{"id":"529d6212-3b2e-4912-b115-cf855f83de81","arxiv_id":"2501.13490","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A time-derivative subtraction of axial-vector correlators removes leading pion-nucleon contamination from the nucleon induced pseudoscalar form factor, yielding plateau values that match the pion-pole-dominance model.","lead":"Lattice QCD simulations of the nucleon's induced pseudoscalar form factor have been contaminated by unwanted pion-nucleon excited states. The authors introduce a subtraction method based on time derivatives of axial-vector correlators and show it removes the contamination, yielding values of g_P* and g_piNN consistent with experiment.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The subtraction in Eq. (15) exactly cancels pi-N contamination only under the assumed two-exponential form of Eq. (13), which the paper does not validate on the same data; without a multi-state or GEVP comparison, the method's flat plateaus do not by themselves establish the central claim.","rationale":"The proposal is a clever linear combination that exploits the redundancy in determining F_P from the A_i and A_4 currents. The algebraic derivation of Eq. (15) is sound: given the assumed form (13), the time-derivative identity (14) is correct and the cancellation of Delta_+ is exact. The numerical demonstration is striking, and the two lattice spacings give a consistent discretization estimate. However, the correctness of the result is only as secure as the assumed shape of the contamination. The paper explicitly labels Eqs. (11), (13) and (16) as assumptions and does not provide a same-data validation. The reader's weakest_assumption points to exactly this. I agree with the reader that the missing check is the load-bearing issue. Because the concern is addressable by a straightforward re-analysis of the existing data, the appropriate verdict remains CONDITIONAL: the method is promising and internally consistent, but the central claim of complete elimination is not yet independently supported. A multi-state fit or GEVP comparison on the same ensembles would either validate Eq. (13) or reveal the residual contamination.","tokens_in":10244,"tokens_out":13650,"duration_ms":128272,"concrete_test":"On the fine 160^4 ensemble, perform a correlated simultaneous fit of the un-subtracted ratios R~_{A_i}(t,t_sep;q) and R_{A_4}(t,t_sep;q) for all t_sep = 13, 16, 19 and each q to the Ansatz in Eqs. (11)-(13) with free F_A, F_P, B, C and free energies DeltaE_1, DeltaE_2. Test whether the fitted DeltaE_1 and DeltaE_2 agree with E_pi - (E_N - M_N) and E_pi + (E_N - M_N), and whether the fitted F_P matches the value from Eq. (15). If the fitted energies deviate by more than the statistical error, or if adding a third exponential significantly improves chi^2/dof, the exact cancellation in Eq. (15) is not realized in the data and the central claim should be weakened to approximate removal of the leading contamination.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the second term in Eq. (15) completely eliminates the leading pi-N contamination holds only if the contamination in the subtracted spatial ratio R~_{A_i}(t,t_sep;q) and in the temporal ratio R_{A_4}(t,t_sep;q) is exactly of the form Delta_+- (t,t_sep;q) = B exp(-DeltaE(q,-q) t) +/- C exp(-DeltaE(0,q)(t_sep-t)) with non-interacting energies, and with identical coefficients B,C in both ratios. This form is asserted on the basis of leading-order baryon ChPT but is not verified on the data; in particular, the definition of R~_{A_i} subtracts a ratio at a different momentum direction q0, so the claim that its residual contamination is the same Delta_+ is not automatic. For G_P, the step relies on Eq. (18), stated as a consequence of the axial Ward-Takahashi identity but not derived for the actual ratio combination. If higher excited states, scattering-state energy shifts, or momentum-dependent coefficients modify these exponentials, the cancellation in Eq. (15) is only partial, and the flat plateaus in Figs. 2-3 could still hide a residual systematic. This is a validation gap rather than an internal inconsistency; it can be closed by a same-data comparison with a correlated multi-state fit or GEVP analysis.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes a simple subtraction method to remove the leading πN excited-state contamination from the lattice QCD determination of the nucleon induced pseudoscalar form factor F_P and pseudoscalar form factor G_P. The method assumes that the πN contamination in the spatial and temporal axial-vector ratios has the two-exponential form of Eq. (13) with non-interacting energies, and then uses the combination in Eq. (15), involving time derivatives of the ratios, to cancel the Δ± terms. For G_P, the axial Ward-Takahashi identity is used to relate the pseudoscalar contamination to Δ+ via Eq. (18), leading to the subtracted expression in Eq. (19). The method is applied to the existing PACS10 data at two lattice spacings, and the resulting F_P and G_P show flat plateaus in t and t_sep that are consistent with the pion-pole dominance model and with experimental values for g_P* and g_πNN.","tokens_in":10520,"tokens_out":4287,"duration_ms":39576,"significance":"If the cancellation in Eq. (15) is exact, this is a practically valuable method: it avoids expensive GEVP or multi-state fits for the notoriously difficult F_P and G_P channels and exploits the previously noisy A_4 correlator. The algebra in Eqs. (11)–(15) is internally consistent, all inputs such as meson and nucleon masses, Z_A, and m_PCAC come from prior independent analyses, and the PPD model is used only for comparison, not in the extraction. The numerical results show clean plateaus at two lattice spacings and for several source-sink separations, with g_P* and g_πNN close to experiment. The main weakness is that the central cancellation is conditional on an assumed functional form for the πN contamination that is not validated on the same data; this is a validation gap rather than an internal inconsistency.","major_comments":[{"comment":"The exact cancellation claimed in Eq. (15) rests on the assertion that Δ±(t,t_sep;q) = B e^{-ΔE(q,-q)t} ± C e^{-ΔE(0,q)(t_sep-t)} with non-interacting energies and with the same coefficients B and C in both ŒR_{A_i} and R_{A_4}. This form is motivated by leading-order baryon ChPT but is not tested against the present data. The flat plateaus in Figs. 2 and 3 can only establish the method if this assumed form is actually the dominant contamination; without a same-data correlated multi-state fit or a GEVP analysis including πN operators, the statement that the leading πN contributions are 'completely eliminated' is not supported by the data shown.","section":"Sec. 3, Eq. (13)"},{"comment":"The definition of ŒR^{5z}_{A_i}(t;q) subtracts R^{5z}_{A_3}(t;q0) with q0=(q1,q2,0) and |q0|=|q|. It is not automatic that the πN contamination in this subtracted combination has exactly the same coefficients B and C as the contamination in R^{5z}_{A_4}. The paper should either derive this equality from the ChPT representation of the πN contributions or verify it numerically from the same correlators before Eq. (15) can be regarded as an exact cancellation.","section":"Sec. 3, Eq. (11)"},{"comment":"The relation Δ_P = Z_A B_0 Δ_+ is stated as a consequence of the axial Ward-Takahashi identity in Eq. (17), but Eq. (17) holds for the full correlators. Transferring it to the leading πN components requires that the identity applies order by order in the excited-state expansion and that the same coefficient Z_A M_π^2/(2m_PCAC) controls the πN part of the pseudoscalar ratio. This nontrivial assumption is not derived for the ratio combinations used here; it should be validated, for example by checking the t_sep-independence of the subtracted G_P with B_0 varied within its uncertainty and by comparing with an independent method.","section":"Sec. 3, Eq. (18)"},{"comment":"The plateau plots after subtraction are shown only for the fine 160^4 ensemble, while the coarse 128^4 results appear only in the final q^2 plots of Fig. 4. Since the paper claims the method works at both lattice spacings, the t- and t_sep-dependence of the subtracted F_P and G_P should be shown for the coarse ensemble as well, or it should be explicitly stated that the behavior is analogous. In addition, the systematic uncertainty from using non-interacting energies in ΔE(q,-q) and ΔE(0,q), and from higher excited states beyond the πN state, is not propagated into the quoted errors for g_P* and g_πNN.","section":"Sec. 4, Figs. 2–3"}],"minor_comments":[{"comment":"The relation q^2 = 2M_N(E_N(q)-M_N) for the final rest frame should state the Euclidean sign convention explicitly; in particular, the values plotted on the horizontal axes of Fig. 4 should be identified with q^2 > 0 in this convention.","section":"Sec. 2, after Eq. (7)"},{"comment":"The notation ∂4 is used for the time derivative, but on the lattice this derivative must be implemented as a finite difference; the precise discretization should be specified.","section":"Sec. 3, Eq. (14)"},{"comment":"The caption refers to 'standard' and 'F_P' panels but the text uses F_P^std and F_P; please align the notation in the captions, text, and figures.","section":"Sec. 4, Fig. 2 caption"},{"comment":"The statement that the discretization error is less than 3–4% is not supported by any explicit continuum extrapolation; the paper should either show the extrapolation or phrase this as an estimate of the finite-a effect.","section":"Sec. 4, final paragraph"},{"comment":"Reference [21] is cited for comparison plots of g_P* and g_πNN; since the present paper is self-contained, it would be helpful to include the comparison explicitly or make the cited proceedings available.","section":"Sec. 5, summary"}],"recommendation":"major_revision","confidential_remarks":"This is a proceedings-style contribution with a promising but not fully validated central claim. The algebraic derivation is sound, and the numerical demonstration is suggestive, but the exact-cancellation claim depends on an assumed form for the πN contamination that is not checked against multi-state fits or GEVP on the same data. I would be comfortable with publication after the validation gap is addressed, either by adding such a comparison or by explicitly and carefully qualifying the claim as conditional on Eq. (13)."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nWhat you should know: this is a short proceedings paper with one new idea: combine time derivatives of the spatial and temporal axial-vector ratio correlators so that the leading piN excited-state contamination cancels exactly, provided it has the two-exponential form of Eq. (13). On the PACS data at two lattice spacings, the method turns visibly sloping and t_sep-dependent plateaus into flat ones, and the extracted g_P* and g_piNN line up with experiment and the PPD model. That is a concrete, useful result.\n\nThe paper does several things well. The algebra from Eqs. (11) to (15) is transparent and internally consistent. The numerical demonstration is honest: they show the standard method's slopes and the new method's plateaus side by side for both F_P and G_P. They also do not oversell; the summary lists what the method does and what it does not. The debt to Bär's analysis of the linear t-dependence is explicitly acknowledged.\n\nThe soft spot is exactly the one the stress test identifies. Eq. (15) cancels Delta+ and Delta- only if those are governed by non-interacting piN energies and if the same B and C appear in the two ratio combinations. That form is motivated by leading-order baryon ChPT, but it is asserted rather than verified on the data. No multi-state fit or GEVP analysis on the same ensembles is shown to confirm that the residual contamination indeed has that shape. If higher excited states or momentum-dependent coefficients are present, the subtraction is partial and the flat plateaus could hide a residual systematic. For G_P the extra step via Eq. (18) is even more assumption-heavy: the PCAC proportionality for the contamination is taken from a previous study, not derived for the actual ratio combination. These are validation gaps, not mathematical errors, and they are addressable.\n\nWho is this for? Lattice QCD practitioners working on nucleon structure, especially those extracting F_P and G_P. It is a methods note, so the audience is narrow. It deserves a serious referee: the idea is novel, the derivation is clean, and the numerics are striking. I would send it to review, but acceptance should hinge on adding a same-data comparison with a multi-state fit or GEVP, or at least a clear statement that the assumed form is a limitation.\n\nRecommendation: engage with it. Cite it if you do nucleon structure. It is not a finished theory, but it is a useful tool in progress.","headline":"A genuinely new derivative-based subtraction that flattens the piN contamination in F_P and G_P on two PACS10 ensembles, but the assumed two-exponential form of the contamination is not cross-checked on the same data, so the method is promising but not yet fully nailed down.","tokens_in":11114,"tokens_out":2976,"would_cite":true,"duration_ms":26211,"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":"A linear combination of axial-vector rati correlators and their time derivatives completely removes the leading pion-nucleon contamination from the nucleon's induced pseudoscalar and pseudoscalar form factors.","keywords":["lattice QCD","nucleon form factors","induced pseudoscalar form factor","pion-nucleon contamination","axial-vector current","pseudoscalar form factor","PCAC relation","pion-pole dominance"],"falsifier":"Apply the same subtraction formula to data analyzed with explicit interacting pion-nucleon energies, for example from a two-state fit or a variational basis that includes $\\pi N$ operators, and compare the cleaned form factors; if the subtracted $F_P$ or $G_P$ still shifts with $t_{\\rm sep}$ or disagrees with the operator-based extraction, the non-interacting-energy assumption is insufficient and the method has not isolated the ground state.","tokens_in":10042,"feed_emoji":"⚛️","tokens_out":11417,"duration_ms":92466,"temperature":0.7,"pith_summary":"Lattice QCD calculations of the nucleon's induced pseudoscalar form factor $F_P(q^2)$ and the related pseudoscalar form factor $G_P(q^2)$ have long been pulled down by contamination from intermediate pion-nucleon ($\\pi N$) states, leaving results far below the pion-pole-dominance expectation and disjoint from experiment. This paper proposes a subtraction method that removes that contamination rather than trying to suppress it by increasing the source-sink separation. The idea is to form a linear combination of the usual three-point correlator ratios with their time derivatives, exploiting a derivative identity that the leading $\\pi N$ exponentials satisfy. Applied to existing data from two large-volume physical-point ensembles, the method turns both form factors into flat plateaus with no residual dependence on the current insertion time or the source-sink separation, consistent with pion-pole dominance. From the cleaned $F_P(q^2)$ the paper extracts the induced pseudoscalar charge $g_P^\\ast$ and the pion-nucleon coupling $g_{\\pi NN}$ with uncertainties comparable to or better than experiment.","feed_headline":"A derivative identity erases pion-nucleon contamination","feed_subtitle":"Reanalyzed lattice data now match pion-pole dominance and experiment for the nucleon's pseudoscalar form factors.","key_machinery":"The central object is the subtraction identity Eq. (15), which defines the cleaned form factor as the standard ratio value plus a correction involving time derivatives of the axial-vector ratio correlators:\n$$\\widetilde F_P($q^{2}$) = -\\frac{K\\,\\widetilde $R^{{5z}}$_{A_i}}{q_i q_3} + \\frac{K}{\\$\\Delta$ $E_N^{2}$ - E_\\$pi^{2}$}\\left[\\$\\Delta$ E_N\\,\\frac{\\partial_4 \\widetilde $R^{{5z}}$_{A_i}}{q_i q_3} + \\frac{\\partial_4 $R^{{5z}}$_{A_4}}{i q_3}\\right],$$\nwhere $\\Delta E_N = E_N - M_N$ and $K=\\sqrt{2E_N(E_N+M_N)}$. The coefficient multiplying the derivative terms is chosen so that, after using the identity $\\partial_4 \\Delta_\\pm = -E_\\pi\\Delta_\\mp + \\Delta E_N \\Delta_\\pm$, the exponentials in $\\Delta_+$ and $\\Delta_-$ cancel identically. For the pseudoscalar form factor, a second identity (Eq. (19)) uses the axial Ward-Takahashi relation $\\Delta_P = Z_A B_0 \\Delta_+$ to build an analogous cancellation, where $B_0 = M_\\pi^2/(2m_{\\rm PCAC})$. The method is 'simple' in the sense that it only recombines existing ratios and their discrete time derivatives; it requires no new operators, no additional gauge ensembles, and no multi-exponential fits.","core_discovery":"The paper's central claim is that the leading $\\pi N$-state contamination in the nucleon's induced pseudoscalar form factor is exactly cancellable using a linear combination of the ratio correlators for the spatial and temporal axial-vector currents and their time derivatives. The contamination enters through two functions $\\Delta_\\pm(t,t_{\\rm sep};\\mathbf{q})$ that have the exponential form $B e^{-\\Delta E(\\mathbf{q},-\\mathbf{q})t} \\pm C e^{-\\Delta E(0,\\mathbf{q})(t_{\\rm sep}-t)}$ with non-interacting energies, and these two functions obey the identity $\\partial_4 \\Delta_\\pm = -E_\\pi \\Delta_\\mp + (E_N-M_N)\\Delta_\\pm$. Substituting this identity into the ratio formulas makes both exponentials vanish, leaving only the ground-state form factor; the ground-state part of the combination is unchanged because it is a redundant linear combination of two determinations of the same $F_P$. For $G_P$, the same subtraction is applied through the axial Ward-Takahashi identity, which connects the pseudoscalar contamination $\\Delta_P$ to $\\Delta_+$. On the two ensembles, the subtracted $F_P$ and $G_P$ show no visible $t$ or $t_{\\rm sep}$ dependence and agree with the pion-pole-dominance model, yielding $g_P^\\ast$ and $g_{\\pi NN}$ values that are consistent with experimental determinations and are more precise than the experimental $g_P^\\ast$.","pith_inferences":["The same derivative-subtraction trick could be adapted to other form factors or channels where a single dominant intermediate state with a known exponential time dependence contaminates the ratio, for example channels contaminated by the Delta resonance.","If this subtraction proves equally effective on finer lattices and at higher momenta, the long-standing low-$q^2$ suppression of lattice $F_P$ relative to pion-pole dominance would be largely resolved.","A direct numerical test on synthetic correlation functions with a known inserted excited state could verify the exactness of the cancellation and quantify the errors introduced by using non-interacting energies.","The method makes the temporal axial-vector current useful again, so data sets that previously discarded the noisy $A_4$ correlator may now be reanalyzable."],"forward_implications":["Removing the two leading $\\pi N$ exponentials eliminates both the $t$-dependence and the $t_{\\rm sep}$-dependence of $F_P(q^2)$ and $G_P(q^2)$ in the analyzed data.","The extracted $F_P$ and $G_P$ become consistent with the pion-pole-dominance model and with experimental muon-capture and pion-electroproduction measurements.","The cleaned data yield values for $g_P^\\ast$ and $g_{\\pi NN}$ that show no residual $t_{\\rm sep}$ dependence, with uncertainties smaller than experiment for $g_P^\\ast$ and comparable for $g_{\\pi NN}$.","Because the method only recombines existing ratio correlators and their time derivatives, it can be applied a posteriori to any previously measured dataset that includes the $A_4$ and $A_i$ three-point functions.","For $G_P$ the method converts the axial Ward-Takahashi identity into a working subtraction, making the pseudoscalar channel usable for physics at low $q^2$."],"supporting_citations":[{"why":"Provides the generalized Goldberger-Treiman relation and the asymptotic ratio formulas that the standard extraction is based on.","marker":"[3]"},{"why":"Supplies the first of the two lattice data sets (fine lattice) reanalyzed here with the new subtraction method.","marker":"[5]"},{"why":"Supplies the second lattice data set (coarse lattice) and the verification that the axial Ward-Takahashi identity holds for the three-point functions, used for the G_P subtraction.","marker":"[6]"},{"why":"Reported the linear t-dependence of the A4 ratio correlator that exposes the pion-nucleon contamination.","marker":"[11]"},{"why":"Explains that t-dependence as the leading pion-nucleon contribution in baryon chiral perturbation theory, giving the exponential parametrization of the contamination.","marker":"[12]"},{"why":"GEVP study showing pion-nucleon contributions are strong in F_P and G_P but not in F_A, supporting the assumption that only the pseudoscalar channels need this subtraction.","marker":"[15]"}],"fun_headline_variants":["Derivative identity exactly cancels pion-nucleon contamination","Lattice QCD derivative identity removes πN pollution from form factors","Exact cancellation of πN states in nucleon pseudoscalar form factors","Derivative identity yields precise gP* and gπNN from lattice QCD","Simple lattice QCD method cancels pion-nucleon contamination exactly"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The subtraction cancels the contamination only if the leading pion-nucleon contribution takes the two-exponential form with non-interacting energies used in Eq. (13) and, for the pseudoscalar form factor, only if the axial Ward-Takahashi identity links its contamination to $\\Delta_+$ exactly as in Eq. (18); higher states or interacting energies would leave part of the contamination behind.","fun_headline_variants_meta":{"raw":{"variants":["Derivative identity exactly cancels pion-nucleon contamination","Lattice QCD derivative identity removes πN pollution from form factors","Exact cancellation of πN states in nucleon pseudoscalar form factors","Derivative identity yields precise gP* and gπNN from lattice QCD","Simple lattice QCD method cancels pion-nucleon contamination exactly"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000605,"raw_usage":{"total_tokens":2901,"prompt_tokens":1107,"completion_tokens":1794,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":723,"completion_tokens_details":{"reasoning_tokens":1699}},"tokens_in":723,"tokens_out":1794,"duration_ms":11321,"temperature":1.0,"reasoning_tokens":1699,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T15:53:20.967476+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Apply the same subtraction formula to data analyzed with explicit interacting pion-nucleon energies, for example from a two-state fit or a variational basis that includes $\\pi N$ operators, and compare the cleaned form factors; if the subtracted $F_P$ or $G_P$ still shifts with $t_{\\rm sep}$ or disagrees with the operator-based extraction, the non-interacting-energy assumption is insufficient and the method has not isolated the ground state.","supporting_citations":[{"cited_title":"Nucleon form factors from quenched lattice QCD with domain wall fermions","cited_arxiv_id":"0709.3150","evidence_quote":"Provides the generalized Goldberger-Treiman relation and the asymptotic ratio formulas that the standard extraction is based on."},{"cited_title":"Toward $N$ to $N\\pi$ matrix elements from lattice QCD","cited_arxiv_id":"2211.12278","evidence_quote":"GEVP study showing pion-nucleon contributions are strong in F_P and G_P but not in F_A, supporting the assumption that only the pseudoscalar channels need this subtraction."}],"review_version":1}