{"id":"e2117194-d4da-4335-b98a-90e3b622197e","arxiv_id":"2505.10998","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Using large-volume lattice QCD at physical quark masses, the PACS Collaboration shows that a new excited-state subtraction makes the nucleon pseudoscalar and induced-pseudoscalar form factors consistent with pion-pole dominance up to q^2 ~ 0.42 GeV^2.","lead":"This paper uses large-scale lattice QCD simulations to compute the weak-interaction form factors of the nucleon and checks whether low-energy rules like pion-pole dominance hold at physical quark masses. It matters because neutrino oscillation experiments need these form factors to reconstruct neutrino energies.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central claim rests on the unvalidated single-πN-state subtraction in Eq. (43); without a multi-state or variational check, the observed GGT/PPD agreement could be an artifact of the method.","rationale":"The reader identified the single-πN assumption in Eq. (43) as the weakest assumption, and my review confirms this is the most load-bearing concern. The central claim—that the lattice data reproduce GGT and PPD after subtraction—cannot be established without verifying that the subtraction removes all relevant excited-state contamination. The paper's internal consistency is good: the traditional analysis shows clear deviations from unity that decrease with increasing tsep, and the new analysis brings the ratios to unity, which is suggestive. However, this behavior is exactly what would be expected if the subtraction model partially absorbs the contamination, regardless of whether the ground-state matrix elements truly satisfy the relations. The circularity issue (GP extraction uses AWT) further weakens the independence of the GGT and R4 tests. The paper's strengths include large physical-volume ensembles, physical quark masses, multi-tsep checks for gA, and agreement of g*_P and gπNN with experiments; these give credibility to the analysis, but they do not substitute for a direct test of the subtraction ansatz. The requested check—a variational or multi-state analysis, or a significantly larger-tsep comparison—is standard practice for excited-state control in nucleon matrix elements and would settle the concern. Since the paper currently lacks such a check, the reader's CONDITIONAL verdict remains appropriate; no stronger action is warranted because the method is plausible and supported by prior work, and the authors are transparent about ongoing continuum-extrapolation efforts.","tokens_in":43910,"tokens_out":3919,"duration_ms":40651,"concrete_test":"Re-analyze the PACS10/L160 three-point functions with a two-state fit that adds a second excited state with a distinct energy gap to the single-πN form of Eq. (43), or perform a variational analysis with a basis of interpolators including N and explicit Nπ operators as in Refs. [149,150]. Compare the resulting FP(q^2), GP(q^2), and the ratios R1+R2 and R3 with the single-πN-subtraction results. Alternatively, extract FP and GP at significantly larger tsep (e.g., tsep≈1.4–1.6 fm) where any residual excited-state contamination is further suppressed; if the form factors or the ratios shift by more than the quoted statistical errors (and the claimed 5% agreement deteriorates), the single-πN assumption is inadequate and the central claim is method-dependent.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim (Secs. 7.2 and 8) is that after the leading πN subtraction, the lattice form factors satisfy the GGT relation (R1+R2=1) and the PPD model (R3=1) at the 5% level for q^2≲0.1 GeV^2, with PPD for FP valid to <10% up to q^2∼0.42 GeV^2. This conclusion depends entirely on the assumption in Eq. (43) that the entire excited-state contamination in FP and GP is a single πN intermediate state with t-independent coefficients B(q) and C(q). The paper provides no variational or multi-state validation of this ansatz; Sec. 5.3 asserts 'we have succeeded in completely removing the leading πN contribution' without evidence that other states (e.g., N(1440), ρN) are negligible at the simulated tsep≈1.0–1.2 fm. If additional excited states contribute, the subtraction is incomplete, and the extracted FP and GP are biased. The observed R1+R2≈1 and R3≈1 would then be artifacts of the subtraction, not evidence that the lattice data inherit continuum AWT physics. Moreover, the GP extraction in Eq. (46) uses the AWT-derived relation between the πN contamination in pseudoscalar and axial channels (Ref. [60]), so the GGT and R4 tests are partially circular: they verify a relation that was partly used to remove contamination. The paper does not cite an explicit multi-state analysis; Refs. [148–150] describe such approaches but are not applied here. This is the weakest link in the central argument.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript reanalyzes PACS Collaboration lattice data for the isovector nucleon axial form factors FA, FP, and GP at physical quark masses on (10 fm)^3 volumes with lattice spacings a≈0.09 and 0.06 fm, together with a smaller-volume ensemble. The central methodological claim is that a leading πN excited-state subtraction, Eqs. (40)-(46), removes the dominant contamination in FP and GP, yielding couplings gA, gP*, and gπNN consistent with experiment. The paper then uses the extracted form factors to test the PCAC/GGT/PPD relations through R1+R2=1, R3=1, and R4=1 (Eq. 65), and maps their q² validity, claiming roughly 5% agreement for q²≲0.1 GeV² and validity of the PPD form for FP to within less than 10% up to q²≈0.42 GeV². It also introduces a nucleon-based PCAC mass mnucl_PCAC (Eq. 53) and reports agreement with the pion-based mπ_PCAC in the low-q² region.","tokens_in":44328,"tokens_out":7803,"duration_ms":79215,"significance":"If the central claims hold, this is a valuable contribution: physical-point, large-volume lattice data in the low-q² region directly relevant to neutrino-event generators, with a practical demonstration of how far the pion-pole-dominance model remains valid beyond the chiral limit. The paper has notable strengths: multiple tsep values, jackknife error estimation, volume checks, a clear traditional-versus-new analysis comparison, tabulated ratio data in Appendix A, and an independent correlation-function-level PCAC check in Sec. 6. However, the validation of the GGT/PPD statements is weakened by two load-bearing issues: the single-πN-state ansatz in Eq. (43) is not independently tested, and the GP extraction in Eq. (46) shares the same PCAC/GMOR input that the R4 test is supposed to verify. These issues must be addressed before the 5% and 10% statements can be taken as established.","major_comments":[{"comment":"The new analysis assumes that the entire excited-state contamination in the FP and GP ratios is a single πN intermediate state with t-independent coefficients B(q) and C(q) in Eq. (43). No variational or multi-state analysis is performed to test this assumption; Refs. [148-150] are cited as examples of such methods but are not applied here. The extracted FP and GP, and therefore the claims R1+R2≈1 and R3≈1, are only as good as this ansatz. The assertion in Sec. 5.3 that 'we have succeeded in completely removing the leading πN contribution' is not supported by a check that other states, such as N(1440)π or ρN, are negligible at the simulated tsep≈1.0-1.2 fm. A multi-state or variational cross-check, or at least a comparison with an independent extraction for one ensemble, is needed before the 5% statements can be accepted.","section":"Sec. 3.2, Eq. (43); Secs. 5.3 and 7.2"},{"comment":"The GP extraction in Eq. (46) subtracts a term proportional to Z_A B0 = Z_A Mπ²/(2m_PCAC), where B0 is the GMOR low-energy constant introduced in Eq. (21). The ratio R4 defined in Eq. (64) is exactly the same combination (up to renormalization factors), so reporting R4≈1 is partly circular: the PCAC/GMOR relation used in the subtraction is being presented as a verified consequence. The R2 component of the GGT test also inherits this input through GP. The independent mnucl_PCAC comparison in Sec. 6 is a genuine, non-circular check and supports the low-q² region, but it does not by itself justify the form-factor-level subtraction. To make the test informative, the authors should either extract B0 from the data without imposing Eq. (21), or compare the extracted GP with an independent determination that does not use Z_A B0.","section":"Sec. 3.2, Eq. (46); Sec. 7.1, Eqs. (63)-(64)"},{"comment":"The high-q² extension to q²≈0.42 GeV² is based on a single coarse ensemble (PACS5/L64, a≈0.09 fm) without a continuum limit, and at the largest momentum Q8 the mnucl_PCAC comparison yields no signal, as Sec. 8 explicitly acknowledges. Nevertheless, the new analysis uses the PCAC relation mnucl_PCAC=mπ_PCAC in the entire range including Q8 as the input to Eq. (46). The subsequent claims that R1+R2 and R3 remain within 10% up to 0.42 GeV² therefore rest on an input that the paper itself cannot verify at that momentum. This limitation should be stated in the abstract and conclusions, and the 10% numbers should be labeled as upper bounds subject to uncontrolled discretization effects.","section":"Sec. 8, Table 6 and Fig. 21"}],"minor_comments":[{"comment":"There are several typos: 'performe' and 'reffered to' in Sec. 1, and 'spearing parameters' in Sec. 4.3.","section":"Sec. 1 and Sec. 4.3"},{"comment":"The caption repeats 'Results for tsep/a={12,14,16} are plotted from top to bottom panels' after correctly listing {13,16,19} for PACS10/L160; the duplicate sentence should be removed.","section":"Fig. 16 caption"},{"comment":"The notation mPCAC is used both for the bare quark mass and in figure labels such as '2mPCAC eGP'; define the symbol once in Sec. 7.1 and use it consistently in the figure axes and captions.","section":"Sec. 7.1 and figures"},{"comment":"Equation (46) is central to the paper, but its derivation is delegated to Ref. [60]. Since this manuscript applies the method to new physics tests, a short derivation or a clear restatement of the assumptions would improve standalone readability.","section":"Sec. 3.2, Eq. (46)"},{"comment":"The abstract says calculations are carried out with 'two of three sets' of configurations; the status of the third ensemble and its planned role in the continuum extrapolation is only stated later in Sec. 5.4 and Sec. 9. Consider making this explicit near the ensemble description.","section":"Abstract and Sec. 4.1"}],"recommendation":"major_revision","confidential_remarks":"This manuscript is largely a summary and reanalysis of results from companion papers (Refs. [56,57,58,60]), and the technical derivation of the leading πN subtraction is in Ref. [60]. The editor should weigh whether the incremental contribution—the R1-R4 tests and the q² applicability study—is sufficient for a standalone publication. My major_revision recommendation assumes that the circularity of the R4 test and the missing validation of the single-state ansatz can be addressed with additional analysis; if these issues cannot be resolved, the central claims would need to be substantially weakened."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The useful thing to know first: this is not a new simulation paper. Most data existed in earlier PACS publications; the genuinely new part is the systematic application of the same collaboration's leading-πN subtraction method to test PCAC, GGT, PPD and GMOR relations at the physical point, plus an extension of the q^2 range to about 0.42 GeV^2 using one coarse, smaller-volume ensemble. On the plus side, the analysis is careful, jackknife errors and tsep/volume checks are handled cleanly, and the authors are candid that the continuum limit is still missing. Agreement of gA, g*P and gπNN with experiment is useful confirmation. The soft spots are real and worth naming. The central claim—that after subtraction the form factors satisfy R1+R2=1 and R3=1 to 5–10%—depends entirely on Eq. (43), which assumes the whole excited-state contamination is a single πN state with t-independent coefficients. There is no variational or explicit multi-state check. The text asserts they have completely removed the leading πN contribution, but that is the assumption, not a demonstrated result. If other excited states matter at tsep≈1.0–1.2 fm, the extracted FP and GP are biased and the good GGT/PPD agreement becomes an artifact of the method. The circularity point is also fair: the GP extraction in Eq. (46) uses the same AWT/PCAC relation whose consequences are then tested in R1+R2 and R4. Those tests are therefore consistency checks of the method, not independent verifications. In addition, the whole q^2≲0.42 GeV^2 analysis rests on one coarse ensemble with no continuum extrapolation, and at the highest momentum transfer (Q8) no valid mPCAC signal is obtained, yet the PCAC relation is still used there. None of this makes the paper worthless. The tests are a reasonable first pass, the q^2 extension is new, and the authors do not hide the missing continuum limit. But the strongest statement in the abstract and Sec. 8—that lattice data correctly inherit continuum AWT physics—outruns the evidence until the single-state ansatz is checked or replaced by a variational analysis. The paper is mainly for neutrino cross-section modelers and lattice QCD practitioners. I would send it to a knowledgeable referee who can push on that excited-state point; it is worth engaging with, but not as a settled result.","headline":"A careful large-volume lattice QCD study of nucleon axial form factors whose central verification claims rest on an unvalidated single-πN-state subtraction ansatz and partly circular use of the same PCAC relation.","tokens_in":44912,"tokens_out":2085,"would_cite":true,"duration_ms":23065,"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":"Lattice QCD at physical quark masses shows the pion-pole dominance model for nucleon axial form factors holds to ten percent.","keywords":["nucleon axial form factors","lattice QCD","physical point","pion-pole dominance","generalized Goldberger-Treiman relation","PCAC relation","excited-state contamination","neutrino oscillation inputs"],"falsifier":"Repeat the analysis with a variational basis that includes an explicit $\\pi N$ operator or with a multi-state fit that adds a second excited state, and check whether $R_1+R_2$ and $R_3$ remain consistent with unity; a shift beyond the quoted few-percent level would show the single-$\\pi N$ subtraction is incomplete.","tokens_in":43732,"feed_emoji":"⚛️","tokens_out":3692,"duration_ms":36755,"temperature":0.7,"pith_summary":"The paper aims to establish that large-volume lattice QCD at physical quark masses can reliably determine the nucleon's axial form factors—the axial-vector, induced pseudoscalar, and pseudoscalar form factors—and that these form factors obey the continuum axial Ward-Takahashi relations. Its central claim is that after subtracting the leading pion-nucleon excited-state contamination, the generalized Goldberger-Treiman relation ($R_1+R_2=1$) and the pion-pole dominance form ($R_3=1$) hold to about five percent for $q^2\\lesssim 0.1\\ \\mathrm{GeV}^2$, with the pion-pole dominance form for $F_P$ remaining valid to less than ten percent up to $q^2\\sim 0.42\\ \\mathrm{GeV}^2$. This matters because neutrino oscillation experiments rely on the axial form factors as inputs, and a pion-pole dominance model that works at the physical point would give neutrino event generators a theoretically grounded approximation.","feed_headline":"Pion-pole dominance holds in lattice QCD at physical quark masses","feed_subtitle":"Large-volume simulations at the physical point reproduce the Goldberger-Treiman relation and give neutrino-experiment inputs.","key_machinery":"The central object is the leading $\\pi N$ subtraction ansatz: the residual time dependence of the correlator ratios is written as $\\Delta_\\pm(t,t_{\\mathrm{sep}};q)=B(q)e^{-(E_\\pi+M_N-E_N)t}\\pm C(q)e^{-(E_\\pi-M_N+E_N)(t_{\\mathrm{sep}}-t)}$, with $t$-independent coefficients $B(q)$ and $C(q)$. The time-derivative property of these functions, together with the axial Ward-Takahashi identity, lets the $\\pi N$ contamination be removed from the $F_P$ and $G_P$ extraction, which is the step that makes the low-energy relations testable.","core_discovery":"The paper claims that the long-standing excited-state contamination that biased lattice determinations of the induced pseudoscalar form factor $F_P$ and the pseudoscalar form factor $G_P$ is dominated by a single $\\pi N$ intermediate state, and that removing this state with the proposed subtraction yields $F_P$ and $G_P$ whose $q^2$ dependence matches the pion-pole dominance predictions and satisfies the generalized Goldberger-Treiman relation. On the paper's own terms, the lattice data at the physical point, analyzed with this subtraction, reproduce the low-energy relations derived from the axial Ward-Takahashi identity within the quoted statistical precision, and the pion-pole dominance model—strictly valid only in the chiral limit—continues to describe the induced pseudoscalar form factor at the physical point.","pith_inferences":["If the single-$\\pi N$ subtraction survives independent checks, the same technique could be applied to other nucleon matrix elements where pion-nucleon excited states contaminate the signal, extending the reach of plateau methods.","The paper leaves implicit that the success of the PPD model at the physical point does not automatically constrain the model's use at larger $q^2$ or at off-physical pion masses; those regimes still require separate lattice checks.","A testable extension would be to compare the subtracted form factors with results from a variational analysis using an explicit $\\pi N$ operator; agreement would confirm that the omitted higher excited states are genuinely negligible.","The approximate ten percent discretization uncertainty seen in the axial radius suggests that a precise continuum limit, not just the low-energy relations, is the next bottleneck for neutrino-flux predictions."],"forward_implications":["If the central claim is correct, lattice QCD at the physical point can provide first-principles input for the axial form factors used in neutrino oscillation analyses, bypassing model assumptions for $F_A$ and $F_P$.","The pion-pole dominance form for $F_P$, previously justified only in the chiral limit, would be a quantitatively reliable approximation for $q^2\\lesssim 0.42\\ \\mathrm{GeV}^2$ at the physical point.","The generalized Goldberger-Treiman relation, which appears violated in the traditional plateau analysis, would be restored once the leading $\\pi N$ contamination is removed, confirming that the violation is an excited-state artifact rather than new physics.","The agreement between the two PCAC quark masses—one from pion two-point functions and one from nucleon three-point functions—would indicate that the lattice data inherit the continuum axial Ward-Takahashi physics within the quoted precision.","The comparison of coarse and fine lattice results would justify continuing toward a continuum limit with a third, finer lattice spacing, with the expectation that the low-energy relations remain satisfied."],"supporting_citations":[{"why":"Provides the PACS10 coarse-lattice ensemble and earlier nucleon form factor results that this paper reanalyzes.","marker":"[53]"},{"why":"Supplies the fine-lattice PACS10/L160 data and the z-expansion analysis framework for the form factors.","marker":"[56]"},{"why":"Introduces the leading $\\pi N$ subtraction method that the central claim depends on.","marker":"[58]"},{"why":"Proves that the $\\pi N$ contamination in the pseudoscalar form factor ratio has the same functional form via the axial Ward-Takahashi identity, underpinning the subtraction.","marker":"[60]"},{"why":"Derives the generalized Goldberger-Treiman relation and the PPD form in the nucleon three-point function context.","marker":"[116]"},{"why":"Introduced the $R_1+R_2$, $R_3$, and $R_4$ tests on different ensembles, providing the comparison target for the present results.","marker":"[154]"},{"why":"Connects the ratio of $G_P$ and $F_P$ to the GMOR low-energy constant $B_0$, used for the $R_4$ test.","marker":"[155]"}],"fun_headline_variants":["Lattice QCD pins down pion-pole dominance at physical point","Single πN state removal clears nucleon axial form factors","Pion-pole dominance verified by new lattice analysis","Axial form factors match pion-pole predictions after subtraction","Nucleon axial form factors confirm pion-pole dominance"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire analysis rests on the assumption that the only excited-state contamination in the $F_P$ and $G_P$ ratios is a single $\\pi N$ intermediate state described by the two constants $B(q)$ and $C(q)$; if other excited states contribute, the subtraction is incomplete, the extracted form factors are biased, and the agreement with the Goldberger-Treiman and pion-pole relations becomes an artifact.","fun_headline_variants_meta":{"raw":{"variants":["Lattice QCD pins down pion-pole dominance at physical point","Single πN state removal clears nucleon axial form factors","Pion-pole dominance verified by new lattice analysis","Axial form factors match pion-pole predictions after subtraction","Nucleon axial form factors confirm pion-pole dominance"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000641,"raw_usage":{"total_tokens":2983,"prompt_tokens":1010,"completion_tokens":1973,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":626,"completion_tokens_details":{"reasoning_tokens":1891}},"tokens_in":626,"tokens_out":1973,"duration_ms":13063,"temperature":1.0,"reasoning_tokens":1891,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T21:00:16.378057+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the analysis with a variational basis that includes an explicit $\\pi N$ operator or with a multi-state fit that adds a second excited state, and check whether $R_1+R_2$ and $R_3$ remain consistent with unity; a shift beyond the quoted few-percent level would show the single-$\\pi N$ subtraction is incomplete.","supporting_citations":[{"cited_title":"A proposal for removing $\\pi N$-state contamination from the nucleon induced pseudoscalar form factor in lattice QCD","cited_arxiv_id":"2501.13490","evidence_quote":"Proves that the $\\pi N$ contamination in the pseudoscalar form factor ratio has the same functional form via the axial Ward-Takahashi identity, underpinning the subtraction."},{"cited_title":"Nucleon form factors with 2+1 flavor dynamical domain-wall fermions","cited_arxiv_id":"0904.2039","evidence_quote":"Connects the ratio of $G_P$ and $F_P$ to the GMOR low-energy constant $B_0$, used for the $R_4$ test."}],"review_version":1}