{"id":"55ae787f-ffb8-4589-9efc-1ecb57ac1a83","arxiv_id":"1908.06987","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":8.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"MiNNLOPS matches NNLO QCD to parton showers without reweighting or merging scales, preserving leading-logarithmic shower accuracy for transverse-momentum-ordered showers.","lead":"MiNNLOPS is a new method that attaches next-to-next-to-leading-order QCD corrections to parton-shower event generators for LHC processes, illustrated here for Higgs and Drell-Yan production. It achieves this accuracy directly while generating events, removing the need for the slower reweighting step used in earlier NNLO plus parton-shower methods.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The NNLO claim rests on [D(pT)]^(3) in eq. (2.21)/(4.34) containing all O(alpha_s^3/pT) singular terms; this is imported from the two-cluster resummation formula (4.2) and not independently verified against fixed order, so a missing term would shift inclusive zero-jet observables.","rationale":"The paper is careful and the numerical validation is substantial; the b-space appendix provides an internal cross-check of the coefficient shifts. However, the central claim is formally conditional on the completeness of the resummation input, which is not independently demonstrated in the manuscript. The reader's CONDITIONAL verdict is appropriate: the method is plausible and well supported, but the missing independent fixed-order verification of [D(pT)]^(3) is a real, load-bearing gap. My concern matches the reader's weakest assumption, and the concrete expansion test above would settle it. I do not change the verdict.","tokens_in":36934,"tokens_out":19988,"duration_ms":215695,"concrete_test":"Perform an independent fixed-order check: analytically expand eq. (4.34) to O(alpha_s^2) at fixed ΦF, using the unitarity relation of the POWHEG factor to integrate out the second emission, and compare the coefficient of (alpha_s/2pi)^2 in dσ/dΦF with the known NNLO rapidity distribution from MATRIX/DYNNLO for pp→H and pp→Z at a fixed y (e.g., y=0). If any term in eqs. (C.3)-(C.5) is missing, the coefficient will deviate by more than the quoted scale uncertainty. As a second leg, restore the regular terms omitted in eq. (2.20) in the code and verify that the inclusive cross section and rapidity distribution shift by less than the N3LO estimate (~0.2% for DY, ~1% for Higgs).","verdict_should_be":"UNCHANGED","load_bearing_attack":"The master formula (4.34) achieves NNLO accuracy for inclusive (zero-jet) observables only if the sum [alpha_s/(2pi)] [dσFJ/dΦFJ]^(1)(1+[S]^(1)) + [alpha_s/(2pi)]^2 [dσFJ/dΦFJ]^(2) + [alpha_s/(2pi)]^3 [D]^(3) is the correct expansion, to O(alpha_s^3(pT)) in singular terms, of d[e^{-S}L]/dpT + Rf in eq. (2.16). The paper argues this by power counting (2.17) and states that [D]^(3) of eq. (2.21) reconstructs all terms that are singular as pT→0 at this order from the two-cluster momentum-space formula (4.2), imported from refs. [26,27]. The non-trivial content is that the inclusive correlated cluster decomposition (4.16) and the azimuthal-integration step leading to the coefficient shifts (4.24) do not miss or misassign any O(alpha_s^2) singular or constant term. This is cross-checked internally against the b-space formulation in Appendix E, and the numerical validation (Table 2, Figs. 2-4) is consistent, but the Higgs total cross section is 7.9% below the NNLO central value. Since the fixed-order scales are m_H rather than the dynamical pT scales, this difference can absorb an O(alpha_s^2) term at the few-percent level, so the numerical agreement alone does not prove completeness of [D]^(3). The regular terms omitted in eq. (2.20) are a separate but smaller instance of the same issue: their suppression is asserted by power counting and a numerical check that is not shown. If [D]^(3) were missing a term (e.g., in [dL/dpT]^(3) of eq. (C.5)), the inclusive rapidity distribution would be shifted by an O(alpha_s^2) term, violating the central claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents MiNNLOPS, a method for matching NNLO QCD calculations to parton showers for colour-singlet production at hadron colliders. The method builds on the previously existing MiNLO' procedure and on transverse-momentum resummation in momentum space. The central object is the master formula, eq. (4.34), in which the MiNLO' formula is supplemented by a term [D(pT)]^(3) that supplies the missing O(alpha_s^2) singular and constant terms of the pT spectrum. The derivation is presented in Sections 2.3 and 4, with technical details in Appendices A-E. The authors claim that the resulting generator is NNLO accurate in the zero-jet phase space, NLO accurate in the one-jet phase space, has no merging scale, is substantially more efficient than reweighting-based NNLOPS, and preserves the leading-logarithmic accuracy of transverse-momentum-ordered showers. Proof-of-concept results for hadronic Higgs production and for the Drell-Yan process are validated against the independent fixed-order codes MATRIX, HNNLO, and DYNNLO. Overall, the manuscript is carefully written and the central construction is sound, but the completeness of the [D(pT)]^(3) term, and therefore the core NNLO accuracy claim, rests on an imported resummation result plus numerical validation that is not fully conclusive; this needs to be addressed before the claim is fully established.","tokens_in":37430,"tokens_out":4422,"duration_ms":51260,"significance":"If the central claim survives scrutiny, MiNNLOPS is a significant methodological advance: it replaces the multidimensional reweighting of earlier NNLOPS approaches with a direct, efficient calculation of NNLO corrections at event-generation time, and it avoids any merging scale between jet multiplicities. The paper provides explicit analytic expressions for all ingredients, including the [D(pT)]^(3) term in Appendix C and scale-dependence formulae in Appendix D, cross-checks the momentum-space derivation against the impact-parameter formulation in Appendix E, and offers a thorough numerical validation against independent fixed-order codes. The claimed CPU overhead of only 50% relative to MiNLO' makes the method suitable for processes such as vector-boson pair production. These are concrete strengths that make the paper a strong candidate for publication once the completeness issue discussed below is settled.","major_comments":[{"comment":"The central NNLO accuracy claim depends on the assertion that [D(pT)]^(3) of eq. (2.21), combined with the NLO FJ cross section, reconstructs all O(alpha_s^2) singular and constant terms of the pT spectrum. This completeness is imported from the two-cluster momentum-space resummation formula (4.2) of refs. [26,27], and the internal cross-check against the b-space formulation in Appendix E does not constitute an independent verification. The numerical validation is not conclusive: in Table 2 the Higgs total cross section is 7.9% below the NNLO central value, and because MiNNLOPS uses dynamical pT-dependent scales whereas the fixed-order result uses scales of order m_H, a missing or misassigned O(alpha_s^2) term at the few-percent level could be absorbed by the different scale treatment. I request a direct fixed-order consistency check, for example comparing the O(alpha_s^2) expansion of eq. (4.30) with the singular part of the pT spectrum from an independent computation, or a quantitative decomposition showing that no term of order alpha_s^2/pT is omitted.","section":"Sections 2.3 and 4, eqs. (2.20), (4.34)"},{"comment":"The paper states that the regular terms omitted from eq. (2.20) were 'explicitly verified' to give a subleading numerical effect, but no verification is shown. The power-counting argument in eq. (2.17) is plausible, yet the numerical check is asserted rather than documented. Since the master formula is presented as a derivation with a definite accuracy, the reader should be able to see the size of the omitted terms, at least in an appendix. This is a smaller instance of the completeness concern raised in the first major comment, but it should be addressed with an actual number or plot.","section":"Section 2.3, paragraph after eq. (2.20)"},{"comment":"The spreading of [D(pT)]^(3) over the FJ phase space via the factor F_corr and the large-pT cutoff modifications via the parameter p in eq. (3.8) are introduced as arbitrary choices whose consistency with NNLO accuracy is argued by power counting and by the property (3.2). The numerical flatness of the jet observables in Figs. 3 and 6 supports the chosen default, but the manuscript does not state precisely what conditions on F_corr and on the large-pT damping are sufficient to preserve the claimed accuracy for an arbitrary choice. I am not asking for an exhaustive proof, but a formal statement of these conditions would turn an ad-hoc assumption into a checked property and would strengthen the paper.","section":"Section 3, eqs. (3.1), (3.8), (3.9)"}],"minor_comments":[{"comment":"The text says 'with an on-shell top-quark mass' in the context of the infinitely heavy top-quark approximation; this wording is confusing and should be clarified to avoid implying that top-quark mass effects are included.","section":"Section 5.1, setup"},{"comment":"The damping parameter p is fixed to 6 with a comment that variations give 'very moderate effects', but no result is shown. A small table or plot documenting this stability would be useful.","section":"Section 5.1, eq. (3.8)"},{"comment":"The ratio insets for the rapidity distributions are flat in the central region, but the bins are large and statistical fluctuations are hard to assess; showing the statistical uncertainty of the ratios would improve the validation plots.","section":"Figures 2 and 4"},{"comment":"There is a typo 'prodcution' in the sentence introducing the Higgs hard-virtual coefficients; also, the phrase 'Drell-Y an' appears in the Section 5 heading and should be corrected.","section":"Appendix B"},{"comment":"The code is said to be made publicly available within POWHEG-BOX, but no URL or version identifier is given. The final version should include the actual release information.","section":"Section 1, end of Introduction"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is from leading authors in the field and the method has already attracted considerable attention. The main issue is the completeness of the [D(pT)]^(3) term: the derivation is convincing and the numerical validation against independent fixed-order codes is strong, but the explicit verification of the regular-term suppression is promised rather than shown, and the 7.9% Higgs total cross-section difference means the numerical agreement alone does not close the completeness question. I believe the paper is publishable after the authors provide a direct fixed-order cross-check and document the claimed subleading-term verification."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe thing to know about arXiv:1908.06987 is that it works: MiNNLOPS is a genuinely new way to match NNLO QCD to parton showers, and the central claim survives reading. The authors connect MiNLO' to the momentum-space resummation of their earlier papers and derive the [D(pT)]^(3) correction; that puts the NNLO terms in at generation time, with no reweighting and no merging scale. That's a real improvement over the reweighting-based NNLOPS approach, and it matters for practical LHC predictions.\n\nThe derivation is careful, and the validation is genuinely independent: they compare against MATRIX, HNNLO, and DYNNLO. For Drell-Yan the total cross section is 1.7% below NNLO, well inside the overlapping uncertainty bands. For Higgs the difference is 7.9%, which is larger but still consistent with the large perturbative corrections in gluon fusion and with the different scale settings. I don't see that as evidence against the method.\n\nThe soft spots are real but minor. The central formal claim—that [D(pT)]^(3) contains all O(alpha_s^3/pT) singular terms—is supported by power counting and by an internal cross-check in Appendix E, but not by an independent fixed-order calculation shown in the manuscript. A missing term would shift inclusive observables at O(alpha_s^2). The DY agreement makes that unlikely, but it is a gap in the presentation. Similarly, the regular terms dropped in eq. (2.20) are asserted to be subleading; the authors say they checked numerically but don't show the check. These are presentation gaps, not demonstrated errors. The code isn't shipped in this version, so I can't rerun anything, but the external validation is strong evidence.\n\nThe citation pattern is honest: they cite their own resummation work because they are building directly on it, and the validation against external fixed-order results breaks any real circularity. No issues there.\n\nBottom line: this is an important paper, it deserves a serious referee, and I'd bring it to the next group meeting. If I were the editor, I'd send it to review. The only requests I'd make are to show the regular-term check and to lay out the completeness argument for [D(pT)]^(3) more explicitly.\n\nBest","headline":"MiNNLOPS is a genuinely new and correct method for NNLO+PS matching; the central claim holds up, with minor presentation gaps around the completeness of the [D(pT)]^3 term.","tokens_in":38000,"tokens_out":2894,"would_cite":true,"duration_ms":29067,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"MiNNLOPS matches NNLO QCD to parton showers by adding one resummed third-order term.","keywords":["NNLO+PS matching","parton shower","transverse-momentum resummation","MiNLO' method","colour-singlet production","Higgs production","Drell-Yan process","LHC phenomenology"],"falsifier":"Take the Drell-Yan implementation, remove $[D(p_T)]^{(3)}$, and compare the total cross section and rapidity distribution to the full MiNNLOPS result: if the shift is not a subleading $O(\\alpha_s^3)$ effect, the singular reconstruction is incomplete. A sharper check is an order-by-order comparison of the expanded formula with a standard NNLO subtraction at fixed $\\Phi_F$ and integrated over $p_T$, looking for any residual $1/p_T$ singularity beyond the claimed accuracy.","tokens_in":36740,"feed_emoji":"⚛️","tokens_out":13463,"duration_ms":112447,"temperature":0.7,"pith_summary":"The paper sets out a method, called MiNNLOPS, for attaching full next-to-next-to-leading-order (NNLO) QCD accuracy to parton-shower simulations of heavy colour-singlet production at the LHC. It builds on the MiNLO' procedure, which already makes a one-jet NLO calculation NLO-accurate for inclusive observables, and injects the missing NNLO information by connecting that procedure to transverse-momentum resummation. The key step is the addition of a single third-order term, $[D(p_T)]^{(3)}$, computed from resummation coefficients at event-generation time. The paper claims that the resulting master formula (4.34) is NNLO accurate for zero-jet observables, NLO accurate for one-jet observables, requires no merging scale, and preserves the leading-logarithmic structure of transverse-momentum-ordered showers. Proof-of-concept results for Higgs and Drell-Yan production reproduce fixed-order NNLO predictions within scale uncertainties at only about 50% more CPU time than MiNLO'.","feed_headline":"NNLO QCD now matched to parton showers without reweighting","feed_subtitle":"For Higgs and Drell-Yan, inclusive observables reach NNLO while jet rates stay NLO — all at generation time.","key_machinery":"The central object is the MiNNLOPS master formula, eq. (4.34): $d\\sigma/d\\Phi_{FJ} = \\exp[-\\tilde{S}(p_T)]$ times an $\\alpha_s$-expanded bracket containing the NLO one-jet cross section and the new $(\\alpha_s/2\\pi)^3 [D(p_T)]^{(3)} F^{\\rm corr}(\\Phi_{FJ})$ term, multiplied by the POWHEG radiation probability that generates the second emission and hands the remaining radiation to the shower. The load-bearing ingredient is $[D(p_T)]^{(3)}$, eq. (2.21), the third-order expansion of $D(p_T) = - (d\\tilde{S}/dp_T) L(p_T) + dL/dp_T$, built from the resummation anomalous dimensions $A^{(1)}, A^{(2)}, A^{(3)}, B^{(1)}, \\tilde{B}^{(2)}$, the hard-virtual coefficients $H^{(i)}$, the collinear coefficient functions $C^{(i)}$ and $G^{(i)}$, and the luminosity factors $L(p_T)$. Its role is to insert into MiNLO' all NNLO singular terms of the $p_T$ spectrum in the $p_T \\to 0$ limit, so that after integration over $p_T$ the inclusive cross section is NNLO; $F^{\\rm corr}(\\Phi_{FJ})$ spreads those terms over the one-jet phase space in a way that matters only beyond the claimed accuracy.","core_discovery":"The central claim is that eq. (4.34) is a valid master formula for NNLO+PS matching: a fully differential NNLO calculation is embedded in an event generator, with the NNLO corrections computed during event generation rather than imposed by reweighting. In the zero-jet phase space, meaning the Born kinematics of the colour singlet, the formula is NNLO accurate; in the one-jet phase space it is NLO accurate; the two multiplicities are combined without an unphysical merging scale; and for showers ordered in transverse momentum the leading-logarithmic accuracy of the shower is preserved. The argument works by writing the singular transverse-momentum spectrum of the colour singlet as a total derivative, $\\exp[-\\tilde{S}(p_T)] L(p_T)$, whose third-order expansion supplies exactly the singular terms at $O(\\alpha_s^2)$ that MiNLO' is missing. Adding $[D(p_T)]^{(3)}$ to the MiNLO' formula and spreading it over the one-jet phase space with a correlation factor $F^{\\rm corr}$ makes the $p_T$-integrated result NNLO while leaving jet observables at NLO. The paper validates this on Higgs production in gluon fusion and on on-shell $Z$ (Drell-Yan) production at 13 TeV, showing agreement with NNLO fixed-order results for inclusive and rapidity distributions and agreement with MiNLO' for jet distributions.","pith_inferences":["If the master formula is as accurate as claimed, the same construction should transfer to top-quark pair production, where the heavy system is coloured; the paper identifies this as future work, and the needed input would be the corresponding transverse-momentum resummed spectrum.","A direct test of the method's power-counting assumption is to implement the next term, $[D(p_T)]^{(4)}$, and check that the inclusive cross section changes only by $O(\\alpha_s^3)$ rather than by a leading shift; the paper does not make this claim.","The freedom in the spreading factor $F^{\\rm corr}(\\Phi_{FJ})$ means different choices should differ only beyond NNLO; comparing the uniform and collinear-splitting choices in forward-rapidity regions would quantify the size of those subleading effects."],"forward_implications":["Inclusive and Born-level observables for Higgs and Drell-Yan production, such as the rapidity of the boson and the lepton distributions, reach NNLO accuracy and agree with fixed-order NNLO within scale uncertainties.","One-jet observables, such as leading-jet rapidity, rapidity differences, and azimuthal angles, remain NLO accurate, and hard jet configurations are essentially unchanged relative to MiNLO'.","No unphysical merging scale separates the zero- and one-jet multiplicities, so the matched sample is a single smooth event sample.","The leading-logarithmic accuracy of transverse-momentum-ordered showers is preserved, because the method generates only the first two hardest emissions and lets the shower handle the rest.","The scheme is efficient enough for complex colour-singlet processes: the paper reports about 50% more CPU time than MiNLO' and no reweighting, making vector-boson pair production a direct next target."],"supporting_citations":[{"why":"Supplies the MiNLO' procedure being extended: NLO accuracy in both zero- and one-jet phase spaces without a merging scale.","marker":"[7]"},{"why":"Establishes direct-space transverse-momentum resummation for the Higgs pT spectrum, the starting point for the singular structure used in the method.","marker":"[26]"},{"why":"Provides the momentum-space resummation formula (eq. 4.2) from which the derivative structure and the [D(pT)]^(3) term are derived.","marker":"[27]"},{"why":"Defines the NLO-plus-shower matching whose Sudakov radiation probability appears in the MiNNLOPS master formula.","marker":"[28]"},{"why":"Prior NNLOPS simulation of Higgs production by reweighting; the benchmark that MiNNLOPS reproduces without reweighting.","marker":"[16]"},{"why":"Prior NNLOPS simulation of Drell-Yan production by reweighting; benchmark for the new method's inclusive accuracy.","marker":"[18]"},{"why":"Shows that transverse-momentum-ordered dipole showers are leading-logarithmic accurate for the pT distribution, the accuracy the matching preserves.","marker":"[35]"}],"fun_headline_variants":["MiNNLO_PS: NNLO accuracy at generation time, no reweighting","NNLO QCD matched to parton showers without a merging scale","Higgs and Drell-Yan at NNLO with parton showers, all at generation time","MiNNLO_PS: NNLO corrections embedded in the parton shower","Efficient NNLO+PS matching for heavy systems: MiNNLO_PS"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The derivation rests on the assumption that the singular part of the transverse-momentum spectrum at $O(\\alpha_s^2)$ is fully captured by the momentum-space resummation formula (4.2) built from inclusive correlated clusters, so that the single term $[D(p_T)]^{(3)}$ in eq. (2.21) supplies all NNLO singular corrections; the paper supports this by power counting and numerical validation, but does not prove it with an independent fixed-order calculation.","fun_headline_variants_meta":{"raw":{"variants":["MiNNLO_PS: NNLO accuracy at generation time, no reweighting","NNLO QCD matched to parton showers without a merging scale","Higgs and Drell-Yan at NNLO with parton showers, all at generation time","MiNNLO_PS: NNLO corrections embedded in the parton shower","Efficient NNLO+PS matching for heavy systems: MiNNLO_PS"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000433,"raw_usage":{"total_tokens":2234,"prompt_tokens":999,"completion_tokens":1235,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":615,"completion_tokens_details":{"reasoning_tokens":1129}},"tokens_in":615,"tokens_out":1235,"duration_ms":11845,"temperature":1.0,"reasoning_tokens":1129,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T12:29:49.867013+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the Drell-Yan implementation, remove $[D(p_T)]^{(3)}$, and compare the total cross section and rapidity distribution to the full MiNNLOPS result: if the shift is not a subleading $O(\\alpha_s^3)$ effect, the singular reconstruction is incomplete. A sharper check is an order-by-order comparison of the expanded formula with a standard NNLO subtraction at fixed $\\Phi_F$ and integrated over $p_T$, looking for any residual $1/p_T$ singularity beyond the claimed accuracy.","supporting_citations":[],"review_version":1}