{"id":"574f3eaf-1f4b-4985-b1b5-1fefea33c6dc","arxiv_id":"2412.18166","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"The PACS collaboration obtains preliminary charge radii of 0.423(10) fm^2 for pi+ and 0.373(4) fm^2 for K+ at a single lattice spacing, consistent with experiment.","lead":"A lattice QCD calculation on a very large volume at physical quark masses reports preliminary charge radii for pions and kaons using a method that avoids fitting the form factor shape. The kaon result is statistically sharper than the experimental value, but the quoted errors omit some known systematic effects.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (9) rests on an unquantified cancellation: α1, α2, h in Eq. (3) are not derived in the manuscript, and t_sink is fixed, so the quoted statistical precision may omit the dominant systematic.","rationale":"The reader's weakest assumption is exactly the unquantified cancellation in Eq. (3) and the fixed sink time, and I agree with that assessment. The central values are plausible and consistent with PDG and earlier lattice results, which is real evidence in the paper's favor. However, the advertised advantage of the model-independent method—freedom from fit-ansatz error—depends on the coefficients α1, α2, h actually removing the higher-order Q^2 contamination to well below the statistical errors, and the paper provides no numerical or analytic demonstration of that. The original-versus-improved comparison is helpful but shared between two constructions that both rely on the same plateau and similar moment-based logic, so it does not independently validate the absolute scale. The appropriate disposition remains CONDITIONAL: the method and preliminary values are worth reporting, but the quoted precision cannot be taken at face value until the residual contamination is quantified or the sink-time dependence is checked.","tokens_in":884,"tokens_out":823,"duration_ms":124043,"concrete_test":"Independently derive the explicit formulas for α1, α2, h from the cancellation conditions at the PACS10 geometry (L=128, p=2π/L, physical masses) and evaluate the size of the first uncancelled term in the Taylor expansion of the integrand in Eq. (3), using the measured form factor from the traditional method as input. If this residual contributes more than half the jackknife error (0.005 fm^2 for π+, 0.002 fm^2 for K+) to the flat-region value of R_MI(t), then the higher-order contamination is not sufficiently suppressed and Eq. (9) is not yet a precision result.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative output, Eq. (9), is presented as coming from a model-independent method free of fit-ansatz error, with small quoted errors (0.010 and 0.004 fm^2). The extraction is a constant fit to R_MI(t) in Fig. 1, where R_MI is defined in Eq. (3) as α1 C^(1) + α2 C^(2) + h. The manuscript never states how α1, α2, h are determined; it only says they are 'set to cancel out the higher-order contamination.' If the cancellation leaves a residual at L=10.9 fm comparable to the leading term—or if the next uncancelled Taylor coefficient contributes more than the quoted 0.010/0.004 fm^2—the central values are biased by exactly the systematics the method claims to avoid. The agreement between the original and improved model-independent methods is evidence that the two variants share the same behavior, but it does not independently bound the absolute residual. Likewise, t_sink=36 is never varied, so the 'time-independent region' in Fig. 1 can have a common excited-state offset that is invisible in a single plateau. These are not merely presentation gaps: they directly affect whether the error bars on Eq. (9) describe the actual uncertainty.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports preliminary lattice QCD results for the pi+ and K+ charge radii on the coarsest PACS10 ensemble (a = 0.085 fm, spatial extent 10.9 fm, physical light and strange quark masses). The authors use a 'model-independent' spatial-moment method (Eq. 3) and compare it with a traditional form-factor analysis using six fit ansaetze. They quote <r^2>_{pi+} = 0.423(10) fm^2 and <r^2>_{K+} = 0.373(4) fm^2 in Eq. (9), state that both are consistent with PDG22 and previous lattice calculations, and note that the K+ result has a smaller quoted error than the experimental value. The paper is a proceedings contribution and explicitly acknowledges that source-sink separation and continuum-extrapolation systematics are not yet included.","tokens_in":6396,"tokens_out":8294,"duration_ms":84591,"significance":"If the quoted numbers survive a full systematic analysis, the work would demonstrate a useful cross-check of charge-radius determinations that avoids fit-ansatz bias, and the K+ radius could become one of the most precise available values. The strengths are the physical-point, large-volume ensemble, the comparison of six form-factor ansaetze, the agreement between the original and improved spatial-moment variants, and the transparency about missing systematics. However, the current version does not provide the quantitative residual bounds needed to turn Eq. (9) into a precision statement; at present the quoted errors are statistical only.","major_comments":[{"comment":"The coefficients alpha1, alpha2 and h that enter R_MI(t) are not specified in this manuscript, and no numerical estimate is given for the residual higher-order Taylor contamination that they are meant to cancel. Since the central values in Eq. (9) come from a constant fit to R_MI(t), the extraction is only as model-independent as this cancellation. The authors should either give the explicit coefficients and the derivation of the cancellation in the text, or provide a quantitative bound from the next uncancelled term at L = 10.9 fm; agreement between the original and improved variants does not by itself bound the absolute residual.","section":"Section 2, Eq. (3) and Section 3.3, Eq. (9)"},{"comment":"All results are obtained at a single source-sink separation t_sink = 36, and the 'time-independent region' shown in Fig. 1 is not sufficient to exclude a common excited-state offset. The manuscript should show at least one additional t_sink value or an equivalent excited-state analysis to demonstrate that the flat plateau in R_MI(t) corresponds to the ground-state matrix element; otherwise the quoted error bars on Eq. (9) omit a potentially dominant systematic effect.","section":"Section 3.2 and Fig. 1"},{"comment":"The calculation is performed on a single lattice spacing a = 0.085 fm, and no estimate of discretization effects is given, even though the collaboration has finer PACS10 ensembles. Consequently, the agreement with PDG22 shown in Fig. 3 is only a statistical comparison, and the statement that the K+ radius is 'more accurate than the experimental value' should be restricted to statistical precision. The text should either include a continuum-extrapolation estimate or explicitly frame Eq. (9) as a single-lattice-spacing check.","section":"Section 3.1 and Section 4"}],"minor_comments":[{"comment":"The derivative identity in Eq. (2) is written for the unnormalized momentum-space correlation function, while the moments in Eq. (4) are normalized by the sum over x of C_3pt(t;x); please clarify the normalization so that the relation to R_MI(t) in Eq. (3) is unambiguous.","section":"Eq. (2) and Eq. (4)"},{"comment":"Please state the exact fitting window and the criterion used to select the flat region for the constant fits to R_MI(t), since the final values in Eq. (9) depend on that choice.","section":"Section 3.3 and Fig. 1"},{"comment":"The improved model-independent method 'with log function' is not defined in the text; please include the defining equation or indicate precisely which equations of Refs. [3,4] are being used.","section":"Section 2 and Fig. 2"}],"recommendation":"major_revision","confidential_remarks":"This is a competent and readable proceedings paper, and the missing systematics are acknowledged in the text. The main issue is that the precision claim for the kaon radius is presented without the systematic bounds needed to support it; this is fixable in revision. I would not require the authors to complete the continuum extrapolation in a proceedings article, but they should at least re-frame Eq. (9) as a statistical-only result and add the residual-contamination and plateau-stability checks described above."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a solid proceedings paper, not a finished precision measurement. The genuinely new part is the application of the model-independent spatial-moment method to the coarsest PACS10 ensemble for both pi+ and K+, giving <r^2>_pi+ = 0.423(10) and <r^2>_K+ = 0.373(4) fm^2. Those central values are consistent with PDG and with previous lattice calculations, and the paper is honest in saying the results are preliminary.\n\nWhat it does well: the method is explained clearly, the plateaus in Fig. 1 look flat, the traditional analysis checks six fit ansatze, and the summary explicitly lists the missing source-sink and continuum systematics. That transparency is real and should be credited.\n\nThe soft spots are also the predictable ones. The coefficients alpha1, alpha2, h in Eq. (3) are not derived in the manuscript; the paper only says they cancel higher-order contamination. They come from the cited previous work [2-4], so a specialist can track them down, but a reader of this paper alone cannot check whether the cancellation is adequate at this volume and these momenta. The agreement between the original and improved variants is reassuring but does not bound the absolute residual. And t_sink is fixed at 36 with no excited-state variation, so the quoted errors on Eq. (9) are statistical only. The claim that the K+ radius is about eight times more precise than experiment is therefore premature until those systematics are under control. To the authors' credit, they say exactly this in the summary.\n\nThe stress-test concern about an unquantified cancellation is legitimate but not disqualifying. This is a proceedings that labels itself preliminary and flags the missing systematics. The central values are believable, but the error bars should be read as lower bounds.\n\nRecommendation: send it to peer review as a proceedings contribution. If the authors plan a full journal paper, I would ask them to derive the coefficients in Eq. (3), vary t_sink, and include continuum extrapolation before making precision claims. For what it is, it is a well-written status report. I would not cite it for the numbers, but I would cite it as an application of the method.","headline":"A clean preliminary lattice report that earns its place in the proceedings, but the headline K+ precision rests on coefficients and systematics the paper itself does not yet control.","tokens_in":6923,"tokens_out":2642,"would_cite":false,"duration_ms":26850,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81V05","81T25"],"pacs":["12.38.Gc","13.40.Gp"],"model":"deepseek-v4-flash","headline":"This paper establishes that pion and kaon charge radii can be extracted from lattice QCD without any fit ansatz, reporting $\\langle r^2\\rangle_{\\pi^+}=0.423(10)\\,\\mathrm{fm}^2$ and $\\langle r^2\\rangle_{K^+}=0.373(4)\\,\\mathrm{fm}^2$ on the…","keywords":["lattice QCD","charge radius","pion","kaon","electromagnetic form factor","model-independent method","spatial moment","PACS10"],"falsifier":"Repeat the extraction on the same ensemble at a different source-sink separation, such as $t_{\\mathrm{sink}}=48$, and on the two finer PACS10 lattice spacings; if the plateau value of $R_X^{\\mathrm{MI}}(t)$ shifts by more than the quoted errors, the radii are contaminated by excited states or by uncancelled higher-order momentum terms. A complementary check is to compare the model-independent slope with the numerical derivative of directly computed form factors at sufficiently small $Q^2$ that the Taylor remainder is negligible.","tokens_in":5918,"feed_emoji":"⚛️","tokens_out":8081,"duration_ms":68467,"temperature":0.7,"pith_summary":"This paper reports preliminary lattice QCD charge radii for the pion and kaon using a model-independent spatial-moment method that computes the first derivative of the electromagnetic form factor at zero momentum transfer without assuming a fit function. On the coarsest PACS10 ensemble, a physical-point lattice with extent $(10.9\\,\\mathrm{fm})^4$ and spacing $0.085\\,\\mathrm{fm}$, the method gives $\\langle r^2\\rangle_{\\pi^+}=0.423(10)\\,\\mathrm{fm}^2$ and $\\langle r^2\\rangle_{K^+}=0.373(4)\\,\\mathrm{fm}^2$. These values are consistent with PDG22 and with conventional fit-ansatz analyses on the same ensemble, but the kaon radius comes with an uncertainty about eight times smaller than the experimental value. The paper's message is that one of the four standard systematic errors in lattice charge radii, the fit ansatz, can be removed outright when the volume is large enough for the moment combination to suppress higher-order momentum contamination.","feed_headline":"Kaon charge radius computed to 8x higher precision than experiment","feed_subtitle":"No-fit spatial-moment method gives pion radius 0.423(10) fm^2 and kaon 0.373(4) fm^2.","key_machinery":"The central object is the normalized second spatial moment of the three-point function, $C_{X,\\mathrm{3pt}}^{(1)}(t)=\\sum_x x^2 C_{X,\\mathrm{3pt}}(t;x)/\\sum_x C_{X,\\mathrm{3pt}}(t;x)$, which in infinite volume equals half the derivative with respect to $p^2$ of the momentum-space three-point function at $p^2=0$. Because the lattice volume is finite, the paper forms the linear combination $R_X^{\\mathrm{MI}}(t)=\\alpha_1 C_{X,\\mathrm{3pt}}^{(1)}(t)+\\alpha_2 C_{X,\\mathrm{3pt}}^{(2)}(t)+h$, choosing $\\alpha_1$, $\\alpha_2$, and $h$ so that the unwanted higher-order contamination from $Q^4$, $Q^6$, and beyond cancels. The flat plateau of $R_X^{\\mathrm{MI}}(t)$ in the source-sink time window then gives the first derivative of the electromagnetic form factor at zero momentum transfer directly, bypassing any assumed functional form. This combination is the mechanism by which the fit-ansatz systematic error is eliminated, and the improved log-moment variant is evaluated only as a consistency check.","core_discovery":"The collaboration applies the model-independent spatial-moment method to the coarsest PACS10 ensemble, a $128^4$ lattice at $a=0.085\\,\\mathrm{fm}$ with physical pion and kaon masses in a $(10.9\\,\\mathrm{fm})^4$ box. The central claim is that the combination $R_X^{\\mathrm{MI}}(t)=\\alpha_1 C_{X,\\mathrm{3pt}}^{(1)}(t)+\\alpha_2 C_{X,\\mathrm{3pt}}^{(2)}(t)+h$ has a time-independent plateau whose value directly equals $-\\langle r^2\\rangle_X/6$, with the coefficients chosen to cancel the $Q^4$ and higher terms in the form-factor Taylor expansion. From this plateau they obtain $\\langle r^2\\rangle_{\\pi^+}=0.423(10)\\,\\mathrm{fm}^2$ and $\\langle r^2\\rangle_{K^+}=0.373(4)\\,\\mathrm{fm}^2$. The same ensemble analyzed with monopole, polynomial, z-expansion, and NLO chiral perturbation theory fits gives mutually consistent results with visible ansatz-to-ansatz spread; the model-independent values lie within that spread with smaller errors. The paper concludes that the fit-ansatz error is removed rather than estimated, and that the resulting $K^+$ radius is about eight times more precise than the PDG22 experimental value.","pith_inferences":["The same moment construction should transfer to other meson and baryon form-factor slopes, such as the neutron electric radius, since nothing in the derivation depends on the pion's quantum numbers.","A direct test of the ground-state assumption would be to repeat the extraction at a longer source-sink separation, such as $t_{\\mathrm{sink}}=48$, on the same ensemble; the paper does not report such a variation.","The method fixes only the slope at $Q^2=0$, not the shape of $F(Q^2)$; combining the plateau value with a few low-$Q^2$ form-factor points would give a parameter-free curvature check that could be compared with z-expansion fits.","If the same precision survives the continuum extrapolation at the two finer PACS10 spacings, the combined result could reduce the pion charge radius uncertainty below the current lattice average and sharpen the comparison with electron-scattering measurements."],"forward_implications":["Fit-ansatz error can be dropped from the systematic-error budget for pion and kaon charge radii on physical-point, large-volume lattices.","The $K^+$ charge radius, $0.373(4)\\,\\mathrm{fm}^2$, is determined from this lattice calculation more precisely than from experiment.","The model-independent and traditional analyses agree on the same ensemble, so the ansatz-to-ansatz spread in the traditional method is confirmed as a genuine systematic rather than statistical noise.","The remaining work on this ensemble is to evaluate the source-sink time separation and continuum extrapolation, which the paper explicitly leaves for future study."],"supporting_citations":[{"why":"Supplies the original model-independent spatial-moment construction for the pion charge radius that this paper applies to the PACS10 ensemble.","marker":"[2]"},{"why":"Introduces the improved log-moment variant of the method used here as a consistency check.","marker":"[3]"},{"why":"Provides the protocol for comparing model-independent and fit-ansatz analyses and for evaluating the ansatz systematic error.","marker":"[4]"},{"why":"Is the PACS10 gauge configuration at the physical point on which all measurements in this paper are made.","marker":"[9]"},{"why":"Supplies the PDG22 experimental charge radii that the lattice results are compared against.","marker":"[19]"},{"why":"Documents the previous lattice-review status of charge-radius systematic errors that motivates removing the fit ansatz.","marker":"[1]"}],"fun_headline_variants":["Model-independent meson radii: pion 0.423, kaon 0.373 fm^2","Kaon charge radius 8x more precise than experiment via no-fit method","Pion and kaon radii from lattice, no fit ansatz needed","Meson radii: model-independent method avoids fit bias","Lattice QCD: pion radius 0.423(10) fm^2, kaon 0.373(4) fm^2"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the coefficients $\\alpha_1$, $\\alpha_2$, and $h$ in Eq. (3) cancel the higher-order $Q^2$ contamination of the form-factor Taylor expansion on the PACS10 volume to well below the quoted statistical errors, with the flat region of $R_X^{\\mathrm{MI}}(t)$ in Fig. 1 dominated by the ground state at $t_{\\mathrm{sink}}=36$.","fun_headline_variants_meta":{"raw":{"variants":["Model-independent meson radii: pion 0.423, kaon 0.373 fm^2","Kaon charge radius 8x more precise than experiment via no-fit method","Pion and kaon radii from lattice, no fit ansatz needed","Meson radii: model-independent method avoids fit bias","Lattice QCD: pion radius 0.423(10) fm^2, kaon 0.373(4) fm^2"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00089,"raw_usage":{"total_tokens":3847,"prompt_tokens":962,"completion_tokens":2885,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":578,"completion_tokens_details":{"reasoning_tokens":2769}},"tokens_in":578,"tokens_out":2885,"duration_ms":20924,"temperature":1.0,"reasoning_tokens":2769,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T04:58:44.797387+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the extraction on the same ensemble at a different source-sink separation, such as $t_{\\mathrm{sink}}=48$, and on the two finer PACS10 lattice spacings; if the plateau value of $R_X^{\\mathrm{MI}}(t)$ shifts by more than the quoted errors, the radii are contaminated by excited states or by uncancelled higher-order momentum terms. A complementary check is to compare the model-independent slope with the numerical derivative of directly computed form factors at sufficiently small $Q^2$ that the Taylor remainder is negligible.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the PDG22 experimental charge radii that the lattice results are compared against."}],"review_version":1}