{"id":"4fa3772f-bad9-4758-8f85-e1d3a28abf38","arxiv_id":"2412.10727","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A new NLO and NNLO global QCD fit to HERA, Drell-Yan, and W/Z data yields proton PDFs, a strange-sea ratio near 1.07, and projections that EIC data would reduce gluon and alpha_s uncertainties.","lead":"This paper builds new maps of the proton's internal quarks and gluons from HERA, Tevatron, and LHC data, and projects how the future Electron-Ion Collider would make those maps sharper. A generalist might read it to see how precision collider data and a planned experiment constrain the strong force and the proton's strange quark content.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Reported strange-sea ratio rs=1.069 at x=0.023 is internally inconsistent with the Eq. (6) parameterization: for Fit D, xs/xdbar at that x equals rs*(1-x)^(Cs-Cdbar) ≈ 0.83, not 1.069.","rationale":"The reader identified parameterization flexibility as the weakest assumption. My read agrees that the parameterization is central, but I found a more specific and objective problem: the reported strange ratio is not what the stated parameterization yields at the claimed kinematic point. This is not a disagreement with external PDF sets; it is an internal inconsistency that can be checked directly from Table III. If the check confirms the discrepancy, the abstract, Section VIII, Table VIII, and Fig. 21 need correction, and the comparison with ATLAS/NNPDF/MMHT would need to be redone. The rest of the analysis—the global fit, chi2 values, and Hessian uncertainty procedure—appears standard, and the paper contains no machine-checked proofs or public grids, but the core fitting methodology is plausible. Because the error, if confirmed, is localized to the strange-quark result and its interpretation, it does not by itself invalidate the full PDF extraction; a conditional acceptance with a required correction remains appropriate. I therefore leave the reader's CONDITIONAL verdict unchanged, while noting that the specific correction needed is more concrete than a general request for more flexible parameterization.","tokens_in":48532,"tokens_out":8311,"duration_ms":78504,"concrete_test":"Compute the physical ratio from the Fit D best-fit parameters in Table III: r_s^phys = 1.069 * (0.977)^{16.4-5.68}, with uncertainties propagated from C_s, C_dbar, and rs. If r_s^phys differs from 1.069 by more than the quoted uncertainty, the published value is not the ratio at x=0.023. Independently, obtain the Fit D LHAPDF grid and evaluate x s(x,Q0^2)/x dbar(x,Q0^2) at x=0.023, Q0^2=1.9 GeV^2; compare with 1.069±0.053. A third check is to refit with the strange normalization explicitly defined as rs = s(x0)/dbar(x0) at x0=0.023, e.g., by absorbing the factor (1-x0)^{C_dbar-C_s} into A_sbar, and see whether the quoted central value and uncertainty change.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing concern is internal rather than a matter of PDF-phenomenology convention. The paper defines rs as the physical strange-to-down sea ratio at Q0^2=1.9 GeV^2 and x=0.023 (Eq. 5 and Section VIII), and quotes rs=1.069±0.053 for Fit D. But Eq. (6) parameterizes x sbar(x) = A_sbar * rs * x^{B_sbar} (1-x)^{C_s}, with A_sbar=A_dbar and B_sbar=B_dbar. Therefore the implied physical ratio is xs/xdbar = rs (1-x)^{C_s - C_dbar}. Using the Fit D Table III values C_s=16.4±1.5 and C_dbar=5.68±0.32, at x=0.023 the factor (1-x)^{C_s-C_dbar} ≈ 0.977^{10.7} ≈ 0.78, so the physical ratio is ≈0.83±0.05, not 1.069±0.053. This is a roughly 4-5 sigma discrepancy. Either the quoted rs is merely the un-evaluated fit parameter, in which case the abstract, Table VIII, and Fig. 21 mislabel it as the ratio at x=0.023, or the strange-quark normalization is not what Eq. (6) states. Because rs is one of the paper's headline results and is compared to ATLAS, NNPDF3.0, and MMHT14, this inconsistency directly undermines a central claim and raises the question of whether other parameterization-dependent quantities (e.g., alpha_s in Table III) are reported as intended.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript describes a global QCD analysis at NLO and NNLO using the xFitter framework. It fits combined HERA I+II inclusive DIS data, ATLAS and E866 Drell-Yan data, and W/Z production data from ATLAS, CMS, CDF, and D0 in four configurations (Fit A through Fit D), with Fit D as the nominal set. It reports Hessian PDF uncertainties, a strange-to-down sea ratio r_s, a strong-coupling extraction α_s(M_Z), comparisons with CT18, MSHT20, and NNPDF4.0, and projections based on EIC pseudodata and HERA jet/dijet data.","tokens_in":49086,"tokens_out":12500,"duration_ms":111392,"significance":"If the quantitative claims were sound, the paper would provide a useful independent PDF set and an illustration of the constraining power of W/Z and Drell-Yan data beyond HERA. The fits use a standard, widely validated framework, report reasonable total χ²/dof values (1.149–1.253), and are transparent about dataset selection. The Hessian uncertainty-reduction pattern across Fits A–D is plausible, and the comparison with established PDF sets is a useful sanity check. However, the reported r_s is internally inconsistent with the stated parameterization, the α_s values are strongly dataset-dependent without a stability analysis, and the EIC projections are in-sample forecasts. These issues affect the paper's headline quantitative results, so they need to be fixed before the PDF set can be endorsed as a precision release.","major_comments":[{"comment":"The quoted quantity r_s is not the physical ratio at x=0.023 under the stated parameterization. Equation (6) gives x s(x) = A_\\bar{d} r_s x^{B_\\bar{d}} (1-x)^{C_s}, and the text states A_\\bar{s}=A_\\bar{d}, B_\\bar{s}=B_\\bar{d}. Since x \\bar{d}(x)= A_\\bar{d} x^{B_\\bar{d}} (1-x)^{C_\\bar{d}}, the physical ratio defined in Eq. (5) is x s / x \\bar{d} = r_s (1-x)^{C_s - C_\\bar{d}}. Using the Fit D values C_s=16.4±1.5 and C_\\bar{d}=5.68±0.32 from Table III, at x=0.023 the factor is (0.977)^{10.72}≈0.78, so the physical ratio is ≈0.83±0.05, not 1.069±0.053. Either r_s is only a fit-normalization parameter, in which case the abstract, Table VIII, and Fig. 21 mislabel it as the ratio at x=0.023, or the strange-quark normalization is not what Eq. (6) states. Because r_s is a headline result compared with ATLAS, NNPDF3.0, and MMHT14, this inconsistency must be resolved by refitting or by correcting the definition and all reported values.","section":"Secs. IV A and VIII; Eq. (6); Table VIII"},{"comment":"The strong coupling constant extracted from the same parameterization varies from 0.13005±0.0010 (Fit B) to 0.1075±0.0030 (Fit C), and the nominal Fit D value 0.1128±0.0014 is about 3.7σ below the PDG 2024 world average of 0.1180. The quoted Hessian uncertainties clearly do not cover the dataset-selection spread; adding jet/dijet data changes α_s from 0.1128 to 0.1192 (Table VIII). The manuscript does not discuss these tensions or attempt a stability test, such as leaving one experiment out, varying Q_0^2, or relaxing the fixed C_g'=25. Without such a test, the claimed α_s precision from Fit D cannot be regarded as reliable, and the EIC-improvement statement in Sec. IX compares two uncertain baselines.","section":"Table III; Secs. V A and IX"},{"comment":"The EIC projections are in-sample. The pseudodata are generated from HERAPDF2.0NLO and HERAPDF2.0NNLO (Sec. VI) and are then fitted with the same HERAPDF-like functional form of Eq. (6), so the reported reductions in the gluon uncertainty and in α_s (from 0.0014 to 0.0008, and to 0.0003 with jets) are consequences of the assumed input rather than independent forecasts. No closure tests with alternative generator PDFs or alternative parameterizations are presented. The conclusions in Sec. XI that EIC data 'could play a crucial role in constraining α_s' should be rephrased as an illustrative projection, or substantiated by varying the pseudo-data generator and the fit parameterization.","section":"Sec. VI; Tables VI and VIII"},{"comment":"The Hessian uncertainty procedure is not fully specified. Equation (13) gives the error-propagation formula, but the manuscript never states the Δχ² or tolerance criterion used to define the eigenvector displacements, nor how the resulting uncertainties are normalized to the '68% CL' claimed in Sec. V D. Without this information, the central quantitative claim that Fit D uncertainties are smaller than those of CT18, MSHT20, and NNPDF4.0 cannot be reproduced or compared on an equal footing. This is a standard but mandatory detail for a Hessian PDF release.","section":"Sec. IV C and Sec. V D"}],"minor_comments":[{"comment":"The table contains a duplicated row for 'ATLAS W+ [48]' (two identical 15/11 entries). The text states that Fit D uses 1355 data points, and the totals in the table are consistent with that number, but the printed rows sum to 1366; the duplicate should be removed or corrected.","section":"Table II"},{"comment":"In the W/Z production rows, the ATLAS 7 TeV data are listed with 'L = 4.6 pb−1'; the unit should be fb−1 for the 4.6 fb−1 dataset referenced as [45].","section":"Table I"},{"comment":"The statement that PDF sets are available 'via email upon request' is not a satisfactory release mechanism for a PDF publication; the LHAPDF grids should be deposited with a permanent DOI or URL, and the exact Δχ² tolerance used for the eigenvector sets should accompany them.","section":"Availability of proton PDFs sets"},{"comment":"Several real-data χ² values worsen substantially when EIC pseudodata are added: ATLAS W/Z changes from 104.8/91 to 111.3/91, D0 W/Z from 67/51 to 77/51, and E866 Drell-Yan from 50/39 to 70/39. This tension is not discussed in Sec. VI and should be addressed.","section":"Table VI"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper is a competent, incremental global PDF fit: standard xFitter setup, HERAPDF-like parameterization, a clean ladder of datasets (HERA, then +DY, then +W/Z, then all), and Hessian uncertainties. The strange-sea result and EIC projections are the selling points. It deserves a serious referee, but I would not take the headline numbers at face value until two issues are addressed.\n\nFirst, the internal inconsistency in rs. The paper defines rs = (s+sbar)/(2 dbar) and quotes rs=1.069±0.053 for Fit D at Q^2=1.9 GeV^2 and x=0.023. But the parameterization in Eq. (6), with A_sbar=A_dbar and B_sbar=B_dbar, gives xs/xdbar = rs(1-x)^{Cs-Cdbar}. Using the Table III values Cs=16.4 and Cdbar=5.68, that factor is about 0.78 at x=0.023, so the actual ratio is ~0.83, not 1.069. Either the quoted rs is just the fit parameter and the text/Fig. 21 mislabel it, or the equation is not what was implemented. Either way, a headline result is currently inconsistent with the paper's own equations.\n\nSecond, the alpha_s spread. Across Fit A–D the central value moves from 0.1170 to 0.1300 to 0.1075 to 0.1128, with quoted uncertainties of 0.001–0.004. Fit D sits about 3.5 sigma below the world average, Fit B is ~10 sigma above. That spread is not discussed anywhere, and it suggests the datasets are pulling alpha_s in different directions (the CDF W asymmetry chi2/dof of 3.6 in Fit D hints at real tension). A reader cannot trust a single alpha_s extraction without an explanation.\n\nThe EIC pseudo-data section is a reasonable projection exercise, but since the pseudo-data are generated from HERAPDF2.0, the improved precision is partly baked in. That is standard for this literature, but should be flagged more explicitly. Also, the PDF sets are said to be in LHAPDF, but the text says they are available 'via email upon request.' That is not the same as a public release, and it makes independent checks harder.\n\nWhat the paper does well: it is honest about tensions in the data, the fit ladder is pedagogically clean, and the comparisons with CT18/MSHT20/NNPDF4.0 are useful. If the rs issue is fixed and the alpha_s spread is explained, this becomes a citable reference for EIC projections and strange-sea constraints.\n\nRecommendation: send to peer review. A good referee will force the authors to reconcile rs and to discuss the alpha_s instability.\n\nBest","headline":"Competent incremental PDF fit, but the headline strange ratio is internally inconsistent with the paper's own parameterization and alpha_s swings 0.1075–0.1300 across fits; worth refereeing, not citable as-is.","tokens_in":49554,"tokens_out":8261,"would_cite":false,"duration_ms":69245,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A new global QCD fit to HERA DIS, Drell-Yan, and W/Z data yields NLO and NNLO proton PDFs with reduced uncertainties, a strange-sea ratio of 1.069 ± 0.053, and a strong coupling of 0.1128 ± 0.0014.","keywords":["parton distribution functions","global QCD analysis","HERA deep inelastic scattering","Drell-Yan production","W/Z boson production","strange sea","strong coupling constant","Electron-Ion Collider"],"falsifier":"Refit the same data with a more flexible parameterization—freeing $C_{g'}$ and the strange-sea powers, and dropping the equality between $\\bar{d}$ and $\\bar{u}$ low-$x$ behavior—and check whether $r_s$ moves outside $1.069 \\pm 0.053$ and $\\alpha_s(M_Z)$ outside $0.1128 \\pm 0.0014$; a shift beyond those bands would show that the quoted uncertainties are understated. A simpler check: the nominal $\\alpha_s$ must be compared with the world average; if the difference exceeds the quoted error, the fit is biasing the coupling.","tokens_in":48369,"feed_emoji":"🎯","tokens_out":17336,"duration_ms":132065,"temperature":0.7,"pith_summary":"This paper attempts to establish that a global QCD fit combining the combined HERA deep-inelastic scattering data with Drell-Yan pair-production data and W/Z boson production data from the LHC and Tevatron yields new NLO and NNLO proton PDFs whose uncertainties are meaningfully reduced. In the nominal NNLO fit, the strange-to-down sea ratio is $r_s = 1.069 \\pm 0.053$ at $Q^2 = 1.9$ GeV$^2$ and $x = 0.023$, and the strong coupling is $\\alpha_s(M_Z) = 0.1128 \\pm 0.0014$. The paper further claims that simulated inclusive DIS data from the future Electron-Ion Collider, especially when supplemented by HERA jet and dijet data, would tighten $\\alpha_s(M_Z)$ to $0.1183 \\pm 0.0003$ and reduce gluon uncertainties for $x \\le 0.2$. If these results hold, the released PDF grids give an independent, Hessian-based set of proton PDFs for precision analyses at the LHC and the EIC.","feed_headline":"New proton PDF fit pins down strange sea and shrinks errors","feed_subtitle":"Nominal NNLO fit: r_s = 1.069 ± 0.053, α_s = 0.1128 ± 0.0014; EIC plus jets cut α_s error to ±0.0003.","key_machinery":"The engine of the analysis is the input parameterization of Eq. (6) at the starting scale $Q_0^2 = 1.9$ GeV$^2$, evolved with DGLAP equations and fitted with the Hessian method for uncertainty propagation. The parameterization uses six independent distributions—$xu_v$, $xd_v$, $xg$, $x\\bar{u}$, $x\\bar{d}$, and $xs = x\\bar{s}$—with the simplifying assumptions $A_{\\bar{d}}=A_{\\bar{u}}$, $B_{\\bar{d}}=B_{\\bar{u}}$, $s=\\bar{s}$, $A_s=A_{\\bar{d}}$, $B_s=B_{\\bar{d}}$, and a fixed coefficient $C_{g'}=25$; the strange-to-down ratio $r_s$ and the strong coupling $\\alpha_s(M_Z)$ are free parameters of the fit. The complementarity of the datasets is the operative mechanism: DIS fixes the overall quark content, Drell-Yan data separate the sea quark flavors, and W/Z rapidity distributions decompose valence and sea contributions, in particular pinning down the strange quark density.","core_discovery":"The central discovery is a set of NLO and NNLO proton PDFs extracted from a global QCD analysis of the combined HERA I+II DIS data together with Drell-Yan pair production and W/Z boson production data from the LHC and Tevatron. The nominal fit yields an unsuppressed strange sea, $r_s = 1.069 \\pm 0.053$ at $Q^2 = 1.9$ GeV$^2$ and $x = 0.023$, and $\\alpha_s(M_Z) = 0.1128 \\pm 0.0014$ at NNLO, with the Hessian method providing the uncertainty sets. The same analysis projects that the EIC will reduce the $\\alpha_s$ uncertainty to $\\pm 0.0008$, and that adding HERA jet/dijet data on top of EIC data will bring it to $\\pm 0.0003$ while shrinking gluon PDF uncertainties for $x \\le 0.2$. The resulting PDFs and their eigenvector variations are released in standard grid format so that the improved precision can be used directly in collider predictions.","pith_inferences":["The four fits in Table III produce strongly dataset-dependent values of $\\alpha_s(M_Z)$, from $0.13005 \\pm 0.001$ (Fit B) to $0.1075 \\pm 0.0030$ (Fit C); we infer that the parameterization, or the treatment of dataset-specific systematics, is imprinting on the coupling, and a more flexible functional form could shift the nominal value beyond the quoted $\\pm 0.0014$.","If $r_s \\approx 1.07$ survives a parameterization-free fit, non-perturbative mechanisms that usually suppress strangeness in the nucleon sea would need to be revisited, because the data would no longer require such suppression.","The projected $\\alpha_s$ precision of $\\pm 0.0003$ from EIC-plus-jet pseudodata depends on the assumed smearing, normalization uncertainties, and experimental systematics; real EIC data may not yield the same precision if these assumptions differ.","Because the sea symmetry assumptions $A_{\\bar{d}}=A_{\\bar{u}}$, $A_s=A_{\\bar{d}}$, and $B_s=B_{\\bar{d}}$ are imposed rather than fitted, freeing these parameters in a future analysis would test whether the central value of $r_s$ is stable or a consequence of the assumed sea flavor symmetry."],"forward_implications":["The released NLO and NNLO PDF grids, complete with Hessian eigenvector sets, provide an independent input for precision calculations of LHC processes such as W/Z production, Higgs production, and new-physics searches.","A strange-sea ratio near unity at low $x$ implies that strange quarks are not suppressed relative to down quarks, which directly affects predictions for processes such as $W+c$ and $Z+c$ production that depend on the strange density.","Adding simulated EIC inclusive DIS data to the fit lowers the uncertainty on $\\alpha_s(M_Z)$ from $\\pm 0.0014$ to $\\pm 0.0008$, and adding HERA jet/dijet data on top further reduces it to $\\pm 0.0003$, quantifying the future gain in precision.","The better fit quality at NNLO than at NLO, especially for the W/Z data, supports the use of NNLO theory for electroweak precision measurements at the LHC.","Gluon uncertainties are reduced for $x \\le 0.2$ when EIC and jet/dijet data are included, which benefits gluon-fusion Higgs production and searches for high-mass states."],"supporting_citations":[{"why":"Provides the combined HERA I+II DIS cross-section data that form the baseline of all fits in the analysis.","marker":"[44]"},{"why":"Supplies the LHC W/Z production cross sections whose rapidity dependence drives the strange-to-down ratio $r_s$.","marker":"[45]"},{"why":"Provides the proton-deuteron Drell-Yan data that constrain the sea quark flavor asymmetry.","marker":"[30]"},{"why":"Low-mass dilepton Drell-Yan data are used to constrain the sea quark distributions at low $x$.","marker":"[46]"},{"why":"High-mass dilepton Drell-Yan data extend the quark sensitivity to larger $x$.","marker":"[47]"},{"why":"W/Z cross-section data are used specifically to determine the strange quark density, informing the $r_s$ parameter.","marker":"[48]"},{"why":"Provides the input parameterization and starting-scale conventions adopted for the PDFs in the fit.","marker":"[66]"},{"why":"The Hessian formalism is used to propagate parameter uncertainties into the reported PDF eigenvector sets.","marker":"[69]"}],"fun_headline_variants":["Global QCD fit sharpens proton PDFs and α_s","Strange sea ratio r_s = 1.069 from new NNLO fit","EIC projected to slash α_s uncertainty to ±0.0008","New proton PDFs: r_s = 1.069, α_s = 0.1128 ± 0.0014","Jets plus EIC cut α_s error to ±0.0003"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the input functional form for the parton distributions, with fixed $C_{g'}=25$ and with the up, down, and strange sea quarks forced to share the same small-$x$ power behavior, is flexible enough that the extracted $r_s$ and $\\alpha_s(M_Z)$ are dictated by the data rather than by the parameterization.","fun_headline_variants_meta":{"raw":{"variants":["Global QCD fit sharpens proton PDFs and α_s","Strange sea ratio r_s = 1.069 from new NNLO fit","EIC projected to slash α_s uncertainty to ±0.0008","New proton PDFs: r_s = 1.069, α_s = 0.1128 ± 0.0014","Jets plus EIC cut α_s error to ±0.0003"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000329,"raw_usage":{"total_tokens":1893,"prompt_tokens":1061,"completion_tokens":832,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":677,"completion_tokens_details":{"reasoning_tokens":722}},"tokens_in":677,"tokens_out":832,"duration_ms":6641,"temperature":1.0,"reasoning_tokens":722,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T15:40:48.024022+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Refit the same data with a more flexible parameterization—freeing $C_{g'}$ and the strange-sea powers, and dropping the equality between $\\bar{d}$ and $\\bar{u}$ low-$x$ behavior—and check whether $r_s$ moves outside $1.069 \\pm 0.053$ and $\\alpha_s(M_Z)$ outside $0.1128 \\pm 0.0014$; a shift beyond those bands would show that the quoted uncertainties are understated. A simpler check: the nominal $\\alpha_s$ must be compared with the world average; if the difference exceeds the quoted error, the fit is biasing the coupling.","supporting_citations":[],"review_version":1}