{"id":"661f7a93-e5cd-4d46-b8b7-5f7ddc5d5a3c","arxiv_id":"2507.18168","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"In the light-front dressed quark model, all leading-twist quark Wigner distributions become increasingly distorted and localized as the skewness parameter xi grows from 0 to 0.5.","lead":"This paper computes how quark Wigner distributions, quantum phase-space maps of a quark inside a hadron, change when the hadron's longitudinal momentum differs before and after the probing (nonzero skewness). It finds that increasing skewness deforms these maps into dipole and quadrupole patterns and localizes the quark, a step toward the multidimensional hadron-structure program for electron-ion colliders.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The off-forward Wigner transform in Eqs. (9)-(16) contains an unvalidated Jacobian factor, and the ξ=0 baseline is described inconsistently (circular vs quadrupole).","rationale":"The reader's weakest assumption identifies the off-forward Wigner definition in Eqs. (9)-(10) and (16). This is indeed the most load-bearing point: if the (1−ξ^2) rescaling is wrong, all qualitative statements about skewness-induced deformations, localization, and multipole structure are unsupported. The stress-test makes the concern concrete by noting the Jacobian mismatch between Eq. (10) and Eq. (16), and adds a separate internal inconsistency between Sec. IV A and the conclusion about ρ_UU at ξ=0. Both are checkable by a single re-derivation. Because the reader already conditioned the verdict on this assumption, the present analysis does not move the verdict; it strengthens the condition. No claim of fraud or sloppiness is implied; the issue is that the central construction is imported without derivation and contains an apparent normalization mismatch that must be resolved before the qualitative conclusions can be trusted.","tokens_in":15770,"tokens_out":15048,"duration_ms":137108,"concrete_test":"Independently re-derive Eq. (16) from Eqs. (9)-(15), keeping the explicit spinor normalization in Eq. (13). This single analytical check settles whether substituting D⊥ = Δ⊥/(1−ξ^2) yields a measure d^2Δ⊥/(1−ξ^2)^2 or (after spinor factors) (1−ξ^2)^−3/2, and whether the resulting ξ=0, k⊥=0.4ŷ ρ_UU(b⊥) slice is circular or quadrupolar, directly testing the Fourier convention and the baseline in the conclusion.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Eq. (9) defines D⊥ = Δ⊥/(1−ξ^2); Eq. (10) Fourier-transforms over D⊥. Substituting gives d^2D⊥ = d^2Δ⊥/(1−ξ^2)^2, so Eq. (16) should have a (1−ξ^2)^−2 prefactor unless spinor factors in Eq. (13) generate an additional (1−ξ^2)^{1/2}. The paper instead writes (1−ξ^2)^−3/2 without deriving that factor, citing only refs [39,40]. Since all nine Wigner distributions in Eqs. (16)-(26) inherit this normalization, every plotted pattern and the claimed ξ-dependent localization/multipole enhancement depend on this unvalidated convention. Separately, Sec. IV A says ρ_UU at ξ=0 in b⊥ space has 'approximate rotational symmetry and a quadruple-like structure,' while the conclusion says it 'shows circular symmetry at ξ=0.' A quadrupole is not circular; the zero-skewness baseline is therefore internally contradicted, weakening the claim that multipole structures 'emerge' with skewness.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript studies the skewness (ξ) dependence of the nine leading-twist quark Wigner distributions in the light-front dressed quark model. Starting from published analytic GTMDs with nonzero ξ (Appendix A, taken from Ref. [39]) and from Wigner master formulas quoted from Refs. [39,40], it evaluates ρ for unpolarized, longitudinally, and transversely polarized quarks in targets of each polarization, plotting the distributions in transverse impact-parameter space, transverse momentum space, and a mixed (bx,ky) space for ξ=0, 0.25, 0.5, and for ρ_UU as a function of ξ from 0 to 0.5. The central claim is that increasing ξ distorts the forward-limit distributions, produces dipole and quadrupole patterns, breaks rotational/time-reversal symmetry, and localizes the phase-space support through reduced initial-final overlap and interference between light-front wave function components of different orbital angular momentum. The paper contains no data fitting; all results are numerical evaluations of closed-form model expressions.","tokens_in":16052,"tokens_out":14374,"duration_ms":153725,"significance":"The paper's qualitative claims—ξ-dependent localization, symmetry breaking, and multipole formation in every leading-twist channel—are, if correct, a useful model-level benchmark for off-forward phase-space tomography and could guide lattice QCD and exclusive-process phenomenology. The manuscript deserves credit for covering all nine polarization channels systematically, for working with analytic input, and for not introducing any fit parameters. In its present form, however, the contribution is essentially a numerical elaboration of self-cited analytic results [39,40], and the two load-bearing conventions it imports (the D⊥-space Wigner definition and the form of the GTMDs) are not derived or checked here. The significance is therefore conditional on resolving the technical issues below; the qualitative pattern claims are falsifiable and would be interesting if the definitions are confirmed.","major_comments":[{"comment":"The off-forward Wigner transform is not derived. With D⊥ = Δ⊥/(1−ξ²), the Jacobian is d²D⊥ = (1−ξ²)^{-2} d²Δ⊥, so Eq. (10) combined with the change of variables gives a prefactor (1−ξ²)^{-2}, not (1−ξ²)^{-3/2}, unless the spinor contraction in Eq. (13) supplies an additional (1−ξ²)^{1/2}. The paper simply cites [39,40] for Eqs. (16)–(26), but those equations are the paper's own central definitions and the extra factor is never exhibited. This matters because the overall (1−ξ²)-dependent prefactor rescales every ξ column in Figs. 1–7, so the claimed 'more pronounced' multipole patterns and localization with increasing ξ may be partly an artifact of the normalization convention. The authors should derive one representative Wigner formula from Eqs. (11)–(15), or state explicitly the convention used in [39,40] for the spinor factor.","section":"Sec. III, Eqs. (9), (10), (16)-(26)"},{"comment":"The auxiliary function β in Eq. (A19) is α/[(1−x)(k2Δ1−k1Δ2)], and several GTMDs contain terms without a cross-product factor in the numerator. For example, F1,2 and the second square bracket in F1,3 are proportional to β times quantities such as 4m²ξ(1+x)k⊥·Δ⊥ or 8m²(1−x)²[2(1+x)ξk⊥−(1−x)xΔ⊥]·k⊥, which do not vanish when k∥Δ. As written, these GTMDs therefore have singularities along Δ⊥∥k⊥, and the subsequent 2D Fourier integrals over Δ⊥ would be at least logarithmically divergent unless regularized. This is a load-bearing issue for the numerical analysis because the Wigner plots of ρ_TU, ρ_TL, ρ_TT, and ρ_UL inherit such terms. Please verify these expressions against the original derivation, correct any transcription errors, and state how the numerical integration avoids the singular locus.","section":"Appendix A, Eqs. (A2), (A3), (A9)–(A16), and (A19)"},{"comment":"There is a direct contradiction about the ξ=0 baseline. Section IV A states that at ξ=0 in impact-parameter space ρ_UU has 'approximate rotational symmetry and a quadruple-like structure,' while the concluding paragraph says it 'shows circular symmetry at ξ = 0.' A quadrupole pattern is not circular, and with k⊥ fixed to 0.4 y-hat one would not expect exact circular symmetry at ξ=0. The authors should specify the precise zero-skewness baseline and then formulate the 'emergence' of multipoles with ξ relative to that baseline; as written, the central qualitative claim is internally inconsistent.","section":"Sec. IV.A and Sec. V (Conclusion)"},{"comment":"The numerical setup is under-specified in ways that affect reproducibility and interpretation. The text says 'x was integrated over the DGLAP region (ξ < x < 1),' but ρ in Eqs. (16)–(26) is a function of x and no x-integrated quantity is defined; if x was integrated, the plots should be labeled or the equations changed. In addition, the values of m=0.0033 GeV and Δ_max=1 GeV, the fixed transverse coordinates k⊥=0.4 y-hat and b⊥=0.4 y-hat GeV^-1, and the mixed-space integration ranges [0,0.4] are stated without justification, and no convergence check with respect to Δ_max or the grid is reported. Since the conclusions are purely qualitative statements about the shapes of the plots, a sensitivity check is needed to establish that the observed lobes and localizations are not numerical artifacts.","section":"Sec. IV, Numerical Analysis"}],"minor_comments":[{"comment":"Eq. (10) writes W[Γ](x,ξ,Δ⊥,k⊥;S) but the integration variable is D⊥; after the substitution the argument should be written consistently as a function of D⊥ (or the relation should be stated).","section":"Sec. III, Eq. (10)"},{"comment":"The quantities q⊥, y, q′⊥, and x′ entering D(q⊥,y) and D∗(q′⊥,x′) are never defined in the manuscript, so the appendix is not self-contained; define them in terms of x, ξ, k⊥, and Δ⊥ or state the mapping to Ref. [39] explicitly.","section":"Appendix A, Eq. (A18)"},{"comment":"The phrase 'The and auxiliary functions α, and D are defined as:' contains a typo and should read 'The auxiliary functions α and D are defined as:'.","section":"Appendix A, p. 24"},{"comment":"In the abstract, 'using the analytical expression all leading-twist GTMDs' is missing 'of'; and in Sec. IV, 'The parton longitudinal momentum fraction x was integrated over' conflicts with the x-dependent definitions in Eqs. (16)–(26).","section":"Abstract and Sec. IV"},{"comment":"Figure 1's caption uses 'left, middle, and right panels' but does not label the rows; given that the text refers to top/middle/bottom rows, adding row labels would aid readability.","section":"Fig. 1"}],"recommendation":"major_revision","confidential_remarks":"The manuscript's analytic input is dominated by two self-cited papers [39,40] by overlapping authors, and the new material is numerical evaluation and visual analysis. This is not disqualifying, but the editor should assess whether the level of novelty meets the journal's standard. I would also note that no code or data is provided; given that the core results are plots, sharing the numerical routines would significantly raise confidence in the ξ-dependent claims."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the paper takes the known analytic GTMDs at nonzero skewness and computes all nine leading-twist quark Wigner distributions in b_perp, k_perp, and mixed space. The figures are clean and the organization is good. If you work with this model, this is a handy reference.\n\nWhat is actually new: the systematic numerical survey of xi dependence across polarization channels, and the observation that dipoles, quadrupoles, and localization grow with xi. That is a legitimate extension of the earlier analytic work in refs [39,40], and the qualitative message—off-forward phase space is richer than the forward limit—is plausible.\n\nThe soft spots are in the framing and the normalization. The abstract says previous studies were largely forward-limit, but refs [39,40], including one by the same group, already derived the non-zero-xi GTMDs and the Wigner master formulas. The new content here is re-expression and visualization of those results. Calling it 'one of the most comprehensive analyses' is a stretch.\n\nMore seriously, the transform in Eqs. (9)–(16) uses a (1-xi^2)^(-3/2) prefactor. Under the substitution D_perp = Delta_perp/(1-xi^2), the phase-space Jacobian alone gives (1-xi^2)^(-2); getting to (-3/2) requires a compensating (1-xi^2)^(1/2) from the spinor factors in Eq. (13), which is never shown. The prefactor depends on xi but not on Delta_perp, so the shape in any single panel is likely unaffected, but the relative normalization across xi—and any quantitative localization claim—depends on this convention. It should be checked against the original derivation in refs [39,40].\n\nThere is also an internal inconsistency: Sec. IV A describes rho_UU at xi=0 as having 'approximate rotational symmetry and a quadruple-like structure,' while the conclusion calls it 'circular symmetry.' Those are not the same; the baseline story should be fixed.\n\nMinor points: no derivation of the GTMDs (appendix just lists them), no code or data, and the numerical choices (m=0.0033 GeV, Delta_max=1 GeV, fixed slices) are stated but not convergence-checked. These are minor for a model study.\n\nBottom line: the paper is a useful resource and the central qualitative claim holds up as a model-level prediction. The Jacobian convention and the xi=0 description need a referee's attention, but they are fixable. I would send it to review rather than desk-reject; with the normalization sorted out, it can be a citeable reference. If you are in the subfield, you might want it on your reading list, but it is not a major advance.","headline":"A useful numerical catalog of skewness-dependent quark Wigner distributions in the dressed quark model, but the novelty is overstated and the transform normalization needs a check before the quantitative claims are trusted.","tokens_in":16576,"tokens_out":4587,"would_cite":true,"duration_ms":46705,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["12.38.-t","13.60.Hb","14.20.Dh"],"model":"deepseek-v4-flash","headline":"In the light-front dressed quark model, all leading-twist quark Wigner distributions become skewness-dependent: circular forward-limit patterns give way to dipole and quadrupole lobes, asymmetries, localization, and sign-changing regions…","keywords":["Wigner distributions","skewness","generalized transverse momentum dependent distributions","light-front dressed quark model","dipole and quadrupole patterns","spin-orbit correlations","orbital angular momentum","hadron tomography"],"falsifier":"Recompute the nine Wigner distributions with $\\boldsymbol{\\Delta}_\\perp$ itself (no $(1-\\xi^2)$ rescaling in Eq. (9)) as the Fourier variable. If the dipole and quadrupole structures and the localization trend disappear or change sign as $\\xi$ grows, the paper's skewness effects are artifacts of the rescaling. A second check: integrate $\\rho_{UU}$ over $\\mathbf{b}_\\perp$ and $\\mathbf{k}_\\perp$ and verify the result is independent of $\\xi$; a $\\xi$-dependent normalization would show the distribution is not behaving as a phase-space density.","tokens_in":15562,"feed_emoji":"🌀","tokens_out":11342,"duration_ms":110336,"temperature":0.7,"pith_summary":"This paper asks what happens to the quantum phase-space picture of a quark when the initial and final hadron states carry different longitudinal momentum, measured by the skewness $\\xi$. Working in the analytically solvable light-front dressed quark model, the authors compute all nine leading-twist quark Wigner distributions for unpolarized, longitudinally polarized, and transversely polarized quark and target configurations, at $\\xi = 0$, $0.25$, and $0.5$. They find that nonzero $\\xi$ systematically breaks the circular symmetry of the forward limit, producing dipole and quadrupole patterns, momentum-space shifts, negative density regions, and increasing localization. They interpret these features as spin-orbit correlations and quantum interference between light-front wave function components that differ in orbital angular momentum. If the claim holds, the model gives concrete off-forward predictions for phase-space structure that connect generalized parton distributions and transverse-momentum-dependent distributions.","feed_headline":"Skewness deforms quark phase space into dipole and quadrupole lobes","feed_subtitle":"Longitudinal momentum transfer reshapes quark phase space, exposing spin-orbit correlations in every polarization channel.","key_machinery":"The central object is the quark Wigner distribution, a quantum phase-space quasi-probability distribution over the quark's transverse position $\\mathbf{b}_\\perp$ and transverse momentum $\\mathbf{k}_\\perp$, defined as a Fourier transform of the fully unintegrated quark-quark correlator with respect to the rescaled transverse momentum transfer $\\mathbf{D}_\\perp = \\boldsymbol{\\Delta}_\\perp/(1-\\xi^2)$, including a $(1-\\xi^2)^{-3/2}$ prefactor. The input is the two-particle light-front wave function of a quark dressed by a gluon, which enters the analytic expressions for all leading-twist GTMDs $F_{1i}, G_{1i}, H_{1j}$. The paper inserts those GTMDs into the correlator decompositions of Eqs. (13)-(15), combines them according to the polarization definitions of Eqs. (12), (19), and (23), and numerically Fourier-transforms the results to obtain the nine Wigner distributions, tracking how the phases and $(1-\\xi^2)$ factors alter them as $\\xi$ varies.","core_discovery":"The central discovery is that turning on $\\xi$ alters every quark Wigner distribution in the dressed quark model, not just the size of the phase-space support. The unpolarized $\\rho_{UU}$, approximately circular at $\\xi=0$, distorts and shifts as $\\xi$ grows; $\\rho_{UL}$ and $\\rho^j_{UT}$ show persistent dipole structures in both impact-parameter and momentum space; $\\rho_{LL}$ starts as a quadrupole and develops a dipole-like momentum asymmetry; and $\\rho^i_{TU}$ and $\\rho^i_{TL}$ acquire multipole interference patterns with sign-changing regions. These patterns are shown in transverse impact-parameter space, transverse momentum space, and mixed $(b_x,k_y)$ space. The paper attributes the multipoles to spin-orbit correlations and to interference between light-front wave function components whose orbital angular momentum differs by one or two units.","pith_inferences":["The paper does not compare its rescaled Fourier convention against the alternative of Fourier transforming directly in $\\boldsymbol{\\Delta}_\\perp$; that comparison would show whether the reported multipoles survive under a different off-forward phase-space definition.","A natural next step is to apply the same skewness-dependent machinery to gluon Wigner distributions in the same dressed quark model; if the gluon patterns mimic the quark ones, the multipole mechanism is generic rather than quark-specific.","One could also test the paper's localization claim by computing the variance $\\langle \\mathbf{b}_\\perp^2\\rangle$ as a function of $\\xi$ from the plotted distributions; a monotonic decrease would confirm the squeezing, while a plateau would call the interpretation into question."],"forward_implications":["At nonzero $\\xi$, all nine leading-twist quark Wigner distributions lose the rotational symmetry of the forward limit, so any observable sensitive to off-forward phase space should see dipole or quadrupole lobes and negative regions.","The transverse localization that grows with $\\xi$ means large-skewness kinematics sharply reduce the overlap between initial and final state wave functions, redistributing the quark density into a narrower phase-space region.","The dipole in $\\rho_{UL}$ and the quadrupole in $\\rho_{LL}$ provide model-level signatures of spin-orbit correlation and quark orbital angular momentum that can be compared with other hadron models.","The momentum-space asymmetries, analogous to T-odd transverse-momentum-dependent effects, are enhanced by skewness, so off-forward kinematics amplify spin-momentum correlations.","Because the GTMDs carry explicit $\\xi$ factors such as $(1-\\xi^2)$ and $(x^2-\\xi^2)$, the model makes quantitative predictions for how each multipole moment of the Wigner distribution scales with skewness, testable in lattice QCD or in other light-front models."],"supporting_citations":[{"why":"Supplies the analytic quark GTMDs at nonzero skewness that the paper Fourier-transforms into the Wigner distributions.","marker":"[39]"},{"why":"Establishes the nonzero-skewness GTMD and Wigner distribution formalism in boost-invariant longitudinal space that this paper adopts.","marker":"[40]"},{"why":"Gave the zero-skewness quark Wigner distribution and orbital angular momentum results in the light-front dressed quark model that this work extends.","marker":"[31]"},{"why":"Set the Wigner distribution conventions and the connection to light-cone wave functions and orbital angular momentum used throughout.","marker":"[28]"},{"why":"Provides the GTMD decomposition of the quark-quark correlator used in Eqs. (13)-(15).","marker":"[25]"},{"why":"Shows how quark Wigner distributions are constructed from light-front wave functions, supplying the overlap technique used here.","marker":"[36]"}],"fun_headline_variants":["Skewness reshapes quark phase space into dipole and quadrupole patterns","Nonzero skewness exposes quark spin-orbit correlations in Wigner functions","Skewness turns quark Wigner distributions into multipole interference patterns","Dipole and quadrupole lobes appear in quark phase space under skewness"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The result stands on the convention, inherited from earlier off-forward studies, that the Fourier conjugate to the transverse impact parameter is $\\mathbf{D}_\\perp = \\boldsymbol{\\Delta}_\\perp/(1-\\xi^2)$ with a $(1-\\xi^2)^{-3/2}$ prefactor; if that is not the correct $\\xi$-generalization of the Wigner phase-space definition, every plotted pattern and localization trend changes.","fun_headline_variants_meta":{"raw":{"variants":["Skewness reshapes quark phase space into dipole and quadrupole patterns","Nonzero skewness exposes quark spin-orbit correlations in Wigner functions","Skewness turns quark Wigner distributions into multipole interference patterns","Dipole and quadrupole lobes appear in quark phase space under skewness"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000647,"raw_usage":{"total_tokens":2910,"prompt_tokens":820,"completion_tokens":2090,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":436,"completion_tokens_details":{"reasoning_tokens":2010}},"tokens_in":436,"tokens_out":2090,"duration_ms":16896,"temperature":1.0,"reasoning_tokens":2010,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T14:38:42.097688+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the nine Wigner distributions with $\\boldsymbol{\\Delta}_\\perp$ itself (no $(1-\\xi^2)$ rescaling in Eq. (9)) as the Fourier variable. If the dipole and quadrupole structures and the localization trend disappear or change sign as $\\xi$ grows, the paper's skewness effects are artifacts of the rescaling. A second check: integrate $\\rho_{UU}$ over $\\mathbf{b}_\\perp$ and $\\mathbf{k}_\\perp$ and verify the result is independent of $\\xi$; a $\\xi$-dependent normalization would show the distribution is not behaving as a phase-space density.","supporting_citations":[{"cited_title":"Gluon generalized TMDs and Wigner dis- tributions in boost invariant longitudinal space","cited_arxiv_id":null,"evidence_quote":"Supplies the analytic quark GTMDs at nonzero skewness that the paper Fourier-transforms into the Wigner distributions."},{"cited_title":"Quark generalized tmds at skewness and wigner distributions in boost invariant longitudinal space","cited_arxiv_id":null,"evidence_quote":"Establishes the nonzero-skewness GTMD and Wigner distribution formalism in boost-invariant longitudinal space that this paper adopts."},{"cited_title":"Wigner distributions for gluons in a light-front dressed quark model","cited_arxiv_id":null,"evidence_quote":"Gave the zero-skewness quark Wigner distribution and orbital angular momentum results in the light-front dressed quark model that this work extends."},{"cited_title":"Unified framework for generalized and transverse-momentum dependent parton distributions within a 3Q light-cone picture of the nucleon","cited_arxiv_id":null,"evidence_quote":"Set the Wigner distribution conventions and the connection to light-cone wave functions and orbital angular momentum used throughout."},{"cited_title":"Wigner distribution of sine-gordon and kink solitons","cited_arxiv_id":null,"evidence_quote":"Provides the GTMD decomposition of the quark-quark correlator used in Eqs. (13)-(15)."},{"cited_title":"Quark wigner distributions and spin-spin correlations","cited_arxiv_id":null,"evidence_quote":"Shows how quark Wigner distributions are constructed from light-front wave functions, supplying the overlap technique used here."}],"review_version":1}