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Measurement of off-shell Higgs boson production in the $H^*\rightarrow ZZ\rightarrow 4\ell$ decay channel using a neural simulation-based inference technique in 13 TeV $pp$ collisions with the ATLAS detector

T0 review · 2 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict Solid ATLAS measurement: NSBI improves off-shell H sensitivity, but the uniform K-factor treatment of the interference is the main caveat. read the letter →

arxiv 2412.01548 v2 pith:4BCUYXOL submitted 2024-12-02 hep-ex

ATLAS Collaboration This is my paper · ORCID
classification hep-ex
keywords off-shellHiggsbosontotalwidthneuralsimulation-basedinferenceZZtofourleptonsgluonfusionLHCRun2signalinterferencebackgroundprofilelikelihood
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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 $1.3\sigma$.

What carries the argument

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-$\chi^2$.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

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.

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 (2)
  1. [Section 4, Table 2, Section 6.3] 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.
  2. [Section 7 and Figure 12] 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.
minor comments (4)
  1. [Section 3, Eq. (4)] The parenthetical "(I = SBI - S + B)" is inconsistent with the displayed equation I = SBI - S - B; please correct the sign in the text.
  2. [Section 7, Figure 12 caption] The caption reads "the green solid curve shows the shows the expected distribution"; the duplicated phrase should be removed.
  3. [Table 6] 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.
  4. [Section 6.2] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the analysis is a standard profile-likelihood fit to parameterized Monte Carlo templates, and the width extraction uses an explicitly stated no-BSM assumption rather than any fitted quantity renamed as a prediction.

full rationale

The derivation chain is self-contained. The signal model is specified in Eqs. (2)-(5) from the kappa-framework and fixed MC samples, with the interference terms constructed algebraically as SBI - S + B (Eq. 4) and EW inversions (Eq. 5, Table 1), which are definitions, not fitted outputs. The NSBI estimates of per-event density ratios are trained on those fixed templates and validated on Asimov samples (Figures 7-8, 10), so the statistical inference is a genuine fit of mu_off-shell and nuisance parameters to the data via Eqs. (15)-(17). The expected significances come from Asimov pseudo-data with known signal strength and are sensitivity projections, not data predictions. The only approximations entering as theory inputs are the average NNLO/NLO = 1.2 and N3LO/NNLO = 1.1 K-factors for ggF S/I/B, which are stated as unavailable-for-interference approximations and are covered by scale uncertainties; an unvalidated shape assumption is a modeling risk, not circularity. The combined 2l2nu channel and the NSBI method reference prior ATLAS work [17,31], but those citations are independent supporting inputs or methodological details, and the central 4l measurement is performed and validated in this paper. The Higgs width extraction (Eq. 18) combines on-shell and off-shell rates under the paper's explicit assumption of equal on/off-shell couplings, a physics assumption rather than a circular reduction. No equation in the paper reduces a claimed prediction to a fitted parameter or to a self-citation chain.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The central fit uses a kappa-framework Monte Carlo model with signal, interference, and background components; the parameter of interest is a fitted signal strength, not a derived constant. Free parameters are the measured mu, three data-driven background normalizations, and 127 systematic nuisance parameters. Additional load-bearing assumptions include the local subtraction of interference samples, uniform higher-order K-factors, unbiased NN density ratios, detector simulation, and the no-BSM assumption for the width interpretation. No new physical entities such as new particles, forces, or dimensions are introduced.

free parameters (4)
  • mu_off-shell (4l) = 0.87 +0.75 -0.54 (observed, 4l); 1.06 +0.62 -0.45 (combined with 2l2nu)
    Primary parameter of interest in the likelihood fit; defines the off-shell Higgs signal strength in Equation 3.
  • theta_incl_qqZZ, theta_1j_qqZZ, theta_2j_qqZZ = 1.12 +/- 0.04, 0.85 +/- 0.05, 0.90 +/- 0.07
    Data-driven normalizations of the dominant qq -> ZZ background in njets bins, introduced in Equation 7 and fitted to data.
  • 127 nuisance parameters = Constrained by auxiliary measurements; individual best-fit values not fully listed
    Systematic uncertainties modeled as nuisance parameters affecting both event rates and per-event density ratios, as described in Section 6.3.
  • NN hyperparameters
    Architecture, batch size, ensemble size, and the Dpre threshold were chosen by the authors to pass calibration tests; they affect the estimated density ratios and hence the measurement.
assumptions (7)
  • domain assumption The ggF and EW cross sections factor into signal, interference, and background terms scaling as mu, sqrt(mu), and 1 respectively, as in Equation 3.
    This kappa-framework model defines what is measured; if the kinematics depend on the couplings in a more complicated way, the fitted mu loses its interpretation.
  • domain assumption Interference-only distributions can be obtained by subtracting separately generated SBI, S, and B samples, as in Equation 4, and by inverting the EWSBI1 and EWSBI10 samples, as in Equation 5.
    This requires that the SBI samples contain the same interference terms and that the on-shell contamination in the EW samples is negligible or handled by the mixing procedure.
  • ad hoc to paper Average NNLO/NLO = 1.2 and N3LO/NNLO = 1.1 K-factors apply uniformly to the ggF signal, interference, and background components in the off-shell region.
    Higher-order corrections to the off-shell interference are not fully known, so a common rescaling is assumed for all components, as described in Section 4.
  • domain assumption Neural-network estimates of the density ratios are unbiased after ten-fold cross-validation and ensembling.
    The paper validates this with Asimov reweighting tests and closure tests, but there is no formal guarantee; residual bias would shift the fitted signal strength.
  • domain assumption The Geant4-based ATLAS detector simulation and the chosen Monte Carlo generators describe the 4l final state and jet response accurately enough for the measurement.
    This is the standard ATLAS modeling assumption, inherited from cited performance papers, and cannot be checked externally from this preprint.
  • domain assumption No beyond-Standard-Model physics alters the on-shell and off-shell Higgs couplings differently in the width interpretation.
    Stated in Section 7.2; if false, the derived Gamma_H constraint is not the SM Higgs width.
  • standard math Poisson counting terms and Gaussian auxiliary constraints define the profile likelihood test statistic.
    This is the standard LHC statistical framework, and asymptotic approximations are avoided by using the Neyman construction with pseudo-experiments.

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Cite this review

Pith. "Pith review of Measurement of off-shell Higgs boson production in the $H^*\rightarrow ZZ\rightarrow 4\ell$ decay channel using a neural simulation-based inference technique in 13 TeV $pp$ collisions with the ATLAS detector." pith.science (2026). https://pith.science/paper/4BCUYXOL

@misc{pith2026241201548,
  author       = {Pith},
  title        = {Pith review of: Measurement of off-shell Higgs boson production in the $H^*\rightarrow ZZ\rightarrow 4\ell$ decay channel using a neural simulation-based inference technique in 13 TeV $pp$ collisions with the ATLAS detector},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4BCUYXOL}},
  note         = {Machine review of arXiv:2412.01548}
}
abstract

A measurement of off-shell Higgs boson production in the $H^*\to ZZ\to 4\ell$ decay channel is presented. The measurement uses 140 fb$^{-1}$ of proton-proton collisions at $\sqrt{s}=13$ TeV collected by the ATLAS detector at the Large Hadron Collider and supersedes the previous result in this decay channel using the same dataset. The data analysis is performed using a neural simulation-based inference method, which builds per-event likelihood ratios using neural networks. The observed (expected) off-shell Higgs boson production signal strength in the $ZZ\to 4\ell$ decay channel at 68% CL is $0.87^{+0.75}_{-0.54}$ ($1.00^{+1.04}_{-0.95}$). The evidence for off-shell Higgs boson production using the $ZZ\to 4\ell$ decay channel has an observed (expected) significance of $2.5\sigma$ ($1.3\sigma$). The expected result represents a significant improvement relative to that of the previous analysis of the same dataset, which obtained an expected significance of $0.5\sigma$. When combined with the most recent ATLAS measurement in the $ZZ\to 2\ell 2\nu$ decay channel, the evidence for off-shell Higgs boson production has an observed (expected) significance of $3.7\sigma$ ($2.4\sigma$). The off-shell measurements are combined with the measurement of on-shell Higgs boson production to obtain constraints on the Higgs boson total width. The observed (expected) value of the Higgs boson width at 68% CL is $4.3^{+2.7}_{-1.9}$ ($4.1^{+3.5}_{-3.4}$) MeV.

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Forward citations

Cited by 8 Pith papers

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    hep-ex 2026-08 accept novelty 6.0 of 10

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    No excess over background is found in ATLAS's first search for X→SH→4b, which sets 95% CL upper limits of 0.7 fb–2.6 pb on the production cross-section times branching ratio.

  3. Theoretical modeling of QCD radiation in off-shell Higgs production through gluon fusion

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    A controlled three-generator comparison shows that NLO+PS and LO jet merging differ by up to a factor of two in off-shell gg to H to ZZ to 4l predictions, with MadGraph underproducing sub-leading jets.

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    Updated Gfitter EW fit with new MW average yields SM-consistent indirect observables and, via kappa_V from oblique parameters plus LHC signal strengths, determines Gamma_H to ~10% precision under leading-log assumptions.

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