{"id":"49bb201d-417b-4b40-ac16-f98fd1d3f5b2","arxiv_id":"2412.01548","paper_version":2,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Using neural simulation-based inference, ATLAS improves evidence for off-shell Higgs production in ZZ -> 4l to 2.5 sigma observed (1.3 sigma expected) and measures Gamma_H = 4.3 +2.7 -1.9 MeV.","lead":"ATLAS reports a new measurement of off-shell Higgs boson production in H* -> ZZ -> 4 leptons using neural simulation-based inference on 140 fb^-1 of 13 TeV data, finding an observed (expected) significance of 2.5 (1.3) sigma and constraining the Higgs width to 4.3 +2.7 -1.9 MeV. It is the first ATLAS physics result using per-event neural likelihood ratios and improves the expected reach over the previous histogram-based analysis of the same dataset from 0.5 to 1.3 sigma.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed off-shell significance and Higgs-width constraint rest on an unvalidated uniform 1.2/1.1 K-factor rescaling of the ggF signal, interference, and background; a shape shift from the now-available full-NLO top-mass calculation could move the 2.5 sigma evidence.","rationale":"The reader's weakest_assumption is the same one: the ggF SBI/S/B samples after uniform NNLO/NLO = 1.2 and N3LO/NNLO = 1.1 rescaling are assumed to give unbiased descriptions of signal, interference, and background. The paper explicitly concedes that the relevant higher-order corrections for interference and background, and the full top-quark mass dependence in the NLO K-factors, are not included; it addresses them only by enlarging scale uncertainties. That is a reasonable interim treatment, but it leaves the central value of the interference shape unvalidated. Since the headline evidence is a 2.5 sigma observed effect with only 1.3 sigma expected, and since the interference-dominated regime is precisely where the measurement has most of its sensitivity, a shape error in the interference term can plausibly change the significance and the width constraint. The rest of the statistical analysis is strong: cross-validated NN training, ensemble uncertainty, calibration and reweighting tests, closure of the MLE, and Neyman construction with pseudo-experiments all support the NSBI methodology. The weak point is not the inference machinery but the theoretical model it is fed. The suggested check is therefore narrow and decisive: use the now-available complete NLO top-mass calculation to replace the approximate K-factors and see whether the observed significance and width move. If they do not move materially, the ACCEPT verdict is confirmed; if they do, the evidence claim should be reported as conditional on that missing higher-order input.","tokens_in":72412,"tokens_out":11627,"duration_ms":113916,"concrete_test":"Regenerate or reweight the ggF S, SBI, and B samples in the off-shell region using the complete NLO QCD corrections with full top-quark mass dependence from Ref. [98] (arXiv:2404.05684), replacing the m_ZZ-dependent NLO K-factors and the uniform 1.2/1.1 rescaling, then rerun the full profile-likelihood fit and Neyman construction. If the observed significance for mu_off-shell = 0 drops below 2 sigma or the best-fit Gamma_H shifts by more than about 1 MeV relative to 4.3 MeV, the uniform-K-factor treatment is load-bearing and the evidence claim should be regarded as conditional on the missing higher-order terms.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"Section 4 applies a common average NNLO/NLO correction of 1.2 and an average N3LO/NNLO correction of 1.1 to the ggF signal, interference, and background components entering Eq. (3) through the substitution in Eq. (4) and Table 1. The paper states that NNLO and N3LO corrections for the off-shell interference and background are not available, and that the NLO K-factors lack the complete top-quark mass dependence (Sec. 6.3). The response is to inflate scale uncertainties near the ttbar threshold and for high-pT jets, but this does not test whether the central shapes of S, I, and B are correct. The evidence for off-shell production (observed 2.5 sigma, expected 1.3 sigma) and the combined 3.7 sigma are driven by the interference-dominated low-mu region, so a shape or normalization shift in the interference term changes the best-fit mu and the p-value directly. Because the complete NLO top-mass calculation is now available (Ref. [98]) and is not used, the uniform-K-factor premise is the most load-bearing unvalidated assumption in the argument.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper reports a measurement of off-shell Higgs boson production in the H* -> ZZ -> 4l channel using 140 fb^-1 of 13 TeV ATLAS Run 2 data, analyzed with a neural simulation-based inference (NSBI) technique that estimates per-event likelihood ratios. The observed (expected) off-shell signal strength is 0.87^{+0.75}_{-0.54} (1.00^{+1.04}_{-0.95}) in the 4l channel, with an observed (expected) evidence significance of 2.5 sigma (1.3 sigma). Combining with the previous 2l2nu-channel analysis gives an observed (expected) significance of 3.7 sigma (2.4 sigma), and the combined on/off-shell interpretation yields Gamma_H = 4.3^{+2.7}_{-1.9} MeV observed (4.1^{+3.5}_{-3.4} MeV expected). The paper claims a substantial improvement in expected sensitivity relative to the previous histogram-based analysis of the same 4l dataset and provides extensive validation of the NSBI procedure.","tokens_in":72705,"tokens_out":10334,"duration_ms":95131,"significance":"If the result stands, it demonstrates that NSBI can yield a real sensitivity gain in a low-rate channel dominated by signal-interference quantum effects, and it provides a competitive constraint on the Higgs boson total width that is consistent with the Standard Model. The statistical analysis is careful and unusually well documented: profile likelihood with Neyman construction, Asimov closure tests across a range of signal strengths, reweighting tests, a multidimensional discriminator test, and a systematic uncertainty decomposition are all presented. The main caveat is the uniform rescaling of the ggF signal, interference, and background components by average NNLO/NLO and N3LO/NNLO K-factors, which is not directly tested against the now-available complete NLO top-quark mass calculation.","major_comments":[{"comment":"The analysis applies a common average NNLO/NLO correction of 1.2 and an average N3LO/NNLO correction of 1.1 to the ggF signal, interference, and background components entering Eq. (3) through Eq. (4) and Table 1, while the paper itself states that the NLO K-factors lack the complete top-quark mass dependence and that the full calculation has only recently become available (Ref. [98]). This is a load-bearing modeling premise because the evidence for off-shell production is driven by the interference-dominated low-mu region; a shape or normalization shift in the interference term would directly change the fitted mu_off-shell and the p-value. The inflation of scale uncertainties near the ttbar threshold and for high-pT jets is an envelope-style prescription and does not test whether the central S/I/B shapes are correct. I request a quantitative cross-check using the complete NLO top-mass calculation, for example by reweighting the existing samples or generating an alternative ggF SBI sample, and a statement of how the resulting shift in mu_off-shell and in the observed significance compares with the quoted ggF modeling uncertainty.","section":"Section 4, Table 2, Section 6.3"},{"comment":"The headline claim of 2.5 sigma observed evidence is not accompanied by the corresponding numerical p-value under the no-off-shell hypothesis. The text reports a p-value of 0.11 under the SM hypothesis (1.2 sigma) and then quotes the observed significance of 2.5 sigma, but it does not give the observed p-value under mu_off-shell = 0 nor does it define precisely how the expected significance is computed (e.g., median p-value under the SM hypothesis). Since the evidence claim is the central quantitative result, the p-value under mu = 0 and the definition/algorithm for the expected significance should be stated explicitly in the text so the headline numbers are reproducible from the reported distributions.","section":"Section 7 and Figure 12"}],"minor_comments":[{"comment":"The parenthetical \"(I = SBI - S + B)\" is inconsistent with the displayed equation I = SBI - S - B; please correct the sign in the text.","section":"Section 3, Eq. (4)"},{"comment":"The caption reads \"the green solid curve shows the shows the expected distribution\"; the duplicated phrase should be removed.","section":"Section 7, Figure 12 caption"},{"comment":"The missing expected 95% CL interval for kappa_g,off-shell is explained only in the table footnote; a sentence in the main text clarifying the practical impact of the kappa_g/kappa_V degeneracy on the combined coupling measurement would be helpful.","section":"Table 6"},{"comment":"The reweighting and multidimensional tests are described only briefly and the reader is referred to Ref. [31]; since these tests are central to validating the NSBI density ratios, a short statement of the phase-space coverage and the number of observables tested in the multidimensional discriminator would strengthen the self-contained character of the paper.","section":"Section 6.2"}],"recommendation":"major_revision","confidential_remarks":"This is a strong ATLAS measurement with unusually thorough statistical validation. My main concern is the uniform K-factor treatment of the ggF S/I/B components; the request for a quantitative cross-check against the complete NLO top-mass calculation (Ref. [98]) is meant to close the one genuine load-bearing modeling gap. If the authors can provide that check or argue convincingly that the enlarged scale uncertainties cover the possible shape shift, I would be happy to accept the paper. The missing numerical p-value under mu = 0 is a smaller but still central reporting issue that should be fixed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a well-executed ATLAS measurement showing a real gain from replacing histograms with neural likelihood ratios. The 2.5 sigma evidence is the headline, but the uniform K-factor treatment of the ggF interference is the one place I'd want a referee to push.\n\nWhat's new: first ATLAS physics result using per-event neural likelihood ratios (NSBI) for off-shell H->ZZ->4l. It reuses the dataset and selection from Ref [17], but the expected significance improves from 0.5 to 1.3 sigma, and combining with 2l2nu gives 3.7 sigma. The statistical machinery is thorough: Neyman construction, Asimov closure, reweighting tests, NN ensemble uncertainty, spurious signal from MC statistics. The systematic decomposition is clear and the paper is honest about limitations.\n\nThe stress-test note is on target. Equation (4) infers the interference component from SBI - S - B, then a common 1.2 NNLO/NLO and 1.1 N3LO/NNLO rescaling is applied uniformly to signal, interference, and background. The paper states the NLO K-factors lack the full top-quark mass dependence and that NNLO/N3LO corrections for interference and background are not available (Sections 4 and 6.3). Inflating scale uncertainties near the ttbar threshold and for high-pT jets covers the size of a possible shift but does not re-center the prediction. Since the evidence is driven by the interference-dominated low-mu region, a shape shift from the now-available full NLO calculation (Ref [98]) could move the p-value. That's a real caveat, not a reason to reject: the same approximation was used in the previous histogram analysis, the effect is covered by enlarged uncertainties, and this is moderate evidence, not a discovery. I'd want a sentence in the paper explicitly saying the complete NLO result is now available and was not used, plus a bound on the expected impact.\n\nMinor: no public data or code, so reproducibility rests on the paper's internal tests. That's standard for ATLAS but worth keeping in view. The combination with 2l2nu reuses Ref [17] without re-analysis; fine.\n\nBottom line: serious, careful measurement. The central claim holds up; the K-factor caveat is the most significant unvalidated premise but is disclosed and hedged with inflated systematics. The paper deserves a serious referee, and I'd bring it to a reading group for the NSBI methodology as much as the physics.","headline":"Solid ATLAS measurement: NSBI improves off-shell H sensitivity, but the uniform K-factor treatment of the interference is the main caveat.","tokens_in":73203,"tokens_out":3373,"would_cite":true,"duration_ms":28857,"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":"Using a neural simulation-based inference technique, this analysis finds 2.5 sigma evidence for off-shell Higgs production in H*→ZZ→4ℓ and measures the Higgs width as 4.3 MeV, consistent with the Standard Model.","keywords":["off-shell Higgs boson","Higgs boson total width","neural simulation-based inference","ZZ to four leptons","gluon fusion","LHC Run 2","signal interference background","profile likelihood"],"falsifier":"Re-run the profile-likelihood fit replacing the flat NNLO/NLO $=1.2$ and N3LO/NNLO $=1.1$ rescaling by differential K-factors from a complete NLO QCD calculation with full top-quark mass dependence and from a genuine off-shell N3LO interference calculation; if the fitted $\\mu_{\\text{off-shell}}$ moves by more than its systematic uncertainty, or the observed significance falls below $2\\sigma$, the modeling premise that carries the result is falsified.","tokens_in":72188,"feed_emoji":"⚛️","tokens_out":10659,"duration_ms":86003,"temperature":0.7,"pith_summary":"This paper reports a measurement of off-shell Higgs boson production in the $H^*\\to ZZ\\to 4\\ell$ channel using $140\\,\\text{fb}^{-1}$ of $\\sqrt{s}=13$ TeV proton--proton collision data from the ATLAS detector, analyzed with a neural simulation-based inference (NSBI) method in place of the previous histogram-based analysis. It claims observed (expected) evidence of $2.5\\sigma$ ($1.3\\sigma$) for off-shell production in this channel, and $3.7\\sigma$ ($2.4\\sigma$) when combined with the $ZZ\\to 2\\ell 2\\nu$ channel. Combining off-shell and on-shell production rates gives a Higgs total width of $4.3^{+2.7}_{-1.9}$ MeV observed, consistent with the Standard Model value of $4.1$ MeV. A careful reader would care because the Higgs width cannot be measured directly with current detector resolution, and the NSBI procedure extracts more information from the same dataset than histograms, improving the expected significance from $0.5\\sigma$ to $1.3\\sigma$.","feed_headline":"Neural inference lifts off-shell Higgs evidence to 2.5 sigma","feed_subtitle":"Combined with 2ℓ2ν channel, evidence hits 3.7σ; Higgs width 4.3 MeV matches Standard Model.","key_machinery":"The load-bearing object is the neural-network estimate of the per-event probability density ratio $p(x|\\mu,\\theta)/p_{\\text{ref}}(x)$, where $x$ is a set of fourteen reconstructed observables and the reference process is a fixed mixture of the gluon-fusion signal and one electroweak sample. Each ratio is learned by an ensemble of fully connected networks trained with binary cross-entropy, so the score function $s_X(x)$ yields the ratio through $p_X/p_{\\text{ref}} = s_X/(1-s_X)$. The interference component is not simulated directly: for gluon fusion it is obtained from an SBI sample as $I = \\text{SBI} - S - B$, and for electroweak production two SBI samples with different coupling multipliers are inverted to separate signal, interference, and background. These ratios enter a profile likelihood test statistic, with confidence intervals built from pseudo-experiments because the interference term makes the test statistic non-$\\chi^2$.","core_discovery":"The central claim is that off-shell Higgs boson production is present in the four-lepton final state at an observed significance of $2.5\\sigma$, and that this evidence is obtained with a neural simulation-based inference technique rather than the binned histograms of the earlier result. In the authors' model, neural networks estimate the per-event likelihood ratio between signal-strength hypotheses from simulated signal, interference, and background samples, with the interference term recovered by subtracting separately simulated signal and background samples from a combined SBI sample. Fitting this model to the data yields a signal strength of $0.87^{+0.75}_{-0.54}$ at 68% CL in the $4\\ell$ channel alone, and $1.06^{+0.62}_{-0.45}$ after combining with the $2\\ell2\\nu$ channel. The same fit, combined with on-shell $H\\to ZZ\\to 4\\ell$ production, gives $\\Gamma_H = 4.3^{+2.7}_{-1.9}$ MeV, consistent with the Standard Model and superseding the previous result in this channel.","pith_inferences":["If the modeling premise holds, the same NSBI procedure should push the $4\\ell$ channel past the $5\\sigma$ discovery threshold once the full Run 3 dataset is included, since the expected significance is currently statistics-limited in the interference-dominated region.","The flat NNLO/NLO $=1.2$ and N3LO/NNLO $=1.1$ rescaling factors are placeholders; replacing them with differential higher-order corrections that include the full top-quark mass dependence would provide a direct test of whether the central width value shifts. This is an inference beyond the paper's claims.","The per-event likelihood-ratio construction should transfer to other interference-dominated measurements, such as high-mass $ZZ$ and $WW$ production, where binned observables lose separation power.","The observed agreement with the Standard Model width leaves little room for light new states that modify off-shell couplings, unless such states preserve the on-shell-to-off-shell coupling ratio, a condition the paper's model does not test."],"forward_implications":["The same $140\\,\\text{fb}^{-1}$ dataset yields an expected significance of $1.3\\sigma$ with NSBI versus $0.5\\sigma$ with the histogram-based analysis, and an observed significance of $2.5\\sigma$ in the $ZZ\\to 4\\ell$ channel.","Combining the $4\\ell$ NSBI result with the existing $ZZ\\to 2\\ell2\\nu$ analysis gives observed (expected) evidence of $3.7\\sigma$ ($2.4\\sigma$) for off-shell Higgs production.","Combining off-shell and on-shell production rates constrains the Higgs width to $\\Gamma_H = 4.3^{+2.7}_{-1.9}$ MeV observed, with the expected value $4.1^{+3.5}_{-3.4}$ MeV centered on the Standard Model prediction.","The same framework provides 68% CL intervals for $\\kappa_{g,\\text{off-shell}}$, $\\kappa_{V,\\text{off-shell}}$, and for the ratios $R_{gg}$ and $R_{VV}$ that compare on-shell and off-shell couplings.","Systematic uncertainties dominate for signal-dominated hypotheses ($\\mu_{\\text{off-shell}}>1$), while interference-dominated hypotheses are limited mainly by statistics."],"supporting_citations":[{"why":"The prior histogram-based measurement in this channel and the 2l2nu analysis it is combined with; supplies the dataset, event selection, and the baseline whose expected sensitivity is superseded.","marker":"[17]"},{"why":"Self-contained description of the NSBI implementation, network architecture, hyperparameters, and validation tests used by this analysis.","marker":"[31]"},{"why":"Establishes that the gg→ZZ cross-section rises above the twice-Z-mass threshold, motivating off-shell Higgs measurements.","marker":"[12]"},{"why":"Shows the Higgs width can be constrained by comparing off-shell and on-shell ZZ production.","marker":"[13]"},{"why":"Provides a full analytic calculation of gg→e+e−μ+μ− that underlies the off-shell signal model and width bound.","marker":"[14]"},{"why":"Supplies the m_ZZ-dependent NLO QCD K-factors for the gg→ZZ signal, interference, and background components.","marker":"[60]"},{"why":"Fully differential NNLO corrections to gg→H→ZZ that motivate the common NNLO/NLO = 1.2 correction applied to the gg→ZZ components.","marker":"[61–63]"},{"why":"Inclusive N3LO/NNLO correction of 1.1 extrapolated to the off-shell region for the gg→ZZ components.","marker":"[65]"},{"why":"On-shell H→ZZ→4ℓ measurement used in the joint likelihood to extract the Higgs total width.","marker":"[106]"}],"fun_headline_variants":["Neural SBI spots off-shell Higgs at 2.5 sigma","Off-shell Higgs evidence climbs to 3.7 sigma combined","Neural inference yields 4.3 MeV Higgs width","Four-lepton off-shell Higgs: 2.5 sigma with neural nets","Neural nets sharpen off-shell Higgs to 2.5 sigma"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The measurement stands on the assumption that the simulated ggF SBI, signal, and background samples, rescaled by the same flat NNLO/NLO $=1.2$ and N3LO/NNLO $=1.1$ factors, correctly describe the normalization and shape of the signal, interference, and background in the off-shell region even though the complete NLO top-quark mass dependence and off-shell N3LO interference corrections are not yet available.","fun_headline_variants_meta":{"raw":{"variants":["Neural SBI spots off-shell Higgs at 2.5 sigma","Off-shell Higgs evidence climbs to 3.7 sigma combined","Neural inference yields 4.3 MeV Higgs width","Four-lepton off-shell Higgs: 2.5 sigma with neural nets","Neural nets sharpen off-shell Higgs to 2.5 sigma"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000259,"raw_usage":{"total_tokens":1687,"prompt_tokens":1149,"completion_tokens":538,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":765,"completion_tokens_details":{"reasoning_tokens":447}},"tokens_in":765,"tokens_out":538,"duration_ms":4997,"temperature":1.0,"reasoning_tokens":447,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T04:18:03.793246+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the profile-likelihood fit replacing the flat NNLO/NLO $=1.2$ and N3LO/NNLO $=1.1$ rescaling by differential K-factors from a complete NLO QCD calculation with full top-quark mass dependence and from a genuine off-shell N3LO interference calculation; if the fitted $\\mu_{\\text{off-shell}}$ moves by more than its systematic uncertainty, or the observed significance falls below $2\\sigma$, the modeling premise that carries the result is falsified.","supporting_citations":[{"cited_title":"QCD corrections to ZZ production in gluon fusion at the LHC","cited_arxiv_id":"1509.06734","evidence_quote":"Supplies the m_ZZ-dependent NLO QCD K-factors for the gg→ZZ signal, interference, and background components."}],"review_version":1}