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Constraining new physics from Higgs measurements with Lilith: update to LHC Run 2 results

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Lilith-2.0 turns LHC Run 2 Higgs measurements into a reusable global likelihood, with validated fits pinning the Higgs couplings to better than 10 percent.

desk verdict Genuinely useful software update with an honest but imperfect validation: the limit-to-Gaussian conversions in H→ZZ* and H→μμ are the soft spot; the headline global-fit numbers are safe. read the letter →

arxiv 1908.03952 v2 pith:MIDH7RVE submitted 2019-08-11 hep-ph hep-ex

Sabine Kraml , Tran Quang Loc , Dao Thi Nhung , Le Duc Ninh This is my paper · ORCID
classification hep-phhep-ex
keywords LilithHiggssignalstrengthsglobalfitsreducedcouplingskappaframeworktwo-Higgs-doubletmodelinvisibledecaysLHCRun2
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 presents Lilith-2.0, an updated public Python library that converts published LHC Higgs signal-strength measurements into a global likelihood for theorists to use in constraining new physics. The central claim is that this lightweight tool, together with its new database of ATLAS and CMS Run 2 results for 36 $fb^{-1}$, reproduces the experimental collaborations' own coupling fits closely enough to be trusted as a substitute for the full experimental likelihoods. The technical upgrade replaces the old fixed-width Gaussian approximation with variable-width Gaussian and Poisson likelihood forms and allows correlation matrices of arbitrary dimension, which is what makes the Run 2 data usable. On the physics side, the paper reports that the Run 2 data are perfectly compatible with the Standard Model, determine reduced Higgs couplings to better than 10 percent, and bound the invisible Higgs branching fraction at about 5 percent at 95% CL for Standard-Model-like couplings. A sympathetic reader would take the paper's contribution to be demonstrated reliability and ready availability of this approximation machinery rather than any claim of new physics.

What carries the argument

The carrying object is the signal-strength likelihood: each measured production-and-decay rate, mu(X,Y), is defined as the ratio of the observed to the Standard-Model rate, and the product of per-measurement likelihoods forms the global likelihood used for fits. The upgrade to version 2.0 lies in the shapes allowed for each piece: a variable Gaussian, whose width grows or shrinks with the parameter value to absorb asymmetric errors; a generalised Poisson, a count-based form with a free shape parameter tuned to the quoted uncertainties; and multi-dimensional Gaussians with arbitrary correlation matrices. The translation from rates to physics is made through reduced couplings CX and CY that scale Standard-Model production and decay amplitudes, which the paper identifies with the kappa framework, with the option to profile over invisible and undetected decay widths. This machinery converts the narrow-width, SM-tensor-structure assumption into concrete intervals on coupling combinations, which is what makes a wide class of new-physics models testable with a single downloaded tool.

What would settle it

Extract the true profile likelihoods for the ATLAS H->ZZ* VH and ttH channels from the collaboration's public material and compare them with the database's two-sided Gaussian entries, mu(VH,ZZ*) = 0 +/- 1.89 and mu(ttH,ZZ*) = 0 +/- 3.83; if those true likelihoods are markedly one-sided, the conversion used in DB 19.09 biases the global fits, and the paper's reliability claim would be falsified.

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Extended reading notes

Core claim

On the paper's own terms, the result is that Lilith-2.0 can reconstruct the likelihoods of the current ATLAS and CMS Run 2 Higgs measurements with enough fidelity that its global fits track the official coupling contours, and that the accompanying database DB 19.09 is ready for general use. Combining the ATLAS and CMS Run 2 data, the global fit of the fermionic and vector reduced couplings gives CF = 1.045+0.064-0.063 and CV = 1.068 +/- 0.030, with the two experiments agreeing at about the 1 sigma level. In the same framework, the visible signal strengths alone already constrain the invisible decay branching fraction to about 5 percent at 95% CL for Standard-Model-like couplings. The slight preference for a vector coupling above one, if taken at face value, pushes two-Higgs-doublet models, where CV is bounded by one, deeper into the alignment limit.

Load-bearing premise

The load-bearing premise is that the simplified likelihood shapes stored in the database, built from published best-fit values, uncertainties, and correlations, capture the real experimental likelihoods closely enough that approximate entries, such as H->ZZ* limits converted from 95% CL bounds, do not bias the global fit.

Editorial extensions

If this is right

  • Any new-physics model that only rescales Standard-Model Higgs couplings can be tested immediately against the full Run 2 Higgs dataset by running Lilith-2.0, without re-implementing the experimental likelihoods.
  • The roughly 3-4 percent determination of CV and sub-10 percent determinations of the fermion and vector couplings put concrete pressure on scenarios predicting percent-level coupling deviations.
  • The invisible branching fraction bound of about 5 percent at 95% CL for Standard-Model-like couplings directly restricts Higgs-portal dark-matter models, and tightens to about 4 percent when Run 1 data are added.
  • The preference for CV slightly above one strengthens the case that two-Higgs-doublet models live in the alignment limit, disfavouring large deviations in tan(beta) and cos(beta-alpha).
  • Because the database format now supports arbitrary correlation matrices, the same machinery can be extended with future full-Run-2 and HL-LHC measurements as they are published.

Reading between the lines

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

  • Extension: the accuracy of the DB 19.09 parametrisations will get a natural stress test when ATLAS and CMS release their full 139 fb^-1 Run 2 combinations; if the official profile likelihoods for CV and BR(H->inv) shift markedly from Lilith's, the simplified shapes should be revised.
  • Extension: the paper's own complaints about digitizing plots and hand-typing correlation matrices suggest the next natural step is direct ingestion of STXS-binned data or machine-readable likelihood files, eliminating the lossy reconstruction step.
  • Extension: the same validation-then-fit pattern used here is transferable to other LHC observables where experiments publish only summary statistics, so the methodology is a template beyond Higgs physics.
  • Extension: the headline '5 percent bound' on invisible Higgs decays is conditional on Standard-Model-like couplings; theorists with fermion or vector coupling freedom should quote the roughly 15-16 percent bound instead of the headline value.
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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

3 major / 5 minor

Summary. The paper presents Lilith-2.0, a public Python library for constraining new physics from Higgs signal-strength measurements, together with an updated XML database (DB 19.09) that incorporates ATLAS and CMS Run 2 results at 36 fb^-1. The main technical novelties are the extension from ordinary Gaussian likelihoods to variable-Gaussian and generalized-Poisson parametrizations, the support of arbitrarily large correlation matrices, and the addition of new production modes (ggZH, tH, bbH). The authors document each experimental input, show validation plots against official ATLAS/CMS contours where available, and give updated global fits for reduced couplings, 2HDM Types I and II, and invisible Higgs decays, finding e.g. C_V = 1.068 +/- 0.030 and BR(H -> inv) < 5% at 95% CL for SM-like couplings. The central claim is that Lilith-2.0 with DB 19.09 is ready for use in constraining a wide class of new physics scenarios.

Significance. If the database is reliable, this is a valuable community resource: it is lightweight, Python-based, publicly available, and it makes efficient use of the best public Higgs measurements, including the full 24x24 CMS correlation matrix. The paper is generally transparent about its approximations, explicitly flagging, for instance, the LO treatment of tHW, the assumed WW/ZZ composition of the ttH VV final state, and the fact that the paper updates rather than replaces the Lilith-1.1 manual. The global-fit results are plausible and consistent with the SM. The chief risk is not the statistical formalism but the fidelity of the reconstructed likelihoods for entries that are digitized from plots or converted from limits; those entries feed the global fits and exclusions, so the 'ready to be used' claim rests on their accuracy.

major comments (3)
  1. [Section 5.1, H->WW and H->tau tau; Fig. 3] The conversion of the ATLAS 95% CL upper limits for mu(VH,ZZ*) and mu(ttH,ZZ*) into two-sided Gaussians with sigma = L/1.96 (implemented as 0 +/- 1.89 and 0 +/- 3.83) makes the effective 95% upper bound 1.64 sigma = 0.84 L rather than the published L; if the limits are one-sided, the appropriate Gaussian width would be sigma = L/1.64, so the database is about 16% tighter for positive signal strengths. The authors state that this normalization was chosen because a one-sided assumption gives a less good match to the official C_F vs. C_V contour, which is a tuning against the validation target rather than an independent test. Since these two entries enter all global fits in Section 6, the central claim that DB 19.09 is ready to be used needs a sensitivity study showing how the quoted constraints (C_V = 1.068 +/- 0.030, C_F = 1.045 +/- 0.064, BR(H->inv) < 5%) change when the entries are instead implemented as one-sided Gaussians or with alternative asymmetric widths.
  2. [Section 5.1, H->mu mu] For several ATLAS Run 2 entries the validation is partly circular: the parameters of the approximating likelihood are fitted directly to the experimental 95% CL contour, and the validation plot then compares the Lilith reconstruction with that same contour (e.g., Fig. 3, top-right and bottom panels). This demonstrates internal consistency but not that the parametrization is accurate away from the fitted region or in the tails used for 95% CL exclusions. For these channels no official coupling fit is available, so I ask for an independent cross-check, such as a comparison with the underlying category-level likelihood or a coverage test of the reconstructed likelihood.
  3. [Section 5.1, H->mu mu] The same one-sided/two-sided ambiguity affects the H->mu mu entry: ATLAS reports mu = -0.1 +/- 1.5 with a CLs 95% upper limit of 3.0, and the database implements mu = 0 +/- 1.53. Under a one-sided Gaussian interpretation this corresponds to a 95% upper bound of 1.64 x 1.53 = 2.51, which is more restrictive than the published limit rather than less restrictive. If the intention is to avoid over-constraining, the width should be larger (sigma ~ 1.83 if matching the one-sided limit), or the two-sided interpretation should be explicitly stated and justified.
minor comments (5)
  1. [Section 2] The text 'This does does not always allow' contains a duplicated 'does' and should read 'This does not always allow'.
  2. [Section 5.1, H->tau tau] In the sentence describing the H->tau tau likelihood, 'mu(VBF,WW) ~ 1.20+0.62-0.56' should read 'mu(VBF,tau tau) ~ 1.20+0.62-0.56'.
  3. [Section 5.1, ttH combination] The caveat that the HIGG-2017-02 XML file should not be used when C_Z != C_W is important; the code should ideally issue an explicit warning when this file is loaded under assumptions that violate that condition.
  4. [Section 4] The statement that 8 TeV cross sections are used for sqrt(s) = 7 TeV because differences are negligible would be more helpful if accompanied by a quantitative estimate or a reference for that estimate.
  5. [Appendix A, Fig. 14] The text notes that even with the Poisson form the 95% CL contour for H->ZZ* is still 'quite off' before the auxiliary profile likelihoods are used; this reinforces the sensitivity concerns raised in the major comments and should be discussed in the main text rather than only in the appendix.

Circularity Check

1 steps flagged · score 2.0 of 10

No circular derivation of the physics constraints; the only mild circularity is that one H→ZZ* likelihood parametrization was chosen by matching the official ATLAS contour that is then used for validation.

  1. other [Section 5.1, H→ZZ* (HIGG-2016-22), validation Fig. 2]
    "For the VH and ttH production modes, lacking more information, we convert the given 95% CL limits into µ(VH, ZZ∗) = 0± 1.89 and µ(ttH, ZZ∗) = 0 ± 3.83 using a 2-sided Gaussian (assuming 1-sided limits gives a less good agreement with the ATLAS CF vs. CV fit)."

    The one-sided versus two-sided conversion of the published 95% CL upper limits is selected by requiring better agreement with the official ATLAS CF vs. CV contour, and the same contour is then used as the validation target in Fig. 2. Thus the validation of this database entry is partly self-consistent: the parametrization was tuned toward the very curve it is compared against. This does not make the global coupling fits circular, because the fitted constraints still depend on external ATLAS/CMS measurements, but it weakens the independence of the validation for these two ZZ* limit-derived entries.

full rationale

Lilith-2.0 is a likelihood-reimplementation tool: its inputs are signal strengths, uncertainties, correlations, and likelihood grids taken from ATLAS and CMS publications, and its outputs are global constraints on Higgs coupling modifiers, 2HDM parameters, and invisible branching ratios. The core derivations are therefore self-contained in the sense that the fitted quantities are not defined in terms of the outputs, and the numerical results quoted in Section 6 (e.g., CV = 1.068 ± 0.030, BR(H→inv) < 5%) come from evaluating external measurements through the model relation in Eq. (2). No equation in the paper reduces a predicted quantity to an input by construction, and no load-bearing claim rests solely on a self-citation: the citations to earlier Lilith papers and to the authors' previous global-fit papers provide background and methodology but not the uniqueness or validity of the Run 2 database. The only noteworthy circularity-adjacent step is in Section 5.1, where the choice to represent ATLAS VH and ttH H→ZZ* limits as two-sided Gaussians is justified by better agreement with the official ATLAS CF vs. CV contour, and the same contour is used for validation. This is a tuning of the approximation to the validation target, so the validation is not fully independent for those entries. However, it is a localized implementation choice, not a circular derivation of the paper's physics conclusions; the rest of the database is built from published best-fit values, uncertainties, and correlation matrices. Overall, the central claim that Lilith-2.0 can constrain new physics from Run 2 Higgs data has substantial independent content, and the paper deserves only a low circularity score reflecting the partially self-consistent validation procedure.

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

The database relies on several correlation coefficients and composition fractions that are fitted from plots or chosen by hand, and on SM cross section inputs from the LHC Higgs Cross Section Working Group. There are no invented physical entities.

free parameters (7)
  • rho(H->ZZ ggH,VBF) = -0.41
    Correlation between mu(ggH,ZZ) and mu(VBF,ZZ) in ATLAS HIGG-2016-22, taken from Aux. Fig. 4c; chosen to reproduce the official CF vs CV fit.
  • rho(H->WW ggH,VBF) = -0.08
    Correlation fitted from Fig. 9 of ATLAS-HIGG-2016-07.
  • rho(H->WW ZH,WH) = -0.08
    Correlation fitted from Fig. 8 of ATLAS-HIGG-2017-14.
  • rho(ttH bb,VV) = 0.04
    Correlation estimated from Figs. 17a,b of ATLAS-HIGG-2017-02.
  • rho(ttH tau,VV) = -0.35
    Correlation estimated from Figs. 17a,b of ATLAS-HIGG-2017-02.
  • WW fraction in ttH VV = 0.95
    Rough estimate; valid only if CZ=CW=CV, as stated in Section 5.1.
  • H->mu mu production composition = ggH 90%, VBF 7%, VH 3%
    Estimated from Aux. Table 3 of ATLAS-HIGG-2016-10.
assumptions (7)
  • domain assumption New physics is assumed to affect the 125 GeV Higgs only through scalings of SM-like production and decay amplitudes (same Lorentz structure as the SM); the signal strength framework further relies on the narrow-width approximation.
    Section 1 states this explicitly: 'the assumption that new physics results only in the scaling of SM Higgs processes.'
  • domain assumption Loop-induced couplings Cg and Cgamma are computed from tree-level reduced couplings assuming no new particles in the loops, unless taken as free parameters.
    Section 1: 'If no new particles appear in the loops, Cg and Cgamma are computed...'
  • domain assumption The total width is modified only via a multiplicative factor (1 - BR(H->inv) - BR(H->undet)), i.e., new invisible or undetected decays do not alter the kinematics.
    Eq. (4) in Section 1.
  • ad hoc to paper For sqrt(s)=7 TeV, the 8 TeV cross section values are used; differences are claimed negligible.
    Section 4: 'for the case sqrt(s)=7 TeV, the values at 8 TeV are used.'
  • ad hoc to paper The tHW cross section is computed at leading order with MadGraph, with the given scale choice, because an NLO definition is not straightforward.
    Section 4, Table 2 and text: 'It is noted that the definition of an NLO cross section for the tHW channel is not straightforward.'
  • ad hoc to paper The profile likelihood for Cg vs Cgamma treats BR(H->inv) and BR(H->undet) as free but individually capped at 50% to enforce the physical sum constraint.
    Section 6, footnote 10: 'we demanded that both BR(H->inv.) and BR(H->undet.) be less than 50%.'
  • domain assumption The Higgs mass is fixed to mH = 125.09 GeV.
    Section 6: 'we use mH = 125.09 GeV.'

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Cite this review

Pith. "Pith review of Constraining new physics from Higgs measurements with Lilith: update to LHC Run 2 results." pith.science (2026). https://pith.science/paper/MIDH7RVE

@misc{pith2026190803952,
  author       = {Pith},
  title        = {Pith review of: Constraining new physics from Higgs measurements with Lilith: update to LHC Run 2 results},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MIDH7RVE}},
  note         = {Machine review of arXiv:1908.03952}
}
read the original abstract

Lilith is a public Python library for constraining new physics from Higgs signal strength measurements. We here present version 2.0 of Lilith together with an updated XML database which includes the current ATLAS and CMS Run 2 Higgs results for 36/fb. Both the code and the database were extended from the ordinary Gaussian approximation employed in Lilith-1.1 to using variable Gaussian and Poisson likelihoods. Moreover, Lilith can now make use of correlation matrices of arbitrary dimension. We provide detailed validations of the implemented experimental results as well as a status of global fits for reduced Higgs couplings, Two-Higgs-doublet models of Type I and Type II, and invisible Higgs decays. Lilith-2.0 is available on GitHub and ready to be used to constrain a wide class of new physics scenarios.

Figures

Figures reproduced from arXiv: 1908.03952 by the authors.

Figure 1
Figure 1. Fit of CF vs. CV (left) and Cγ vs. Cg (right) for data from the ATLAS H → γγ analysis [16]. The red, orange and yellow filled areas show the 68%, 95% and 99.7% CL regions obtained with Lilith using best-fit values and uncertainties for the signal strengths as extracted from Aux. Figs. 23a–d of the ATLAS analysis together with the 4 ×4 correlation matrix for the stage-0 STXS. This can be compared to the 68%, 95% CL c… view at source ↗
Figure 2
Figure 2. Fit of CF vs. CV for data from the ATLAS H → ZZ∗ analysis, using µ(ggH, ZZ∗ ) and µ(VBF, ZZ∗ ) as fitted from Aux. Figs. 7a and 7b of [21]; the ggH vs. VBF likelihood is then approximated as a bivariate Poissonian with correlation −0.41 (see text for more details). The 68%, 95% and 99.7% CL regions obtained with Lilith are shown as red, orange and yellow areas, and compared to the 68% and 95% CL contours from ATLAS … view at source ↗
Figure 3
Figure 3. Reconstruction of the experimental likelihood as 2D variable Gaussian; top panels [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: Fit of CF vs. CV from a combination of the ATLAS ttH measurements (see text for details). The 68%, 95% and 99.7% CL regions obtained with Lilith are shown as red, orange and yellow areas, and compared to the 68%, 95% CL contours from ATLAS (in blue). The best-fit point…
Figure 5
Figure 5. Figure 5: Fit of CF vs. CV using best-fit values and uncertainties for the signal strengths for each production (ggH, VBF, WH, ZH, ttH) and decay (γγ, ZZ, WW, τ τ , b ¯b, µµ) mode com￾bination together with the 24 × 24 correlation matrix from the CMS combination paper [12]. The …
Figure 6
Figure 6. Figure 6: Fit of tan β vs. cos(β − α) for the 2HDMs of Type I (left) and Type II (right) using the data from the combined CMS measurement [12]. The beige, orange and red filled areas show the 68%, 95% and 99.7% CL regions obtained with Lilith, while the blue dots mark the 95% CL…
Figure 7
Figure 7. Figure 7: Fit of Cg vs. Cγ using the data from the combined CMS measurement [12] and the search for invisible decays of a Higgs boson [32]. The branching ratios of invisible and undetected decays are treated as free parameters in the fit. The 1σ, 2σ and 3σ regions obtained with …
Figure 8
Figure 8. Figure 8: Fit of CF vs. CV (left) and Cg vs. Cγ (right) using the Run 2 dataset of the current database version, DB 19.09. The 68% and 95% CL regions for the combined ATLAS results are shown in blue, those for CMS in green. 0.8 0.9 1.0 1.1 1.2 1.3 CV 0.7 0.8 0.9 1.0 1.1 1.2 1.3 …
Figure 9
Figure 9. Figure 9: Fit of CF vs. CV (left) and Cg vs. Cγ (right) from a combination of the ATLAS and CMS Run 2 results in DB 19.09; the 68%, 95% and 99.7% CL regions are shown as red, orange and yellow areas, respectively. In addition, the light-blue, dashed contours indicate the 68%, 95…
Figure 10
Figure 10. Figure 10: As Fig. 9 but for a fit of [PITH_FULL_IMAGE:figures/full_fig_p019_10.png]
Figure 11
Figure 11. Figure 11: Fits of tan [PITH_FULL_IMAGE:figures/full_fig_p020_11.png]
Figure 12
Figure 12. Figure 12: Status of invisible Higgs decays. Left: 1D profile likelihood of BR( [PITH_FULL_IMAGE:figures/full_fig_p021_12.png]
Figure 13
Figure 13. Figure 13: Fits of CF vs. CV for the data from ATLAS-HIGG-2016-21 (left) and CMS-HIG￾17-031 (right) using type="n" (ordinary Gaussian) instead of type="vn" (variable Gaussian) in the database XML file. To be compared with the respective plots in Figs. 1 and 5. 0.6 0.8 1.0 1.2 1.…
Figure 14
Figure 14. Figure 14: Fits of CF vs. CV for the data from ATLAS-HIGG-2016-22 (H → ZZ∗ ), using µ(ggH, ZZ∗ ) = 1.11+0.23 −0.21 and µ(VBF, ZZ∗ ) = 4.0 +1.75 −1.46 from [PITH_FULL_IMAGE:figures/full_fig_p023_14.png]
Figure 15
Figure 15. Figure 15: Evolution of the validation for the ATLAS ttH combination. Top left: [PITH_FULL_IMAGE:figures/full_fig_p024_15.png]

Discussion (0). Continue with ORCID to comment.

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