{"id":"441eb676-65fb-4954-a972-ea1eb4c7c36c","arxiv_id":"2411.11523","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"NuWro's MEC hadronic model is upgraded with fitted sampling parameters that reproduce Valencia 2p2h momentum correlations, plus a new 3p3h component.","lead":"The paper adds a new way to model multinucleon knockout events in the NuWro neutrino event generator, using a tuneable function to mimic momentum correlations of outgoing protons and neutrons predicted by the Valencia model. The work matters because experiments such as DUNE and Hyper-Kamiokande rely on generator predictions for hadronic final states when measuring neutrino oscillation parameters.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Fig. 6's 'Valencia after FSI' curve is made by reweighting NuWro events in coarse 2D momentum bins, not by running Valencia events through FSI, so the claimed agreement may be an artifact of that proxy.","rationale":"I agree with the reader's assessment that the universal, energy-independent sampling function is a significant generalizability assumption, and the paper's two-region split test is too coarse to fully relieve it. However, I see a more immediate problem with the evidence for the central claim as stated. The post-FSI agreement in Fig. 6 is computed by reweighting NuWro events to match Valencia in coarse phase-space bins before running FSI; this can hide systematic differences between the models because FSI is sensitive to within-bin details. This does not mean the model is wrong, but it means the paper has not yet demonstrated the claimed approximation quality. The MINERvA comparisons are independent support, but they are mixed (chi2 for |pn| worsens), and they test the full generator, not the isolated hadronic model. A direct simulation of Valencia events through the same cascade would settle the issue. Since the reader already returned CONDITIONAL and this concern strengthens the conditions, I recommend no change to the verdict.","tokens_in":23519,"tokens_out":6946,"duration_ms":73605,"concrete_test":"Use the code of Ref. [18] to generate 2p2h events with full exclusive final-state momenta for E_nu = 1 GeV on 12C, feed these events through the same NuWro FSI cascade that produced the new-model curve in Fig. 6, and compare the resulting leading-proton momentum distribution with the reweighted 'Valencia after FSI' curve. If the two differ by more than the FSI-uncertainty band, the central agreement claim is not established. Repeat at E_nu = 0.5, 2, and 5 GeV to check energy dependence. This test isolates the reweighting approximation from the physics of the sampling function.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the new hadronic model reproduces the 2020 Valencia correlations well enough that, after FSI, the leading-proton momentum matches the Valencia model within FSI uncertainties (Fig. 6). The '2020 Valencia model' curve in Fig. 6 is not a direct transport of Valencia events through the cascade. In Sec. IV C the authors state that they reproduce the Valencia phase space by computing, in each bin of the 2D (leading, subleading) proton-momentum plane, the ratio of Valencia to NuWro event counts, then rescale NuWro weights by that ratio and run NuWro's cascade on the reweighted events. This procedure is exact only if the two models' within-bin joint distributions of nucleon momenta and angular orientation relative to q are identical. Fig. 3 shows they are not: the new model spreads events along the diagonal, while Valencia concentrates them in distinct NDelta and DeltaDelta peaks, and the angular sampling f(cos theta*) is a deliberate modification. FSI is nonlinear and depends on both nucleons' full kinematics, so rescaling by coarse bin counts cannot recover the Valencia final-state distribution after the cascade. The band in Fig. 6 is the FSI-model uncertainty from Ref. [36]; it does not include the systematic error of this reweighting. Thus the agreement that anchors the strongest claim may be an artifact of the validation method rather than evidence that the sampling functions capture the relevant physics.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper describes a new hadronic model for the multinucleon (np-nh) contribution in the NuWro event generator. The inclusive part uses the 2020 Valencia model tables; for the 2p2h component the authors introduce a two-parameter sampling function f(cos theta*) for each final-state isospin pair (pp, np, pn), with six parameters globally fitted to reproduce the Valencia two-dimensional outgoing-nucleon momentum distributions at five neutrino energies (0.5-5 GeV), and they add a 3p3h component with combinatorially assigned isospin and three-body phase-space kinematics. The paper compares the resulting pre-FSI phase spaces with the Valencia model and with the old NuWro hadronic model (Figs. 3-5), estimates the post-FSI leading-proton distribution using a reweighting of NuWro events in two-dimensional momentum bins (Fig. 6), and benchmarks the implementation against MINERvA CC1p0pi data (Figs. 7-9, Tables I-II). The central claim is that the new hadronic model approximates the 2020 Valencia correlations well enough that, after FSI, the leading-proton momentum distribution agrees with the Valencia model within FSI-model uncertainties, and that this is an improvement over the previous NuWro hadronic treatment.","tokens_in":23796,"tokens_out":15865,"duration_ms":150796,"significance":"If the central claim is validated, the paper provides a computationally efficient recipe for implementing Valencia-style nucleon correlations in event generators, and its demonstration that multi-nucleon final-state modeling changes hadronic observables such as delta-alpha_T, delta-p_T, and reconstructed neutron momentum is a useful result for the neutrino-oscillation program. The manuscript's strengths are its explicit algorithmic specification (Sect. III B, Appendices A and B), the analytic derivation of the dynamic Pauli-blocking bound in Appendix A, and the quantitative MINERvA benchmarks (Tables I and II), which are external to the fit and thus provide genuinely out-of-sample evidence. The main limitations are that the six fitted parameters carry no reported uncertainties and that the pre-FSI comparisons in Figs. 3-5 are in-sample, leaving the post-FSI reweighted comparison (Fig. 6) and the MINERvA comparison as the independent tests; the former has a methodology caveat discussed in Major Comment 1.","major_comments":[{"comment":"The central claim that the new hadronic model reproduces the 2020 Valencia leading-proton distribution after FSI within FSI uncertainties is established in Fig. 6 by a reweighting proxy, not by transporting Valencia events through the cascade. The '2020 Valencia model' curve is obtained by rescaling NuWro event weights by the ratio of Valencia-to-NuWro counts in each two-dimensional (leading, subleading) momentum bin and then running NuWro's cascade on the reweighted sample. This is exact only if the within-bin joint distribution of the full nucleon kinematics (momentum magnitudes and orientation relative to q) is identical between the two models. Figure 3 shows this is not the case (the new model smears the NDelta and DeltaDelta peaks along the diagonal), and the angular sampling f(cos theta*) is itself a deliberate modification relative to Valencia. Since the cascade is nonlinear in the full kinematics, the coarse-bin rescaling cannot be assumed to reproduce the Valencia post-FSI distribution, and the band in Fig. 6 (from Ref. [36]) does not include the systematic error of the reweighting. The conclusion that the new model is an improvement over the old model survives this concern, but the specific agreement-within-uncertainties claim needs a validation of the reweighting (for example, a bin-size dependence study, or reweighting that includes angular variables) or a suitably qualified statement.","section":"Sec. IV C, Fig. 6"},{"comment":"The fitted parameters (P,l) are obtained by minimizing the chi-tilde-squared of Eq. (16) against the very 2020 Valencia phase-space distributions that are then displayed as the validation targets in Figs. 3 and 4, so the pre-FSI agreement in those figures and in the pre-FSI curve of Fig. 5 is partly in-sample and should be labeled as such in the presentation. More importantly, Eq. (16) sums only over bins where NuWro already has nonzero counts, so the objective function never penalizes the model for failing to populate kinematic regions where the Valencia model has events. The paper should report the coverage fraction (the fraction of Valencia events lying in NuWro-occupied bins) and test whether the best-fit parameters change when zero-count bins are included with a penalty, since this bears directly on the claim of making the NuWro phase space 'as similar as possible' to the Valencia phase space.","section":"Sec. III C, Eqs. (16)-(20)"},{"comment":"The assumption of a single, energy- and (omega,|q|)-independent sampling function per final-state pair is load-bearing for applying the model at arbitrary beam energies and for other nuclei, but it is tested only via the two-region split of Eq. (21), for which the paper reports 'no significant improvement' without giving the resulting parameters or per-energy chi-tilde-squared values. Because the global fit sums chi-tilde-squared over the five neutrino energies (Eqs. (17)-(18)), a large mismatch at one energy can be masked by good agreement at another. The paper should report per-energy chi-tilde-squared values (or per-kinematic-region agreement) and, ideally, a comparison of the new model and Valencia in bins of (omega,|q|), to substantiate the universality assumption.","section":"Sec. III C, Eq. (21)"},{"comment":"The 2020 Valencia code provides no isospin decomposition for the 3p3h contribution (Sec. III A), so the model assigns 3p3h isospin states by combinatorial counts (Eq. (11)) and uses a three-body phase space for kinematics. Both ingredients are untested, and 3p3h contributes roughly 20% of the MEC cross section (Fig. 2). Since the new model worsens the MINERvA dsigma/d|pn| agreement relative to the old one (Table I: 3.21 vs 2.70), the sensitivity of the predicted hadronic observables to the assumed 3p3h isospin composition and phase-space sampling should be quantified before the model is adopted in oscillation analyses.","section":"Sec. III A and III B 2, Eq. (11)"}],"minor_comments":[{"comment":"In the enumeration of antineutrino 3p3h final states, the text lists 'nnn, nnp, nnn'; presumably the last state should be 'npp' (two protons and one neutron), mirroring the neutrino case 'ppp, ppn, pnn'. Please correct the typo and make the mirror symmetry explicit.","section":"Sec. III B 2"},{"comment":"The column headers in Table II ('-0.2 - 0.2 -0.7 - 0.7') do not identify which columns correspond to the old and new MEC models; please label the four columns explicitly (old/new model times narrow/wide region), as the values are otherwise difficult to interpret.","section":"Table II"},{"comment":"There is a typo in the sentence 'the difference is largly annihilated by FSI effects'; it should read 'largely'.","section":"Sec. IV B 1"},{"comment":"The text after Eq. (9) refers to the lepton scattering angle as theta_{k'} whereas Eq. (9) uses theta_l; please unify the notation. Also, the term 'W5/5 (E'_l + |k'|)' in Eq. (9) should be checked against the original Valencia derivation, since a misprinted coefficient in a central formula could mislead readers even if the implemented tables are correct.","section":"Sec. II B 1, Eq. (9)"},{"comment":"The five-parameter function f(x) in Eq. (B2) is defined piecewise on [0, kappa]; if it is intended for use on [-kappa, kappa] as a nucleon sampling function, the required symmetrization (or the convention x = |cos theta*|) should be stated explicitly.","section":"Appendix B 2"},{"comment":"The caption reads 'The panel from left is for the old hadronic model while the middle panel corresponds to the new hadronic model'; please rephrase this for clarity and consistency with the Fig. 3 caption.","section":"Fig. 4 caption"}],"recommendation":"major_revision","confidential_remarks":"To the editor: this is a technical implementation paper whose headline claim rests on Fig. 6; as argued in Major Comment 1, the reweighting-based 'Valencia after FSI' curve makes the agreement claimed there partly an artifact of the procedure. The pre-FSI validation is in-sample, the fitted parameters have no uncertainties, and the independent evidence base for the model is therefore mainly the global MINERvA comparison, which tests NuWro as a whole rather than the hadronic model in isolation. This is fixable but requires additional validation work, hence my major_revision recommendation. I would also encourage the authors to provide the implementation as an ancillary file or a repository link, since the paper's utility depends on NuWro users being able to reproduce the sampling procedure exactly."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a workmanlike, honest generator paper. The two-parameter sampling function for 2p2h, the separate fitted sets for pp, np, and pn, and the first 3p3h treatment in NuWro are genuinely new. The authors also report the negative results—splitting by (ω,|q|) gave no gain, a five-parameter function didn't beat the two-parameter one—which I trust.\n\nWhat it does well: the algorithm is stated explicitly enough to reproduce (Sect. III B and appendices), the global fit over five neutrino energies is a reasonable calibration strategy, and the pre-FSI phase-space comparisons show clear improvement over the old flat model. The 3p3h contribution at about 20% of the total is quantified. The MINERvA benchmark is a fair, whole-generator test, and the model improves most hadronic observables slightly, with one exception (|pn|, where χ2/ndf worsens from 2.70 to 3.21).\n\nSoft spots, in order of importance. First, the circularity is real: the parameters are fit to the same 2020 Valencia phase spaces used for validation, so the pre-FSI agreement in Figs. 3–4 is partly guaranteed. That leaves the MINERvA comparison as the only fully independent check, and it is supportive but moderate. Second, the stress-test concern about Fig. 6 is legitimate: the \"Valencia after FSI\" curve is not Valencia events through the cascade; it's NuWro events reweighted in coarse 2D bins. This is exact only if within-bin joint distributions match, and Fig. 3 shows they don't—the new model smears the NΔ/ΔΔ peaks and the angular sampling is an explicit approximation. The FSI band from Ref. [36] doesn't include the reweighting error, so \"coincides within FSI uncertainties\" overstates what's demonstrated. The qualitative conclusion—new model closer to Valencia than old—survives, but the paper should say \"through a reweighted proxy.\" Third, no parameter uncertainties and no shipped code. For a tuning paper, those should be requested.\n\nWho is this for: anyone implementing MEC in a neutrino-event generator, and those doing oscillation-systematics studies that need a defensible hadronic model. It deserves a serious referee, not a desk rejection. The referee should ask for parameter errors, a caveat on the reweighting, and ideally the model tables.","headline":"Solid NuWro MEC update with genuinely new hadronic sampling, but the validation is partly circular and the post-FSI Valencia curve is a reweighted proxy—still worth refereeing.","tokens_in":24407,"tokens_out":4241,"would_cite":true,"duration_ms":38363,"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 two-parameter sampling function for outgoing nucleon pairs lets NuWro reproduce the 2020 Valencia model's momentum correlations after final-state interactions.","keywords":["neutrino-nucleus interactions","multinucleon knockout","2p2h and 3p3h mechanisms","meson exchange currents","NuWro Monte Carlo generator","Valencia model","nucleon momentum correlations","final-state interactions"],"falsifier":"Generate 2p2h events with the 2020 Valencia code and with NuWro's new hadronic model at neutrino energies outside the calibration set (for example, 1.5, 3, or 10 GeV) and on a target such as argon rather than carbon; if the two-dimensional pp or np+pn momentum distributions disagree by more than the FSI uncertainty band after the cascade, the universal sampling assumption is falsified.","tokens_in":23269,"feed_emoji":"⚛️","tokens_out":5950,"duration_ms":53516,"temperature":0.7,"pith_summary":"Neutrino oscillation experiments infer neutrino energy from Monte Carlo generators, so the way a generator distributes the nucleons knocked out in multinucleon (np-nh) events matters. This paper tries to establish that NuWro, with a two-parameter nucleon sampling function fitted to the 2020 Valencia model, can reproduce that model's correlations in outgoing nucleon momenta closely enough that, after final-state interactions, the leading-proton momentum distribution agrees within FSI uncertainties. The paper also adds a 3p3h component and shows that the choice of hadronic model changes hadronic observables such as the transverse momentum imbalance by tens of percent, affecting comparisons with experiment. The point is that a cheap, tunable hadronic model can stand in for a computationally expensive exact calculation.","feed_headline":"NuWro's new multinucleon model matches Valencia after FSI","feed_subtitle":"Two fitted parameters reproduce nuclear correlations and shift hadronic spectra by tens of percent.","key_machinery":"The load-bearing element is the two-parameter nucleon sampling function $f(x)$ with $x=\\cos\\theta^*$, defined in Appendix B, where $P\\in[-1,1]$ sets whether nucleons prefer parallel ($P>0$) or perpendicular ($P<0$) emission relative to the boost direction and $l$ (an integer) sets the sharpness of that preference; $P=0$ gives a flat distribution. The function is evaluated on the interval $[-\\kappa,\\kappa]$ fixed by a Pauli-blocking condition that keeps the backward nucleon's lab energy above $m_b+E_F$. The parameters are tuned by a reweighting technique that compares NuWro's pp and np+pn nucleon phase spaces with the 2020 Valencia model's binned two-dimensional distributions through the $\\tilde\\chi^2$ of Eq. (16), minimizing the sum over five neutrino energies.","core_discovery":"The central claim is that correlations in the momenta of outgoing nucleons from 2p2h meson-exchange-current events can be captured by a normalized sampling function $f(\\cos\\theta^*)$ in the hadronic center-of-mass frame, with one direction parameter $P$ and one strength parameter $l$ for each final-state pair (pp, np, pn). Fitting these parameters to the two-dimensional nucleon phase space of the 2020 Valencia model at five neutrino energies gives $(P,l)_{pp}=(0.77,4)$, $(P,l)_{np}=(0.7,3)$, and $(P,l)_{pn}=(0.8,4)$, all with positive $P$, which pushes the pair toward forward/backward configurations and creates the asymmetric leading/subleading proton pattern of the Valencia model. With this hadronic model inside NuWro, the leading-proton momentum distribution after the intranuclear cascade lies inside the FSI uncertainty band of the Valencia model, whereas the old hadronic model lies outside it. The authors therefore claim that the approximation captures the most important features of the exact exclusive model.","pith_inferences":["If the universal, energy-independent sampling functions are not truly universal, disagreement should appear at neutrino energies outside {0.5, 0.7, 1, 2, 5} GeV or for nuclei other than carbon; this can be checked directly against the 2020 Valencia code.","The fit's failure to improve by splitting the $(\\omega,|\\mathbf{q}|)$ plane suggests that the two-peak structure (NΔ versus ΔΔ) produces similar angular correlations in both regions; a direct test would fit separate parameters in the two kinematic regions against exclusive proton data.","Since FSI masks much of the remaining discrepancy, any future reduction of FSI uncertainties would force the hadronic sampling function to be more exact, likely requiring kinematics-dependent parameters."],"forward_implications":["The 3p3h mechanism contributes about 20% of the total MEC cross section at $E_\\nu \\gtrsim 1.1$ GeV, so generators that omit it understate multinucleon knockout strength.","After FSI, the new NuWro hadronic model and the 2020 Valencia model give leading-proton momentum distributions consistent within FSI uncertainties, while the old hadronic model differs significantly.","In MINERvA CC1p0π observables, the new model suppresses the large-$|p_n|$ tail of reconstructed neutron momentum by roughly 40% in the MEC channel and suppresses large $\\delta p_T$ and $\\delta\\alpha_T$ tails by 20–40%, improving $\\chi^2$ for most observables but worsening $d\\sigma/d|p_n|$.","The procedure is not tied to NuWro: the same sampling function and calibration approach can be adopted by other neutrino event generators."],"supporting_citations":[{"why":"Provides the 2020 Valencia model's exclusive-final-state code and the five hadronic-tensor components for 2p2h (pp, np, pn) and 3p3h that the NuWro implementation reproduces.","marker":"[18]"},{"why":"Defines the factorization scheme and the old hadronic model (uniform cos θ* sampling) that the new model replaces and compares against.","marker":"[15]"},{"why":"The original Valencia inclusive model whose tabulated response functions form the old NuWro MEC implementation used as the cross-section baseline.","marker":"[13]"},{"why":"Supplies the FSI uncertainty band (nuclear transparency estimates) used to judge whether the new model agrees with the 2020 Valencia model after the cascade.","marker":"[36]"},{"why":"MINERvA CC1p0π cross-section data for δαT, δpT, and reconstructed neutron momentum used to benchmark the new and old hadronic models.","marker":"[38]"},{"why":"Earlier MINERvA measurement of final-state correlations whose event-selection criteria (pμ, θμ, pp, θp) are adopted in the comparison.","marker":"[39]"},{"why":"Describes the event-reweighting technique used to scan the (P,l) parameter space efficiently during calibration.","marker":"[37]"}],"fun_headline_variants":["NuWro's 2p2h model with fitted correlations matches Valencia post-FSI","After FSI, NuWro's tuned 2p2h model matches Valencia momentum spectra","NuWro adds 3p3h and tuned 2p2h correlations to match Valencia","Two fitted parameters make NuWro's 2p2h match Valencia after FSI"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The assumption that a single, energy-independent two-parameter sampling function $f(\\cos\\theta^*)$ suffices for each final-state pair (pp, np, pn) is load-bearing; if nucleon correlations depend on energy and momentum transfer more strongly than this, the calibrated model will misrepresent events at uncalibrated energies or in other nuclei.","fun_headline_variants_meta":{"raw":{"variants":["NuWro's 2p2h model with fitted correlations matches Valencia post-FSI","After FSI, NuWro's tuned 2p2h model matches Valencia momentum spectra","NuWro adds 3p3h and tuned 2p2h correlations to match Valencia","Two fitted parameters make NuWro's 2p2h match Valencia after FSI"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001064,"raw_usage":{"total_tokens":4448,"prompt_tokens":923,"completion_tokens":3525,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":539,"completion_tokens_details":{"reasoning_tokens":3427}},"tokens_in":539,"tokens_out":3525,"duration_ms":26375,"temperature":1.0,"reasoning_tokens":3427,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T18:24:44.393321+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Generate 2p2h events with the 2020 Valencia code and with NuWro's new hadronic model at neutrino energies outside the calibration set (for example, 1.5, 3, or 10 GeV) and on a target such as argon rather than carbon; if the two-dimensional pp or np+pn momentum distributions disagree by more than the FSI uncertainty band after the cascade, the universal sampling assumption is falsified.","supporting_citations":[{"cited_title":"At the initial steps, we proceed in exactly the same way as in Sect III B 1 (steps (1-5) differ only in the sense that three nucleons are sampled in the initial state)","cited_arxiv_id":null,"evidence_quote":"Provides the 2020 Valencia model's exclusive-final-state code and the five hadronic-tensor components for 2p2h (pp, np, pn) and 3p3h that the NuWro implementation reproduces."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the factorization scheme and the old hadronic model (uniform cos θ* sampling) that the new model replaces and compares against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The original Valencia inclusive model whose tabulated response functions form the old NuWro MEC implementation used as the cross-section baseline."},{"cited_title":"Gonzalez-Garcia and M","cited_arxiv_id":null,"evidence_quote":"Supplies the FSI uncertainty band (nuclear transparency estimates) used to judge whether the new model agrees with the 2020 Valencia model after the cascade."},{"cited_title":"Collaboration, Axial form fac- tors of the nucleon from lattice qcd, Journal of High Energy Physics 2021, 123 (2021)","cited_arxiv_id":null,"evidence_quote":"Earlier MINERvA measurement of final-state correlations whose event-selection criteria (pμ, θμ, pp, θp) are adopted in the comparison."}],"review_version":1}