vanishes in 3He and doubles in 3H relative to the deuteron). The machinery is a simultaneous Bayesian fit that determines free-nucleon PDFs, off-shell functions, higher-twist corrections, and data normalizations from the same global dataset, so that nuclear effects are inferred rather than ass

Load-bearing premise

The load-bearing premise is the assumed isoscalar/isovector decomposition of the off-shell PDFs: that the isovector part vanishes in 3He, doubles in 3H relative to the deuteron, and that only three fitted functions suffice; if this counting is wrong, the extracted isovector signal and EMC ratios are artifacts of the model.

What would settle it

A precision measurement of the 3He/D and 3H/D ratios with an independent normalization—for example, through tagged deep-inelastic scattering from the spectator nucleon—that disagrees with the fitted off-shell predictions, or a direct measurement of F_L^A showing a nuclear dependence of R = F_L/F_T large enough to shift the structure-function ratios, would falsify the extraction.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The MARATHON data normalization based on the heavy-nucleus model biases the extracted neutron structure function; re-extracted ratios shift accordingly.
  • The nuclear EMC effect is shown to persist down to A=2 and A=3, with magnitude tracking the off-shell smearing averages: about −4% for the deuteron, −7% for helium-3, and −9.5% for tritium.
  • The d-quark PDF at x ≳ 0.6 gains modest new constraints from the A=3 data, reducing its uncertainties in that region.
  • The super-ratio R_{3He/3H} is predicted to fall below unity at large x, contrary to the trend in the normalization model used by the experiment.
  • Future A=3 data can discriminate between isoscalar-only and isovector-bearing off-shell scenarios, since the two produce different high-x behavior in the 3H/D ratio.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the isovector off-shell signal holds up, it would imply the medium modification of quark distributions depends on isospin, which is a direct discriminator between mean-field and short-range-correlation mechanisms of the EMC effect—a connection the paper leaves implicit.
  • The same isoscalar/isovector decomposition could be applied to 4He, where the balance between the two components differs, offering a testable prediction using existing EMC data on helium-4.
  • Because the analysis treats the measured cross-section ratios as structure-function ratios, a future direct measurement of F_L for A=3 nuclei could shift the extracted off-shell functions; the size of that shift is not quantified in the paper.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper presents a global QCD analysis of unpolarized PDFs and nucleon off-shell corrections using proton, deuteron, and A=3 data, including the new MARATHON ^3He/D and ^3H/D cross-section ratios. The authors parametrize off-shell effects through isoscalar and isovector components under a specific spectator-isospin decomposition, fit them simultaneously with PDFs in the JAM Bayesian Monte Carlo framework, and find that off-shell corrections are required: the ^3He/D reduced chi^2 drops from 5.10 to 1.04 when they are included. They further report a 'suggestion' of isovector off-shell effects from a fitted δu_1−δd_1 that is negative at x≳0.5, and they find that the extracted EMC ratios R_D, R_3He, and R_3H deviate from KP-model values at x_B=0.31 by about 3.0σ, 2.3σ, and 2.4σ, respectively. They also argue that the KP-based normalizations applied to MARATHON data introduce a significant bias, with the fitted ^3He/D normalization differing from the KP value by 3.2σ.

Significance. If correct, this would be an important step: it provides a global, data-driven determination of light-nucleus off-shell corrections, tests the MARATHON normalization procedure, and gives quantitative EMC ratios for A=2 and A=3 that can be compared with few-body calculations. The analysis is strengthened by its global data set, Bayesian uncertainty propagation, explicit treatment of normalizations, and checks on higher-twist parametrizations. The need for off-shell corrections to describe ^3He/D appears robust from the goodness-of-fit comparison. However, the isovector signal and the quantitative EMC-ratio deviations from KP are conditional on the assumed isoscalar/isovector decomposition and on a model-selection choice that is not fully justified. Those load-bearing points need to be addressed before the central claims can be regarded as established.

major comments (4)
  1. [§III and §II.B] The paper chooses scenario (ii) as default even though scenario (i) has a better total MARATHON chi^2 (50 vs 54), with the only stated reason that scenario (ii) better describes the highest three x_B points of ^3H/D. Since the isovector signal x(δu_1−δd_1)<0 is literally the fitted difference of scenario-(ii) functions, this is a post-hoc model-selection rule. Please provide a formal model-selection or cross-validation justification. More importantly, test a more flexible isoscalar-only model (e.g. more parameters for δq_0) and show whether the high-x ^3H/D points can be described without isovector terms. Without such a test, the 'suggestion of isovector off-shell effects' is not a robust data requirement.
  2. [§II.B, Eqs. (14)–(18)] The isoscalar/isovector decomposition relies on factor-2 combinatorics, the identification of spectator-isospin projections, and the assumption that isovector terms vanish in ^3He. These assumptions are physically motivated but not tested. With only three independent MARATHON ratios constraining three off-shell functions, the extracted signals are strongly shaped by this basis. Please demonstrate sensitivity to these assumptions: allow non-zero isovector contributions in ^3He, vary the combinatorial factors, or use an alternative functional basis for the off-shell corrections, and quantify the shifts in R_D, R_3He, R_3H and δu_1−δd_1. This is also relevant to the abstract's claim of 'without theoretical assumptions about the isospin dependence of nuclear effects,' which is not literally satisfied.
  3. [§III, paragraph on MARATHON cross-section ratios] The paper equates MARATHON cross-section ratios with F_2 structure-function ratios, neglecting the nuclear dependence of R=σ_L/σ_T. The authors acknowledge that this is an assumption but do not estimate its impact. Since the central EMC-ratio claims are at the few-percent level, and high-x data are most sensitive, please provide a quantitative estimate of the resulting systematic uncertainty (e.g. using model estimates of nuclear R or a conservative uncertainty band) or restrict the conclusion to a kinematic region where this effect is demonstrably negligible.
  4. [Table II and Fig. 2] The 3.2σ discrepancy between the fitted ^3He/D normalization and the KP-based normalization is presented as evidence that KP normalizations bias the analysis. However, the normalization and the off-shell shape parameters are fitted simultaneously; a more flexible off-shell model could trade a normalization shift for a shape change. Please show that this discrepancy persists under the alternative off-shell parametrizations suggested above, or characterize the correlation between the normalization parameters and the off-shell functional form.
minor comments (5)
  1. [Fig. 5 caption] The symbol '□' in x(δu_1 □ δd_1) should be a minus sign.
  2. [Conclusions] The symbols R_ht, R_hd, and R_td appear without definition; presumably R_D, R_3He/D, and R_3H/D. Please use consistent notation.
  3. [Fig. 9 caption] The lower panel caption says '3He/D and 3He/D'; the second should likely be '3H/D'.
  4. [Various] Typos: 'constributions' in §II.B; 'T otal' in Table I; 'the shed light' in the Conclusions; 'off-shell isovector δu1−δd1' wording could be clarified.
  5. [Abstract and §II.B] The phrase 'without theoretical assumptions about the isospin dependence' overstates the situation; the analysis employs a specific isoscalar/isovector decomposition and scenario restrictions. Rephrasing to 'without assuming a specific magnitude/shape of the isospin dependence' would be more accurate.

Circularity Check

0 steps flagged

No significant circularity: off-shell corrections are fit outputs compared against an external benchmark; the isovector signal is a fitted parameter, not a construction-forced prediction.

full rationale

The closest step to circularity is the extraction of the isovector off-shell signal: δu1−δd1 is a fitted function (Sec. IV.B, Fig. 5) obtained from the same MARATHON data used to argue for it. But this is a normal likelihood-fit output, not a prediction; the data could in principle have returned δu1=δd1=0, and the nonzero result is an inference, not an identity. The preference for scenario (ii) over (i) is explicitly data-driven (Sec. III: 'scenario (ii) was found to better describe the highest 3 data points in x_B for the 3H/D data, suggesting a potential signature of the isovector EMC effect'); this is model selection based on a few data points, which is fragile but not circular. The EMC-ratio deviations from the KP model are comparisons of fit outputs to an external benchmark; the KP model's unity-at-x=0.31 condition is not imposed in the fit, so the disagreement is not by construction. The self-citation to the earlier JAM analysis [32] is confirmatory rather than load-bearing: the current fit includes new 3He/D and 3H/D data and re-derives the result. The acknowledged model dependence (Sec. IV: 'the central values of the nuclear EMC ratios, as well as their uncertainties, are significantly influenced by the modeling of the off-shell functions') is a limitation on robustness, not circularity. No equation in the paper reduces to its input by construction, and no fitted parameter is relabeled as a prediction.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 0 invented entities

No new particles or forces are invented. The cost is paid in parametrization: roughly 74 fitted parameters plus model assumptions about the off-shell decomposition, the W^2 cut, and the treatment of higher twists. The paper's central quantitative claims—the isovector signal and the EMC-ratio deviations from KP—depend on these assumptions.

free parameters (5)
  • Onshell PDF shape parameters (33) = not quoted in text
    Parameters of template Eq. (23) for u_v, d_v, bar-u0, bar-d0, s0, bar-s0, g, S1, S2; fitted to the global dataset.
  • Off-shell function parameters (9) = not quoted in text
    Three parameters each for delta_q0, delta_u1, delta_d1 in Eq. (23), with gamma=0 and eta fixed by the sum rule; these carry the central isoscalar/isovector signal.
  • Higher-twist parameters (10) = not quoted in text
    Independent additive HT functions H^p and H^n in Eq. (9), fitted to large-x and low-Q^2 DIS data.
  • Dataset normalizations (22) = e.g., MARATHON D/p 1.017(4), 3He/D 0.996(6), 3H/D 0.991(5)
    One normalization N_e per dataset, constrained by quoted normalization uncertainties; the fitted 3He/D normalization drives the bias claim against the KP model.
  • W^2 cut = 3.5 GeV^2
    Raised from 3.0 to 3.5 GeV^2, removing the highest-x_B 3He/D and 3H/D points; the text says this significantly improved reduced chi^2 for some datasets.
axioms (6)
  • domain assumption Impulse approximation and convolution formula Eqs. (1)-(2) for nuclear structure functions.
    Assumes incoherent scattering from individual off-shell nucleons, with smearing functions computed from nuclear wave functions.
  • domain assumption Exact charge symmetry relations (7)-(8) between mirror nuclei, with no charge-symmetry violation or Coulomb corrections.
    Used to relate u/d distributions in D, 3He and 3H; the paper does not quantify CSV.
  • ad hoc to paper Isoscalar/isovector decomposition (14)-(18) with factor-2 counting and zero isovector component in 3He.
    Derived from spectator-isospin and meson-exchange reasoning; this decomposition is central to identifying the isovector signal.
  • domain assumption MARATHON cross-section ratios equal structure-function ratios.
    The R = F_L/F_T nuclear dependence is neglected, supported only by a qualitative argument that longitudinal contributions are small at JLab kinematics.
  • domain assumption Off-shell sea-quark and gluon contributions are neglected.
    The analysis focuses on large x_B where valence quarks dominate; this restricts the validity range of the extracted off-shell functions.
  • ad hoc to paper PDF template Eq. (23) and default scenario (ii): symmetric isoscalar and asymmetric isovector off-shell corrections.
    Model choice; scenario (i) gives similar total chi^2, and scenario (ii) is selected partly by its better description of the high-x 3H/D data.

pith-pipeline@v1.3.0-alltime-deepseek · 17872 in / 12376 out tokens · 105861 ms · 2026-08-02T22:27:07.978858+00:00 · methodology

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read the original abstract

We perform a new global QCD analysis of unpolarized parton distribution functions (PDFs) in the nucleon from proton, deuteron and $A=3$ data, including recent measurements of $^3$He/$D$ and $^3$H/$D$ cross section ratios from the MARATHON experiment at Jefferson Lab. Simultaneously inferring the PDFs and nucleon off-shell corrections allows both to be determined consistently, without theoretical assumptions about the isospin dependence of nuclear effects. The analysis provides strong evidence for the need of nucleon off-shell corrections to describe the $A=3$ data, with large isoscalar and a suggestion of nonzero isovector contributions in $A \leq 3$ nuclei. We find that the extracted EMC ratios of nuclear to nucleon structure functions for $A=2$ and 3 differ from those naively extrapolated from heavy nuclei down to low $A$.

Figures

Figures reproduced from arXiv: 2602.16589 by A.W. Thomas, C. Cocuzza, N. Sato, T. J. Hague, W. Melnitchouk.

Figure 1
Figure 1. Figure 1: , where the results of the full fit are shown together with the same fit with off-shell corrections removed and the same fit including only isoscalar off-shell corrections. As is stan￾dard practice in global QCD analyses, the fitted normalizations are used to shift the theory curves, while the experimental data are left unmodified. Consistent with the observation in Ref. [32], for the D/p ratio there is li… view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Ratio [PITH_FULL_IMAGE:figures/full_fig_p017_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Isoscalar nuclear EMC ratio ( [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Ratios of PDFs for [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Off-shell functions [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Off-shell contributions [PITH_FULL_IMAGE:figures/full_fig_p022_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Deuteron to free nucleon EMC ratio [PITH_FULL_IMAGE:figures/full_fig_p024_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Super-ratio [PITH_FULL_IMAGE:figures/full_fig_p025_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (Top panel) Nuclear EMC ratios [PITH_FULL_IMAGE:figures/full_fig_p026_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Nuclear EMC ratios [PITH_FULL_IMAGE:figures/full_fig_p027_10.png] view at source ↗

discussion (0)

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Forward citations

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