{"id":"d2053a2b-03a7-4d67-acd0-fb209acfb2fc","arxiv_id":"2507.11177","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"The VS24 GPD ansatz combined with JHA21 N3LO PDFs gives a reasonable reproduction of nucleon form factors and a proton charge radius of 0.853 fm, but most outputs come from parameters fitted to the same data.","lead":"This paper computes proton and neutron elastic scattering form factors using a specific GPD model, the VS24 ansatz, together with a modern N3LO set of quark distribution functions (JHA21). It compares the results with electron scattering data and derives gravitational form factors and the proton charge radius.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed superiority of VS24+JHA21 over VS24+KKA10 rests on visual comparison without a quantitative fit metric, and the printed radius formula appears to omit a term from the derivative.","rationale":"I read the paper in good faith as a phenomenological parametrization exercise: it combines existing PDFs with a flexible ansatz, fits flavor-separated form factors, and derives gravitational form factors and radii. The central claim, however, is comparative and is asserted from visual inspection. The absence of a quantitative measure is a genuine gap because the same ansatz is fitted separately for each PDF, so a visual difference could be within the parameter uncertainties. The reader's weakest_assumption concerns the flexibility of the VS24 functional form; my concern is adjacent but distinct: even if the functional form is adequate, the evidence for preferring JHA21 over KKA10 is not quantified. I also flag that Eqs. (25) and (36) contain apparent errors that make the numerical results unreproducible as printed. These issues do not by themselves show the physics is wrong—the figures may have been produced with correct formulas—but they justify the conditional verdict already given, requiring quantitative fit quality measures and corrected equations before the claims can be accepted. I therefore leave the reader's CONDITIONAL verdict unchanged.","tokens_in":13197,"tokens_out":9767,"duration_ms":117294,"concrete_test":"Recompute chi-square per degree of freedom for both the VS24+KKA10 and VS24+JHA21 fits against the same experimental F_1^{u,d} and F_2^{u,d} datasets (refs. 44-46), using the reported uncertainties and the same fitted parameter sets from Table I. If Δχ²/dof is not meaningfully negative for JHA21 (e.g., |Δχ²/dof| < 1), the superiority claim is unsupported. Separately, recompute the proton charge radius using the full t-derivative of the VS24 form, namely dF_1^p/dt at t=0 = ∫_0^1 dx (e_u u_v(x) + e_d d_v(x))[-α'''(1-x)^γ ln(x) - β b x^{m'}], then r_E,p from Eq. (35), and compare with 0.853 fm; if the value shifts by more than a few percent, the radius result is an artifact of the printed formula.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is that the VS24 ansatz combined with JHA21 PDFs shows better agreement with flavor-separated form factor data than with KKA10 PDFs, based on Figs. 3-4 and 6. Yet no chi-square, likelihood, or other goodness-of-fit measure is reported, and the five fitted parameters in Table I are tuned separately to the same datasets for each PDF. Without a quantitative comparison, 'better agreement' is a visual impression and cannot be distinguished from parameter noise or overfitting. This is load-bearing because every downstream result—the gravitational form factors A(t), B(t), and the proton charge radius—inherits the fitted functional form. The manuscript also contains internal inconsistencies that block reproduction: Eq. (25) for the neutron Dirac form factor has the wrong charge/Pauli structure (e_d F_2^u + e_d F_2^d instead of e_d F_1^u + e_u F_1^d), and Eq. (36) evaluates β x^{m'} ln(1-bt) at t=0, where it vanishes, so the printed radius formula omits the -β b x^{m'} term that should come from differentiating ln(1-bt). If r_E,p = 0.853 fm was computed using Eq. (36) literally, it is not the correct slope of F_1^p(t).","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a flavor-separated parametrization of zero-skewness unpolarized quark GPDs H and E using the VS24 ansatz, combined with several PDF sets (mainly KKA10 and JHA21 at N3LO). The authors compute nucleon electromagnetic form factors F1, F2 and Sachs form factors GE, GM, compare them with elastic scattering data, then derive gravitational form factors A(t), B(t) and the proton electric charge radius. The central quantitative claim is that VS24 combined with JHA21 PDFs shows better agreement with electron-proton scattering form factor data than VS24 combined with KKA10 PDFs, based on visual comparison of Figs. 3-6; the reported proton charge radius is 0.853154 fm, compared with the experimental 0.831 fm.","tokens_in":13455,"tokens_out":10765,"duration_ms":126510,"significance":"If the parametrization were quantitatively validated, it would provide a simple, analytically tractable flavor-separated description of nucleon electromagnetic and gravitational form factors, with a proton radius in the range of modern measurements. The paper gives no machine-checked proofs or public code; its numerical claims rest on standard integrals and fits. The gravitational form factor results are model outputs rather than independent predictions, and the radius is a derived consequence of the fitted parameters. The potential usefulness of the parametrization is undermined by the absence of any goodness-of-fit metric, by the internal inconsistencies in the printed formulas, and by the fact that the parameters are fitted to the same data used for the comparison.","major_comments":[{"comment":"The central claim that VS24+JHA21 shows better agreement with form factor data than VS24+KKA10 is supported only by visual inspection. No chi-square, likelihood, or other goodness-of-fit statistic is reported for any ansatz or PDF set. Moreover, the parameters in Table I are fitted to the same datasets (Refs. [44-46]) that are shown in the comparison figures, so the agreement is partly built in. Provide quantitative fit metrics, such as chi-square per degree of freedom, for each combination, and state clearly which data points were used in the fits.","section":"Section III, Table I and Figs. 3-6"},{"comment":"The printed formulas for the Dirac mean squared radii are not the correct derivatives of the VS24 ansatz. Differentiating Eq. (22) at t=0 yields an additional term -beta b x^{m'} from the derivative of ln(1-bt), and the factor -6 should be applied to the entire expression including that term. As written, the second term in Eqs. (36)-(37) vanishes at t=0 because ln(1-bt)|_{t=0}=0, and the reported value r_E,p = 0.853154 fm cannot be reproduced from the printed formula. Correct the equations and verify that the numerical radius was computed with the correct slope of F_1^p(t).","section":"Section V, Eqs. (36)-(37)"},{"comment":"The neutron Dirac form factor is written as F_1^n(t) = e_d F_2^u(t) + e_d F_2^d(t). This expression uses the Pauli form factors F_2 rather than the Dirac form factors F_1, and both terms carry the same charge weight; the correct relation is F_1^n = e_u F_1^d + e_d F_1^u (with isospin-symmetric identification of quark form factors), which satisfies F_1^n(0)=0. This equation is load-bearing for the neutron form factor results in Figs. 5 and 6; state whether the corrected expression was actually used in the numerical calculation.","section":"Section III, Eq. (25)"},{"comment":"The paper states 'where t = Q^2 is the four-momentum transfer of the virtual photon'. In the space-like region t is negative, and the ansatz in Eqs. (22)-(23) only has the physically expected t-dependence if t is negative. The sign convention is essential for the behavior of the integrand as x -> 0 and for the reported slopes. Clarify the convention consistently: in Eqs. (8)-(11), (22)-(23), (31)-(34), and (35)-(37), and in the definition of tau in Eq. (28).","section":"Section III, Eq. (28) and the sign of t"}],"minor_comments":[{"comment":"The parameter used in the VS24 ansatz is called alpha''' in Eq. (22) but alpha'' in Table I; use consistent notation.","section":"Table I and Eq. (22)"},{"comment":"The text says 'F1 and F2 are the Pauli and Dirac form factors, respectively'; this is reversed. F1 is the Dirac form factor and F2 is the Pauli form factor.","section":"Conclusion, paragraph 2"},{"comment":"There are numerous typographical errors, including 'gravitional', 'INTRODUCTON', 'Ansatsez', 'T able', 'GP,n', and a duplicated 'As these figures show' in Section VI. A careful proofreading is needed.","section":"Throughout"},{"comment":"The value G^n_E(0)=3.2 x 10^-13 is reported with no meaningful precision; since the symmetry requires G^n_E(0)=0, report 0 or a physically meaningful upper bound.","section":"Table II"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is an incremental application of the authors' own VS24 ansatz to another PDF set. The main scientific claim is not supported by a quantitative fit comparison, and there are serious inconsistencies in the printed formulas (Eq. (25), Eqs. (36)-(37), and the sign of t). These issues are fixable in principle, but the authors should be asked to supply the missing fit metrics and to correct the equations. The paper also contains a substantial number of typos, suggesting the manuscript was not thoroughly edited. I would not recommend acceptance before these points are addressed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. The paper is an incremental re-run of the authors' own VS24 GPD ansatz with the JHA21 N3LO PDF set instead of KKA10, and it claims better agreement with elastic nucleon form factor data. The claim is based on eye-balling figures; no fit quality metric is reported, and the parameters were fitted to the very data being compared. Separately, two equations in the manuscript have concrete errors.\n\nThe paper does have real value. It is transparent about the formalism, gives a table of fitted parameters with standard errors, compares five ansatze and seven PDFs, and includes a lattice QCD curve (MMNS) for the gravitational form factor Au+d(t). The specific VS24+JHA21 combination is new, and the Au+d(0) values across PDFs cluster near 0.45, which is reassuring.\n\nThe soft spots are proportionate to the claims. The headline improvement of JHA21 over KKA10 is not quantified: no chi-square, no likelihood, no propagated uncertainties. Since the five parameters in Table I are adjusted to the same datasets that appear in Figs. 3-6, the visual agreement is partly built into the fit. That is not fatal for a parametrization study, but it means the paper hasn't shown what it claims until a quantitative comparison is added. More concretely, Eq. (25) for the neutron Dirac form factor is wrong as printed: it uses the Pauli-type F2 instead of F1, and the charges are inconsistent. And Eqs. (36)-(37) for the Dirac radius evaluate β x^{m'} ln(1-bt) at t=0, where it vanishes; the derivative should yield a -β b x^{m'} term. If the 0.853 fm radius was computed from the printed formula, it is not the correct slope of F1^p(t). These are not minor typos; they affect a definition and a reported result, though they are easy to fix.\n\nOverall: this is a legitimate but modest phenomenological study. I would not cite it as a major reference, but it deserves a serious referee. The referee should require a quantitative fit metric, corrected equations, and uncertainty propagation on the radius and gravitational form factors. Without those, the central claim is not established.","headline":"A transparent but incremental GPD parametrization paper whose central claim rests on visual comparison; two concrete equation errors need fixing before it can be trusted.","tokens_in":14011,"tokens_out":3537,"would_cite":false,"duration_ms":39809,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Combining the VS24 parametrization with JHA21 quark distributions reproduces measured nucleon form factors and gives a proton radius of 0.853 fm.","keywords":["generalized parton distributions","zero skewness","nucleon electromagnetic form factors","gravitational form factors","parton distribution functions","proton electric radius","flavor separation","VS24 ansatz"],"falsifier":"Measure the proton gravitational form factor $A(t)$ at several nonzero $-t$ values with better precision than current lattice results and compare with the VS24+JHA21 curve: the model predicts a specific slope for $A_{u+d}(t)$, and a systematic deviation would falsify the parametrization. A cheaper out-of-sample check is a precise measurement of the neutron electric form factor $G_E^n$ at $-t>5\\,\\mathrm{GeV}^2$, where the VS24 curves are not constrained by the fit data.","tokens_in":12975,"feed_emoji":"⚛️","tokens_out":11926,"duration_ms":124544,"temperature":0.7,"pith_summary":"This paper aims to establish that the zero-skewness unpolarized generalized parton distributions of the nucleon can be parametrized by the VS24 ansatz, and that using the JHA21 parton distribution functions at N3LO as input produces better agreement with measured electromagnetic form factors than other parametrizations. From that parametrization the authors derive flavor-separated Dirac and Pauli form factors for up and down quarks, the proton and neutron Sachs form factors, and the first-$x$-moment gravitational form factors $A_q(t)$ and $B_q(t)$ that no experiment has directly measured. They obtain a proton electric radius of $0.853\\,\\mathrm{fm}$, compatible with the experimentally determined $0.831\\,\\mathrm{fm}$, and find that the total valence-quark contribution to $A(t)$ at zero momentum transfer is nearly independent of the PDF set, around $0.43$--$0.46$. A sympathetic reading is that the paper provides a single functional family that connects deep-inelastic parton distributions to elastic electron scattering and, by extension, to the nucleon's mass and angular-momentum distributions, which is why the claim matters.","feed_headline":"Proton radius from GPD fit lands at 0.853 fm","feed_subtitle":"It matches electron-scattering data and yields flavor-separated gravitational form factors.","key_machinery":"The machine that carries the argument is the VS24 ansatz, a five-parameter exponential $t$-dependence for zero-skewness GPDs: $H^q(x,t)=q_v(x)\\exp[-\\alpha''' t(1-x)^\\gamma\\ln x+\\beta x^{m'}\\ln(1-bt)]$ and $E^q(x,t)=\\varepsilon^q(x)\\exp[-\\alpha''' t(1-x)^\\gamma\\ln x+\\beta x^{m'}\\ln(1-bt)]$, where $\\varepsilon^q(x)=(\\kappa_q/N_q)(1-x)^{\\eta_q}q_v(x)$ is the Pauli-type ansatz of Eq. (14). The parameters $\\alpha'''$, $\\beta$, $\\gamma$, $\\eta_u$, and $\\eta_d$ are fitted to elastic form factor data with $b=2$ and $m'=0.65$ fixed. Inserting these GPDs into the sum rules $F_1(t)=\\sum_q e_q\\int_0^1 dx\\,H^q(x,t)$ and $F_2(t)=\\sum_q e_q\\int_0^1 dx\\,E^q(x,t)$ yields the electromagnetic form factors, and the first $x$-moments $A_q(t)=\\int_0^1 dx\\,xH^q(x,t)$ and $B_q(t)=\\int_0^1 dx\\,xE^q(x,t)$ yield the gravitational form factors. Thus the one functional family carries the full chain from PDF input to electron-scattering observables to mass distributions.","core_discovery":"The paper's central claim is that the VS24 exponential ansatz, Eqs. (22)--(23), together with the JHA21 N3LO PDFs, yields the flavor-separated zero-skewness GPDs $H^q$ and $E^q$ whose sum-rule integrals reproduce the nucleon electromagnetic form factors more closely than the same ansatz with KKA10 PDFs or than the other ansatz families considered. This is demonstrated by comparing quark-level and nucleon-level Dirac and Pauli form factors with extracted experimental points from electron-proton inelastic scattering over $-t$ from 0 to 5 GeV$^2$. The same parametrization gives gravitational form factors $A_q(t)$ and $B_q(t)$: their flavor-summed value at $t=0$ is $A_{u+d}(0)\\approx0.426$ with JHA21 inputs, within a few percent of the values obtained with six other PDF sets, and the $t$-dependence is qualitatively consistent with lattice QCD. It also yields a proton electric radius $r_{E,p}=0.853\\,\\mathrm{fm}$, which the authors place next to the experimental value $0.831\\,\\mathrm{fm}$.","pith_inferences":["Editorial extension: applying the same VS24 machinery to gluon GPDs at zero skewness would test whether the exponential $t$-dependence is a general feature of the nucleon or an artifact of the valence-quark fit; a gluon version is not derived in the paper.","Editorial extension: the paper does not isolate whether the $0.853$ fm radius reflects the ansatz or the input PDFs; refitting at fixed PDF while varying the ansatz, and vice versa, would separate those sources.","Editorial extension: the neutron electric form factor, which the paper finds particularly well described, is the cleanest out-of-sample discriminator; a future precise $G_E^n$ point at $-t>5$ GeV$^2$ would test the parametrization where it was not fitted."],"forward_implications":["The flavor-separated Dirac and Pauli form factors $F_1^q(t)$ and $F_2^q(t)$ from VS24+JHA21 provide ready inputs for impact-parameter-space pictures of up- and down-quark charge and magnetization distributions in the proton.","The predicted gravitational form factors $A_q(t)$ and $B_q(t)$ for individual flavors give concrete targets for future lattice QCD calculations and for any experimental program that can access the energy-momentum tensor of the nucleon.","The computed proton electric radius $r_{E,p}=0.853\\,\\mathrm{fm}$ is close to the experimental $0.831\\,\\mathrm{fm}$, supporting the VS24 parametrization's low-$|t|$ behavior.","The near-constancy of $A_{u+d}(0)\\approx0.43$--$0.46$ across seven PDF sets indicates that the valence-quark mass fraction at zero momentum transfer is stable, while the slope with $t$ does depend on the PDF choice."],"supporting_citations":[{"why":"introduces the VS24 ansatz whose exponential t-dependence is the functional family tested here","marker":"[22]"},{"why":"supplies the JHA21 N3LO parton distribution functions used as the input for the GPDs","marker":"[24, 25]"},{"why":"supplies the KKA10 N3LO PDFs used as the comparison baseline throughout the paper","marker":"[23]"},{"why":"provides the sum rules linking GPDs to form factors and the Pauli-type ansatz for the E GPD","marker":"[6]"},{"why":"one of the three experimental data sets used to extract and compare the quark form factors","marker":"[44]"},{"why":"second experimental data set used for the form-factor comparison","marker":"[45]"},{"why":"third experimental data set used for the form-factor comparison","marker":"[46]"},{"why":"supplies the lattice QCD gravitational form factor results against which A_{u+d}(t) is compared","marker":"[52]"},{"why":"provides the experimental proton electric radius 0.831 fm against which the model's 0.853 fm is judged","marker":"[56]"}],"fun_headline_variants":["GPD fit places proton radius at 0.853 fm","Proton radius 0.853 fm from zero-skewness GPDs","Flavor-separated form factors from VS24 GPD ansatz","GPD parametrization matches electron scattering data","Proton electric radius from GPDs: 0.853 fm"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The result stands or falls with the assumption that the VS24 exponential functional form, once its free parameters are tuned to the data, is flexible enough to represent the true zero-skewness GPDs over the whole fitted range of momentum transfer; if the true GPDs have a different shape, the agreement with the measured form factors is an artifact of curve fitting, and the derived gravitational form factors inherit the bias.","fun_headline_variants_meta":{"raw":{"variants":["GPD fit places proton radius at 0.853 fm","Proton radius 0.853 fm from zero-skewness GPDs","Flavor-separated form factors from VS24 GPD ansatz","GPD parametrization matches electron scattering data","Proton electric radius from GPDs: 0.853 fm"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000659,"raw_usage":{"total_tokens":2997,"prompt_tokens":913,"completion_tokens":2084,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":529,"completion_tokens_details":{"reasoning_tokens":1993}},"tokens_in":529,"tokens_out":2084,"duration_ms":16121,"temperature":1.0,"reasoning_tokens":1993,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T17:14:42.569069+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the proton gravitational form factor $A(t)$ at several nonzero $-t$ values with better precision than current lattice results and compare with the VS24+JHA21 curve: the model predicts a specific slope for $A_{u+d}(t)$, and a systematic deviation would falsify the parametrization. A cheaper out-of-sample check is a precise measurement of the neutron electric form factor $G_E^n$ at $-t>5\\,\\mathrm{GeV}^2$, where the VS24 curves are not constrained by the fit data.","supporting_citations":[{"cited_title":"Masjuan, E","cited_arxiv_id":null,"evidence_quote":"provides the sum rules linking GPDs to form factors and the Pauli-type ansatz for the E GPD"},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"second experimental data set used for the form-factor comparison"},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies the lattice QCD gravitational form factor results against which A_{u+d}(t) is compared"},{"cited_title":"Pagels, Phys","cited_arxiv_id":null,"evidence_quote":"provides the experimental proton electric radius 0.831 fm against which the model's 0.853 fm is judged"}],"review_version":1}