{"id":"d34b316f-b8ff-4701-9f29-4c063638a081","arxiv_id":"2607.25001","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"low","formal_verification":"none","parameter_count":6,"one_line_summary":"KLS26 is an NNLO polarized PDF set from inclusive DIS that includes TMC, additive and multiplicative higher-twist terms, and positivity, with the largest NNLO shifts in the strange-quark helicity distribution.","lead":"Researchers produced an updated NNLO set of polarized parton distributions (KLS26) from world inclusive polarized DIS data, with target-mass and higher-twist corrections treated consistently. The grids matter for precision nucleon-spin studies and for planning Electron–Ion Collider measurements.","discovery_kind":"extension","skeptic_critique":{"model":"moonshotai/kimi-k3","headline":"The \"NNLO effects most visible in xΔs+\" attribution is confounded: the KLS26-vs-KLSS21 comparison changes αs (0.120→0.118), the positivity reference (MMHT14 NLO→MSHT20 NNLO), and the frozen βs+/βg values simultaneously with the perturbative order, and no single-factor control fit is shown.","rationale":"The reader's weakest assumption (HT functions on a fixed six-node grid absorbing power corrections and possibly biasing Δs+ in the W²≥4 GeV² region) is a genuine soft spot, but the paper partially inoculates itself: it runs two structurally different HT realizations, reports the Δχ²<3 indistinguishability explicitly, shows the HT coefficients are stable under freeing a3/a8 (Fig. 8), and frames HT values as effective and model-dependent rather than physical. The confound I identify is adjacent but distinct: it concerns not the HT modeling but the one-variable-at-a-time hygiene of the flagship NLO→NNLO comparison. I agree with the reader that Δs+ is the fragile sector; I disagree on which mechanism is least secure. On verdict: the PDF determination itself is competently executed and transparently documented (full parameter tables, Hessian moments, covariance ellipses, public LHAPDF grids with eigenvectors), and the descriptive claims are directly supported by the reported fits. The concern targets a single interpretive sentence and the abstract's causal framing, which a cheap control fit — trivially feasible since APFEL++ supports NLO with identical settings — would settle. That is a request for one additional comparison plot, not a reason to withhold acceptance, so I recommend UNCHANGED (ACCEPT), with the attribution claim softened or substantiated in a revision.","tokens_in":23127,"tokens_out":2748,"duration_ms":103118,"concrete_test":"Run one control fit identical to the baseline KLS26 additive-HT setup (same data, W²≥4 GeV² cut, HT node grid, frozen βs+/βg, MSHT20 positivity, αs=0.118) but with APFEL++ evolution and coefficient functions at NLO. Compare xΔs+ at Q²=2.5 GeV² from this NLO-updated fit against both KLS26-NNLO and KLSS21. If the NLO-updated Δs+ already exhibits most of the shift away from KLSS21, the \"NNLO most visible in Δs+\" claim is misattributed to perturbative order and should be re-worded as an input-update effect; if it sits on top of KLSS21, the NNLO attribution is confirmed. Optionally repeat toggling only αs (0.118↔0.120 at NNLO) to complete the factorization.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The descriptive part of the central claim (both HT fits give χ²/n.d.o.f. ≈ 0.76 with compatible PDFs; KLS26 differs from KLSS21 mainly in Δs+) is well supported by Tables I–III and Figs. 3–4. The interpretive part is weaker. In §V.A the paper asserts that \"the inclusion of the higher-order perturbative QCD corrections remains the dominant driver\" of the NLO→NNLO shifts, while noting in the same paragraph that KLSS21 used αs(M_Z²)=0.120 and MMHT14-based positivity, versus αs=0.118 and MSHT20-based positivity here. No fit isolates these factors. This matters most precisely in the channel the paper highlights: Δs+ is (i) normalized through the a8 sum rule, (ii) frozen at large x via βs+=17.99 chosen to track the MSHT20 unpolarized shape, and (iii) radiatively driven by a weakly constrained, positivity-bounded gluon. A ~1.7% change in αs alters the evolution length and the gluon→singlet feeding of Δs+; a different unpolarized reference set changes where the positivity boundary bites in exactly the s+ and g sectors; and βs+/βg were re-frozen to values guided by the new reference. Any of these could move xΔs+ toward less negative values at intermediate x independent of the NNLO coefficient functions. Because the observed Δs+ shift is the paper's signature \"NNLO effect,\" the attribution is load-bearing for the abstract's comparative claim. Note this does not threaten the KLS26 set as a determination — the internal consistency of the two HT fits, the free-a3/a8 stability tests, and the public LHAPDF grids are unaffected — it threatens the causal reading of Fig. 3.","agreement_with_reader":"partial"},"referee_report":{"model":"moonshotai/kimi-k3","summary":"The authors present an NNLO QCD fit of polarized PDFs (KLS26) to the world inclusive polarized DIS data, using APFEL++ evolution with NNLO coefficient functions and splitting functions, target-mass corrections, MSHT20-based positivity constraints, and two phenomenological higher-twist implementations — additive H(x)/Q² and multiplicative (1+C(x)/Q²) — parametrized on a common six-node x-grid with W² ≥ 4 GeV² and Q² ≥ 1 GeV² cuts that retain Jefferson Lab preasymptotic data. Both HT forms give essentially identical fit quality (χ²/n.d.o.f. ≈ 0.76, Table I) and compatible PDFs. Stability tests releasing the axial charges a3, a8 show negligible χ² change, robust Δu+/Δd+, and the expected large degradation of Δs+ (Figs. 6–7, Table III). Comparison with the authors' earlier KLSS21 NLO set shows the largest differences in xΔs+, moderate ones in Δg, and small ones in Δu+/Δd+; the manuscript attributes these primarily to the NNLO corrections. The resulting sets are provided in LHAPDF6 format with Hessian eigenvectors. The fit methodology is standard and, from what can be checked (moment-sum-rule consistency in Table III, partial χ² bookkeeping in Table I), internally consistent.","tokens_in":23616,"tokens_out":5851,"duration_ms":208253,"significance":"If the results hold, the paper delivers a useful and timely resource: an NNLO-accurate polarized PDF set with consistent TMC and HT treatment, released publicly in LHAPDF6 format with the full set of Hessian eigenvectors for four fit variants (additive/multiplicative HT, fixed/free axial charges). The side-by-side additive vs. multiplicative HT comparison and the a8–xΔs+ covariance-ellipse analysis (Fig. 7) are genuinely informative diagnostics, and the free-axial-charge cross-check is a falsifiable stability test rather than a tuned input. The set fills a niche (inclusive-DIS-only, relaxed W² cut, NNLO) complementary to BDSSV24, MAPPDFpol1.0 and NNPDFpol2.0, and is directly relevant to EIC-era spin physics.","major_comments":[{"comment":"§V.A, paragraph following the Fig. 3 discussion (and abstract): the text states that 'the inclusion of the higher-order perturbative QCD corrections remains the dominant driver behind the observed shifts' relative to KLSS21, while noting in the same paragraph that KLSS21 used αs(M_Z²)=0.120 and MMHT14-NLO-based positivity, versus αs=0.118 and MSHT20-NNLO-based positivity here (§III.C). In addition, βs+=17.99 and βg=2.1278 were re-frozen to values guided by the MSHT20 large-x shape (§III.C). The KLS26-vs-KLSS21 comparison therefore changes at least four ingredients simultaneously with the perturbative order, and no single-factor control fit is shown. This matters most in precisely the channel the paper highlights: xΔs+ is normalized through the a8 sum rule, radiatively fed by a positivity-bounded gluon, and pinned at large x by the re-frozen βs+. Any of these could shift Δs+ toward less n","section":"§V.A / abstract"},{"comment":"§V.B, reported χ² values for the free-{a3,a8} fits: for the additive HT case the total χ² *increases* from 504.41 (fixed axial charges, Table I) to 504.61 when a3 and a8 are released as free parameters. At a converged minimum, freeing two parameters cannot raise the minimum χ²; the multiplicative case (501.77→501.61) behaves as expected. Please clarify the origin of the additive-fit increase (minimization tolerance, a different local minimum, or some other difference between the two fits). The numerical claim that 'the overall fit quality changes only marginally' is unaffected in substance, but the direction of the change needs an explanation since the stability narrative of §V.B rests on these numbers.","section":"§V.B"}],"minor_comments":[{"comment":"The χ² function is never defined in the manuscript: the treatment of correlated systematic uncertainties and experimental normalizations, and the counting of free parameters entering n.d.o.f., are not stated (Table I reports only χ²/n.d.o.f. ≈ 0.76). Since all Hessian uncertainties derive from this χ², a brief defining equation and a comment on why χ²/n.d.o.f. is well below unity would make the error analysis self-contained rather than relying on Ref. [12].","section":"§III.D / Table I"},{"comment":"Both HT parametrizations share the same six-node grid and a pure 1/Q² form with no logarithmic Q² dependence (§II.B), so the additive-vs-multiplicative comparison may not span the full HT model uncertainty. Given that the relaxed W² ≥ 4 GeV² cut deliberately retains preasymptotic data, a short discussion of robustness — e.g., sensitivity to node placement or to a W² ≥ 6.5 GeV² variant — would strengthen the claim that HT systematics are quantified.","section":"§II.B / §IV"},{"comment":"Table II: the normalizations A_{u+} and A_{d+} are listed without uncertainties, presumably because they are fixed by the a3 and a8 sum rules, but they are not marked with (*) like βs+ and βg. Please indicate in the caption which parameters are constrained, fixed, or freely fitted.","section":"Table II"},{"comment":"Fig. 4: legends appear only in the top (xΔu+) panels; the xΔd+, xΔs+, and xΔg panels lack visible curve labels, making the multi-set comparison hard to read. Please add legends or a shared legend.","section":"Fig. 4"},{"comment":"Fig. 8: please specify what is plotted — the markers presumably show the effective HT coefficients at the node x-values (or binned averages), and the neutron multiplicative panel uses a very different vertical scale than the proton panel; clarifying units and the meaning of the points would help.","section":"Fig. 8"},{"comment":"Typographical: abstract, 'denoted asKLS26' (missing space); §II.B, 'This flexible method localized' → 'localizes'; §V.B, 'Figure 8 compare' → 'compares'. Ref. [21] cites the MAPPDFpol DIS-only sets as private communication — please update if a public reference becomes available.","section":"misc"}],"recommendation":"minor_revision","confidential_remarks":"This is a competent incremental extension of the authors' KLSS21/LSS framework line (a noticeable fraction of the citations are to that lineage, which is appropriate here but worth noting). The work is squarely within journal scope. My recommendation of minor revision rests on allowing the authors to resolve the attribution concern of Major Comment 1 by rewording; if the editor feels the \"dominant driver\" claim must be substantiated rather than withdrawn, the revision becomes major. I have no concerns about the integrity of the fits themselves — the moment-sum-rule arithmetic and cross-fit consistency checks I performed all hold."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"Punchline: KLS26 is a clean, usable NNLO polarized PDF determination from inclusive DIS only, with dual higher-twist modeling and public LHAPDF grids. That is the product. The comparative claim that NNLO is what moved Δs+ relative to KLSS21 is softer than the abstract suggests.\n\nWhat is actually new is the full NNLO upgrade of their KLSS21 line (APFEL++, NNLO coefficients and splitting functions), simultaneous additive and multiplicative HT on the same six-node grid, free-a3/a8 cross-checks, relaxed W²≥4 cuts that keep the JLab points, and released Hessian sets for all variants. Other NNLO polarized sets already exist (BDSSV, MAP, NNPDF), so this is not a first-to-market result; it is a controlled inclusive-DIS baseline with explicit HT systematics, which many global fits bury or cut away.\n\nThey do the phenomenology carefully. Table I shows both HT forms give χ²/ndf ≈ 0.76 on 682 points; PDFs stay compatible; free axial charges barely move total χ² but correctly blow up Δs+ and expose the a8 correlation (Fig. 7, Table III). TMC, positivity via MSHT20, and moments are documented. Citation pattern is normal for this subfield. Math and fit machinery look standard and solid.\n\nSoft spot, in proportion: the stress-test is right on the interpretive sentence in §V.A. Fig. 3 changes order, αs (0.120→0.118), positivity reference (MMHT14→MSHT20), and frozen βs+/βg together. No control fit isolates NNLO coefficients. That matters exactly where they advertise the biggest effect—Δs+—which is a8-normalized, positivity-bounded, and radiatively fed by a weakly constrained gluon. The descriptive claim (two HT fits agree; KLS26 differs from KLSS21 most in strange) is fine. Calling higher-order QCD the “dominant driver” is not demonstrated. That does not sink the set; it weakens one sentence of narrative.\n\nWho it is for: people who need an inclusive-DIS NNLO helicity baseline, HT uncertainty estimates, or EIC spin phenomenology without SIDIS FF baggage. Not for anyone expecting a resolution of the strange-quark puzzle or a full global NNLO spin fit.\n\nI would send it to peer review. Cite the grids if you work in this area; treat the pure-NNLO attribution of Fig. 3 with a grain of salt until someone runs the single-factor controls.","headline":"Usable NNLO polarized PDF release with honest dual-HT systematics; the NLO→NNLO Δs+ story is real as a difference of sets but over-attributed to pure NNLO.","tokens_in":24090,"tokens_out":651,"would_cite":true,"duration_ms":17406,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"A fully NNLO fit to inclusive polarized DIS data produces helicity PDFs that stay compatible whether higher-twist corrections are additive or multiplicative.","keywords":["polarized PDFs","NNLO QCD","higher-twist corrections","target-mass corrections","helicity distributions","inclusive DIS","nucleon spin","axial charges"],"falsifier":"A new high-precision polarized inclusive DIS data set at moderate Q² and large x that systematically prefers one higher-twist form over the other, or that forces the extracted strange-quark helicity outside the present uncertainty bands when the same NNLO plus TMC framework is reapplied.","tokens_in":23666,"feed_emoji":"⚛️","tokens_out":1042,"duration_ms":27674,"temperature":0.7,"pith_summary":"This paper extracts polarized parton distribution functions at next-to-next-to-leading order from the world set of inclusive polarized deep-inelastic scattering measurements. The new set, called KLS26, folds in target-mass corrections, positivity bounds, and two different models of higher-twist power corrections inside one consistent NNLO framework. Both the additive and multiplicative higher-twist versions describe the data equally well and return polarized PDFs that agree within uncertainties, even though the higher-twist coefficients themselves differ. Relative to the authors’ earlier NLO determination, the largest shift appears in the polarized strange-quark distribution, with moderate change in the gluon and smaller shifts in the up- and down-quark helicities. Freeing the nonsinglet axial charges mainly enlarges the strange-quark uncertainty, confirming that the light-quark sector is robust while the strange sector remains the most assumption-sensitive piece of the spin structure.","feed_headline":"NNLO spin PDFs stay stable under two higher-twist models","feed_subtitle":"Inclusive polarized DIS yields KLS26; strange quark shifts most, light quarks hold firm","key_machinery":"Dual higher-twist parametrizations (additive H(x)/Q² versus multiplicative C(x)/Q²) realized by linear interpolation on a fixed six-node x-grid, combined with NNLO polarized coefficient functions, DGLAP evolution, exact target-mass corrections, and leading-order positivity bounds against unpolarized PDFs.","core_discovery":"Within a fully NNLO treatment that includes target-mass corrections, positivity, and either additive or multiplicative higher-twist terms, the world inclusive polarized DIS data yield a stable helicity PDF set (KLS26) whose fit quality is essentially identical for both higher-twist forms and whose central distributions, especially for up and down quarks, change only modestly from the prior NLO result; the polarized strange quark shows the clearest NNLO-driven and axial-charge-driven shifts.","pith_inferences":["Because the two HT models agree on PDFs while disagreeing on HT coefficients, the data are mainly constraining the leading-twist sector; HT is still under-determined and will need dedicated low-Q² or higher-twist-sensitive observables.","The strong negative correlation between a8 and local xΔs+ implies that any independent lattice or hyperon-decay revision of a8 will translate almost linearly into a shift of the strange helicity at intermediate x.","Keeping only inclusive DIS leaves the gluon largely indirect; adding polarized jet or SIDIS data at the same NNLO-plus-HT standard would test whether the moderate gluon peak survives.","The stability of Δu+ and Δd+ under free axial charges suggests that the proton spin sum rule’s light-quark piece is already close to data-limited rather than theory-limited at this order."],"forward_implications":["KLS26 grids in LHAPDF format can be used directly for NNLO predictions of polarized observables without mixing orders.","Future spin analyses can treat the spread between additive and multiplicative higher-twist fits as a concrete estimate of residual power-correction uncertainty.","The polarized strange-quark distribution remains the dominant source of model dependence once axial charges are freed, guiding where new data or SIDIS input will matter most.","Relaxed kinematic cuts that retain Jefferson Lab large-x points become usable once TMC and HT are treated consistently at NNLO.","Nucleon spin decompositions that rely on first moments of Δs+ and Δg can now quote an NNLO baseline with controlled HT variation."],"fun_headline_variants":["KLS26: NNLO polarized PDFs stable across additive and multiplicative HT","Strange quark shifts most in NNLO helicity PDFs with TMC and HT","NNLO KLS26 set: up/down quarks steady, strange and gluon more sensitive","Two HT models give matching NNLO spin PDF fits from polarized DIS","Axial-charge freedom tweaks strange quark most in updated NNLO PDFs"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"The effective higher-twist functions, built from a fixed six-node grid with no extra logarithmic Q² dependence and with large-x exponents frozen by hand, are assumed to soak up all leftover power corrections without biasing the extracted helicity densities in the moderate-Q² region that is kept in the fit.","fun_headline_variants_meta":{"raw":{"variants":["KLS26: NNLO polarized PDFs stable across additive and multiplicative HT","Strange quark shifts most in NNLO helicity PDFs with TMC and HT","NNLO KLS26 set: up/down quarks steady, strange and gluon more sensitive","Two HT models give matching NNLO spin PDF fits from polarized DIS","Axial-charge freedom tweaks strange quark most in updated NNLO PDFs"]},"model":"grok-4.5","effort":"low","cost_usd":0.00432,"raw_usage":{"total_tokens":1315,"prompt_tokens":838,"num_sources_used":0,"completion_tokens":92,"cost_in_usd_ticks":43204000,"prompt_tokens_details":{"text_tokens":838,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":385,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":838,"tokens_out":92,"duration_ms":6613,"temperature":1.0,"reasoning_tokens":385,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-31T03:53:38.283336+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"A new high-precision polarized inclusive DIS data set at moderate Q² and large x that systematically prefers one higher-twist form over the other, or that forces the extracted strange-quark helicity outside the present uncertainty bands when the same NNLO plus TMC framework is reapplied.","supporting_citations":[],"review_version":1}