{"id":"48f02c92-c592-4294-850a-87e160fe553b","arxiv_id":"2412.09510","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"First NNLO+PS event generator for b-bbar-H production with massive bottom quarks in the four-flavour scheme, showing NNLO corrections resolve the 4FS/5FS tension.","lead":"A new calculation provides the first next-to-next-to-leading-order (NNLO) QCD prediction for Higgs boson production with a bottom-quark pair, matched to a parton shower. The result brings four- and five-flavour scheme predictions into agreement and improves modeling of the b-bbar-H background in di-Higgs searches.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Massification uncertainty at NNLO is assessed only via NLO validation and logarithmic counting, not by a direct power-correction estimate in the phase-space regions used for the scheme-tension claim.","rationale":"The reader's weakest_assumption identifies the same load-bearing concern: massification at NNLO with the leading-colour truncation. My reading of the paper confirms both issues. The paper is honest about the approximation, validates it at NLO, and provides meaningful cross-checks (Appendix B, comparisons with NNLO+NNLL and NNLO 5FS results). The central claim is plausible and well supported. However, the size of the NNLO corrections (+30% inclusive, up to +100% differential) and the ~10% residual 4FS/5FS differences mean that unquantified power corrections at the few-percent level could affect the conclusion. The concrete test described above would settle whether the approximation is truly negligible. Until then, the CONDITIONAL verdict is appropriate; with the code made public and a direct power-correction estimate, it could become ACCEPT.","tokens_in":45093,"tokens_out":1549,"duration_ms":17331,"concrete_test":"Recompute the NNLO+PS predictions with the massified two-loop amplitude replaced by the exact massive two-loop amplitude (or an independent small-mass expansion that includes the first power correction) at representative phase-space points in the 1-b-jet and 2-b-jet fiducial regions. If the inclusive and fiducial cross sections in Tables 1-3 shift by more than ~2-3%, or if the 4FS/5FS differences in Table 2 move by more than the quoted scale uncertainties, the scheme-tension conclusion needs to be softened.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim that NNLO 4FS corrections resolve the 4FS/5FS tension depends on the two-loop amplitude approximation of Sec. 4.1. Eq. (4.1) drops O(mb/mu_Q) power corrections, keeping only logarithmic and constant terms. The paper validates this approximation at NLO (Sec. 5.3.3, Sec. 8), but the NNLO-level checks in Sec. 4.2 and Appendix B are consistency checks (pointwise comparisons, RG-scale dependence) rather than direct tests of the power corrections. The MiNLO' behaviour in Sec. 5.2 shows that the double-virtual logarithms have a numerically large effect at O(alpha_s^2), so the two-loop contribution is not small. The scheme-tension conclusion is based on agreement at the 8-13% level (Table 2), which is within scale uncertainties but comparable to plausible power-correction uncertainties. The default predictions use the leading-colour two-loop amplitude (Sec. 4.2); Appendix B finds subleading colour is -3% to -5% and is not included in the default differential predictions. This does not overturn the central claim, but it means the 'tension resolved' conclusion rests on an untested assumption that massification power corrections are negligible at the few-percent level, especially in the 2-b-jet and HH-background regions where NNLO corrections reach 100%.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper presents the first NNLO QCD calculation of Higgs boson production in association with a massive bottom-quark pair (pp → b bbar H) in the four-flavour scheme, matched to a parton shower through an extension of the MiNNLOPS method. The calculation is exact except for the two-loop virtual contribution, which is evaluated in the small bottom-mass (massification) limit, and for the default implementation of the two-loop amplitude in the leading-colour approximation. The paper provides an extensive phenomenological study: inclusive and differential cross sections, b-jet observables, a detailed four-flavour versus five-flavour scheme comparison at NNLO+PS, and an application to the b bbar H background in di-Higgs searches in the 2b2γ channel. The central conclusions are that NNLO corrections in the four-flavour scheme are large (about 30% inclusive, up to 100% in some jet-observable tails) and that, together with the five-flavour NNLO+PS results of ref. [42], they resolve the long-standing 4FS/5FS tension for inclusive and one-b-jet observables.","tokens_in":45316,"tokens_out":4872,"duration_ms":51689,"significance":"If the result holds, this is a major step for b bbar H phenomenology: it provides the first NNLO+PS event generator in the four-flavour scheme with massive bottom quarks, and it demonstrates that the MiNNLOPS method can handle a heavy-quark pair plus a colour singlet with a scale-dependent Yukawa coupling. The paper also gives a useful treatment of IR-safe flavour-tagging definitions in the five-flavour scheme and an estimate of the b bbar H background in HH searches. Important strengths are the cross-checks of the two-loop implementation against independent libraries, the inclusion of subleading-colour terms in Appendix B, and the explicit NLO-level validation of the massification procedure. The calculation has no free parameters fitted to the target cross section, which supports the credibility of the central claim.","major_comments":[{"comment":"The massification approximation drops power corrections O(mb/mu_Q) in the two-loop amplitude and is validated only at NLO (Secs. 5.3.3 and 8), not at NNLO where it is first used. The MiNLO' behaviour discussed in Sec. 5.2 shows that the double-virtual logarithms are numerically large at O(alpha_s^2), so the two-loop contribution is not subleading. Since the central 4FS/5FS agreement used to claim resolution of the scheme tension is at the 8-13% level (Table 2) and the NNLO corrections reach 100% in the 2-b-jet tails, a several-percent power correction from the massified two-loop term could shift the conclusion. I ask the authors to provide a direct estimate of the neglected power corrections in the relevant phase-space regions, for example by comparing alternative momentum mappings in the massification setup or by assessing the O(mb/mu_Q) terms against the logarithmic terms at representative phase-space points.","section":"Sec. 4.1, Eq. (4.1)"},{"comment":"The default differential predictions use the leading-colour two-loop amplitude, while Appendix B shows that subleading-colour contributions change integrated cross sections by -3% to -5% and are not included in the main differential results for more exclusive regions. The abstract describes the calculation as exact except for the small-mass expansion, which is incomplete in this respect. This is not a fatal issue for the broad qualitative conclusions, but it means that the 'first NNLO' claim and the scheme-comparison plots should either include subleading-colour terms in the default setup or present the central results with a corresponding additional uncertainty band.","section":"Sec. 4.2 and Appendix B"},{"comment":"The paper states that the long-standing 4FS/5FS tension is resolved, but the authors themselves show in Sec. 6.3 that for observables with at least two b-jets (e.g., m_bj1bj2 below 150 GeV and the subleading b-jet pT spectrum) differences of up to 20-30% remain outside the scale uncertainties. The abstract and the conclusion in Sec. 8 should qualify the resolution claim to inclusive Higgs observables and one-b-jet final states, where the agreement is indeed good, or discuss the residual 2-b-jet discrepancy as a known limitation of the five-flavour description at effectively LO+PS accuracy.","section":"Sec. 6.3, Fig. 12, and Sec. 8"}],"minor_comments":[{"comment":"The text contains a typo: 'In what fallows' should be 'In what follows'.","section":"Sec. 5.3.1"},{"comment":"The fiducial-region labels 'H+≤1 b jets' and 'H+≤2 b jets' appear inconsistent with the integrated values and with the notation used in Table 2; they should presumably read 'H+≥1 b jets' and 'H+≥2 b jets'.","section":"Table 4"},{"comment":"The statement that K_Q = 0.25 leads to similar results is not shown; including a short comparison or a reference to a figure would help the reader assess the resummation-scale uncertainty.","section":"Sec. 5.1 and Table 1"},{"comment":"In Table 3, the uncertainty on the fiducial MiNNLOPS cross section is quoted as +2.1%/-9.5%, which is unusually asymmetric; a short explanation of which scale variation drives this pattern would be useful.","section":"Sec. 7, Table 3"}],"recommendation":"major_revision","confidential_remarks":"The paper is a strong, technically impressive contribution that belongs in JHEP. The main issue is not the novelty or the execution of the MiNNLOPS matching, but the fact that the central scheme-tension claim rests on an approximation whose NNLO uncertainty is not directly quantified. I would request a concrete power-correction estimate and a decision on whether leading-colour-only differential predictions are presented as the main result or as a numerically cheaper variant. If the authors address these points, the paper should be acceptable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this is a real first. The paper presents the first NNLO QCD calculation for b bbar H in the four-flavour scheme with massive bottom quarks, and the first NNLO+PS generator for it. That alone justifies attention. What is genuinely good: the MiNNLOPS extension to Yukawa-induced Q Qbar F processes is nontrivial and written out in enough detail to be checked. The phenomenological analysis is extensive, with sensible jet-flavour definitions and an honest comparison between the experimental tagging approach and IRC-safe alternatives. The cross-checks are real: the 4FS Higgs pT spectrum is compared to independent NNLO+NNLL predictions, the rapidity distribution to fixed-order NNLO, and the 5FS comparison is done at both integrated and differential level. Appendix B reports the impact of full-colour two-loop amplitudes even though the default predictions use leading colour for efficiency—that is transparent reporting. There are no parameters fitted to the target cross section; the free parameters are scale choices. The main soft spot is massification. Equation (4.1) drops O(mb/muQ) power corrections, and the validation is at NLO plus logarithmic/RG consistency checks, not a direct NNLO power-correction estimate in the phase-space regions most relevant for the scheme-tension claim—two-b-jet tails and the HH background region. That concern is fair and should be addressed, ideally with an explicit mb/muQ uncertainty estimate or a dedicated study. It is not load-bearing, though: for bottom quarks at LHC energies the neglected power corrections are expected to be small, the NLO validation supports this, and the central agreement in inclusive and one-b-jet observables holds within scale uncertainties. The residual two-b-jet discrepancy below 150 GeV is shown openly, with the explanation that the 5FS is only LO+PS accurate there. The fact that scale-variation bands do not cover the NLO-to-NNLO shift is common for large K-factors and not by itself a defect. The citation pattern is heavily self-referential, but the cited MiNNLOPS work is the legitimate methodological predecessor, and the benchmarks against independent calculations are real. The stress-test note asks the right question about massification, but the paper's own evidence prevents it from being a fatal flaw. Who is this for: LHC Higgs and HH analyzers, and QCD phenomenologists who need a state-of-the-art background model. It deserves a serious referee. Recommendation: send to peer review, and ask for a massification uncertainty estimate plus a public release of the code before the result becomes the standard reference.","headline":"A genuine first—4FS NNLO and NNLO+PS for b bbar H—with a plausible scheme-tension resolution, though the massification approximation deserves a more explicit uncertainty estimate before this becomes the default reference.","tokens_in":709,"tokens_out":871,"would_cite":true,"duration_ms":27788,"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":"This paper presents the first NNLO QCD computation of the bottom-Yukawa contribution to $b\\bar b H$ production in the four-flavour scheme, matched to a parton shower, and claims these NNLO+PS corrections resolve the long-standing…","keywords":["perturbative QCD","Higgs physics","heavy-flavour phenomenology","bottom-quark associated Higgs production","four-flavour scheme","NNLO+PS","parton-shower matching","di-Higgs background"],"falsifier":"Evaluate the exact two-loop amplitude with full bottom-mass dependence at representative phase-space points relevant for bottom jets and the $H\\to b\\bar b,\\gamma\\gamma$ signal region, and compare it with the massified approximation; if the difference exceeds the quoted scale uncertainties in those regions, the central claim that the NNLO corrections resolve the scheme discrepancy would be called into question.","tokens_in":44829,"feed_emoji":"⚛️","tokens_out":7684,"duration_ms":105202,"temperature":0.7,"pith_summary":"The paper presents the first next-to-next-to-leading-order (NNLO) QCD calculation of Higgs-boson production in association with a bottom-quark pair, in the four-flavour scheme where the bottom quark is treated as massive, and matches it to a parton shower (NNLO+PS). The $y_b^2$ contribution is computed exactly except for the two-loop amplitude, which is approximated through a small bottom-mass expansion. The authors' central claim is that these NNLO corrections increase the four-flavour rate by about 30% and bring the four-flavour and five-flavour predictions into agreement within scale uncertainties at the inclusive and bottom-jet level, resolving a long-standing discrepancy between the two schemes. They further show that the corrected $y_b^2$ background to double-Higgs production in the $b\\bar b\\gamma\\gamma$ channel rises by 30\\textendash 50% relative to NLO+PS.","feed_headline":"NNLO corrections erase scheme gap for Higgs-plus-bottom-quark events","feed_subtitle":"First four-flavour NNLO+PS calculation raises the rate about 30% and sharpens the Higgs-pair background.","key_machinery":"The calculation is carried by two ingredients. First, the MiNNLOPS method, a method for matching NNLO QCD to parton showers, is extended to heavy-quark pair plus colour-singlet production and adapted to a Yukawa-induced process with a scale-dependent MS-renormalized bottom-Yukawa coupling; this supplies the NNLO+PS master formula that distributes the NNLO singular contributions over the full phase space. Second, the two-loop amplitude is handled by massification: the finite remainder for massive bottom quarks is related, up to $O(m_b/\\mu_Q)$ power corrections, to the massless two-loop finite remainder through a product of massification factors for each external leg and a soft operator, $\\bar F \\bar S |R_0\\rangle$. The logarithmically enhanced and constant terms in $m_b$ are therefore kept while the power corrections are dropped, and the massless two-loop remainders are evaluated from analytic leading-colour amplitudes for $c\\bar c\\to b\\bar b H$, with subleading-colour corrections added in Appendix B.","core_discovery":"The central discovery claimed is that the first NNLO+PS generator for $b\\bar b H$ production in the four-flavour scheme exists and changes the picture of scheme compatibility. At NLO+PS the four-flavour and five-flavour predictions differ by roughly a factor of two in the Higgs rapidity distribution and are incompatible, whereas at NNLO+PS the two schemes agree within uncertainties for inclusive Higgs observables and for final states with at least one identified bottom jet. The NNLO corrections consistently raise the four-flavour cross section by about 30% and can reach 100% in exclusive bottom-jet distributions, so the previous NLO+PS four-flavour predictions are not reliable. Applied to the $2b2\\gamma$ channel of double-Higgs searches, the $y_b^2$ background grows by 30\\textendash 50% relative to NLO+PS, directly affecting the modelling of the dominant irreducible background.","pith_inferences":["The resolution of the scheme tension is demonstrated within the quoted scale-uncertainty envelopes; a reader who assigns correlated or missing higher-order uncertainties beyond the 7-point scale variation could see a residual gap, especially in the two-bottom-jet distributions where differences up to 30% persist below an invariant mass of 150 GeV.","Because the massification approximation is validated at NLO only, the size of the dropped $O(m_b/\\mu_Q)$ terms at NNLO is the main unquantified risk; a direct or indirect NNLO test, for example through a second scale choice or an approximate massive two-loop calculation, would strengthen the claim.","If these predictions are correct, earlier NLO+PS based estimates of the $y_b^2$ background in Higgs-pair searches are systematically low by tens of percent, so updated sensitivity studies using these NNLO+PS events may shift projected limits.","The same generator structure could be extended to combined four-flavour and five-flavour matching or to charm-associated Higgs production, directions the authors flag as future work."],"forward_implications":["The NNLO+PS four-flavour generator provides event-level predictions for $b\\bar b H$ that are NNLO accurate for inclusive and bottom-jet observables, whereas previous four-flavour generators were NLO accurate.","The long-standing four-flavour versus five-flavour discrepancy is resolved at NNLO+PS for inclusive Higgs observables and for final states with at least one identified bottom jet, within scale uncertainties.","The $y_b^2$ contribution to the $b\\bar b H$ background in the $2b2\\gamma$ channel of double-Higgs searches increases by about 30\\textendash 50% relative to NLO+PS, with strongly reduced scale uncertainties.","NLO+PS four-flavour scale bands do not cover the NNLO central predictions, so NLO accuracy is insufficient for reliable $b\\bar b H$ predictions.","The method provides a route to NNLO+PS generators for other heavy-quark plus colour-singlet processes and for lighter-quark Yukawa processes such as charm-associated Higgs production."],"supporting_citations":[{"why":"Supplies the MiNNLOPS extension to heavy-quark pair plus colour-singlet production that this work adapts to a Yukawa-induced process.","marker":"[57]"},{"why":"Provides the five-flavour NNLO+PS generator to which the new four-flavour predictions are compared and against which the scheme tension is assessed.","marker":"[42]"},{"why":"Defines the original MiNNLOPS matching method and the master formula used here.","marker":"[60]"},{"why":"Gives the two-loop leading-colour massless amplitudes for $c\\bar c\\to b\\bar b H$ used inside the massified double-virtual contribution.","marker":"[38]"},{"why":"Provides the full-colour massless double-virtual amplitudes incorporated for subleading-colour effects in Appendix B.","marker":"[97]"},{"why":"Supplies the massification factors and high-energy behaviour of massive amplitudes used in the small-mass expansion.","marker":"[59]"},{"why":"Establishes the massification procedure for non-abelian gauge theories connecting massless amplitudes to logarithmic mass terms.","marker":"[58]"},{"why":"Previous NLO four-flavour calculation with massive bottom quarks; the baseline that the NNLO corrections modify.","marker":"[33]"},{"why":"Earlier NLO+PS study of the $b\\bar b H$ background to double-Higgs searches that the new NNLO+PS predictions improve.","marker":"[16]"}],"fun_headline_variants":["NNLO+PS resolves scheme gap for Higgs+b quarks","b bbar H: NNLO+PS erases scheme discrepancy","4-flavour NNLO+PS aligns with 5-flavour for bbH","First NNLO+PS for bbH unifies scheme predictions"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes that replacing the two-loop amplitude for massive bottom quarks by a massless two-loop calculation plus logarithmic bottom-mass terms, and dropping power-suppressed terms of order $m_b/\\mu_Q$, is accurate enough; the approximation is tested at NLO but not at NNLO.","fun_headline_variants_meta":{"raw":{"variants":["NNLO+PS resolves scheme gap for Higgs+b quarks","b bbar H: NNLO+PS erases scheme discrepancy","4-flavour NNLO+PS aligns with 5-flavour for bbH","First NNLO+PS for bbH unifies scheme predictions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000739,"raw_usage":{"total_tokens":3311,"prompt_tokens":969,"completion_tokens":2342,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":585,"completion_tokens_details":{"reasoning_tokens":2266}},"tokens_in":585,"tokens_out":2342,"duration_ms":18304,"temperature":1.0,"reasoning_tokens":2266,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T16:58:07.402243+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Evaluate the exact two-loop amplitude with full bottom-mass dependence at representative phase-space points relevant for bottom jets and the $H\\to b\\bar b,\\gamma\\gamma$ signal region, and compare it with the massified approximation; if the difference exceeds the quoted scale uncertainties in those regions, the central claim that the NNLO corrections resolve the scheme discrepancy would be called into question.","supporting_citations":[],"review_version":1}