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Combining five measurements of Higgs production and decay, the paper finds no evidence of CP violation in Higgs–vector-boson interactions and sets the most stringent SMEFT limits on three CP-odd Wilson coefficients.

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2026-08-02 17:45 UTC pith:G54RA4H2

load-bearing objection Solid ATLAS combination with a genuinely new three-operator SMEFT fit; the no-CP-violation conclusion holds, but the EFT-validity caveat for the wide c_HB/c_HWB intervals deserves scrutiny. the 2 major comments →

arxiv 2603.20117 v2 pith:G54RA4H2 submitted 2026-03-20 hep-ex

Combination of measurements of CP properties of Higgs boson interactions with vector bosons using proton-proton collisions at sqrt{s} = 13 TeV with the ATLAS detector

The ATLAS Collaboration This is my paper
classification hep-ex
keywords Higgs bosonCP violationSMEFTWilson coefficientsvector boson fusionelectroweak gauge bosonsLHCATLAS
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Combining five measurements of Higgs boson production and decay, the paper asks whether the Higgs boson's interactions with W and Z bosons respect charge-parity (CP) symmetry. Using 140 fb^-1 of 13 TeV proton–proton collisions, the analysis combines VBF production with H→ττ, H→WW*, and H→γγ, inclusive H→ZZ*, and WH production with H→bb, relying only on the shapes of CP-sensitive angular distributions. No evidence of CP violation is found. In the Standard Model Effective Field Theory (SMEFT), the single-parameter fit gives a 95% confidence interval for the CP-odd Wilson coefficient c_HW~ of [−0.14, 0.49] (linear-only) and [−0.13, 0.60] (linear plus quadratic) at Λ=1 TeV, improving on previous limits by more than 40%. The combination also enables, for the first time, a simultaneous fit of three CP-violating operators, c_HW~, c_HB~, and c_HW~B, yielding the most stringent constraints to date on these coefficients.

Core claim

The central claim is that, after combining the five channels, the data are fully consistent with the Standard Model prediction of a CP-even Higgs boson. The single-parameter fit gives observed (expected) 95% CL intervals for c_HW~ of [−0.14, 0.49] ([−0.28, 0.29]) in the linear-only interpretation and [−0.13, 0.60] ([−0.30, 0.30]) including quadratic terms, at Λ=1 TeV. The simultaneous fit, made possible by the combination, constrains c_HW~, c_HB~, and c_HW~B together, with larger intervals due to correlations; the paper reports best-fit values and 95% CL intervals for each coefficient with the other two profiled. The agreement between linear-only and linear-plus-quadratic results is taken as

What carries the argument

The analysis rests on the SMEFT cross-section expansion O = O_SM [1 + Σ_i A_i c_i/Λ^2 + Σ_i B_i c_i^2/Λ^4 + Σ_{i<j} C_ij c_i c_j/Λ^4], evaluated at Λ=1 TeV in the Warsaw basis, together with shape-only fits of CP-odd observables: optimal observables in H→γγ, H→ττ, and H→ZZ*; the azimuthal jet separation Δφ_jj in H→WW*; and the charge-lepton angular variable Qℓ cosδ+ in WH, H→bb. These observables must have zero mean if CP is conserved, so any asymmetry signals CP violation. The channels are combined in a profile-likelihood fit with correlated systematic uncertainties.

Load-bearing premise

The result assumes the data are described by the Standard Model plus exactly three CP-violating dimension-six operators with a fixed new-physics scale Λ=1 TeV; if the EFT expansion is not valid inside the quoted 95% CL intervals, the Wilson-coefficient limits would not carry their stated physical meaning.

What would settle it

A future measurement of any of the CP-odd observables used here—for instance the optimal-observable mean in H→ZZ* or the Qℓ cosδ+ asymmetry in WH, H→bb—that differs from zero by more than five standard deviations, or a best fit that falls outside the quoted 95% CL intervals, would falsify the claim that the Higgs–gauge sector is CP-conserving.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If the central claim is right, the Higgs boson's couplings to W and Z remain consistent with the Standard Model's CP-even prediction, and no new source of CP violation is required in the Higgs–gauge sector.
  • The over-40% improvement over the best single channel shows that combining VBF, VH, and inclusive decay channels is a powerful route to tightening CP-odd operator constraints.
  • The first simultaneous fit of c_HW~, c_HB~, and c_HW~B makes experimental correlations among the three operators explicit, so future global SMEFT fits can use them directly.
  • The agreement between linear-only and linear-plus-quadratic interpretations supports the adequacy of the dimension-six SMEFT truncation in the probed parameter region.
  • The resulting intervals are the most stringent constraints to date on these Wilson coefficients within the SMEFT Warsaw basis with minimal model dependence.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The newly used Qℓ cosδ+ observable in WH, H→bb could be extended to ZH and to VBF production in later runs, where higher-momentum W/Z bosons enlarge the asymmetry and could sharpen the c_HW~ bound beyond simple luminosity scaling.
  • The elongated contours in the c_HB~–c_HW~B plane suggest that processes with different operator admixtures, such as Higgs-pair production or vector-boson scattering, may break the remaining degeneracy more efficiently than adding data in the same five channels.
  • A direct translation of these limits into bounds on the electron and neutron electric dipole moments would connect this collider result to low-energy CP-violation searches and to scenarios of electroweak baryogenesis; the paper does not perform that translation.
  • If sensitivity continues to scale roughly with the square root of integrated luminosity, the full high-luminosity LHC dataset should push the c_HW~ interval to roughly ±0.1, a region where CP-violating Higgs–gauge couplings could start to be relevant for the baryon asymmetry.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. This paper presents a combination of ATLAS Run 2 measurements (VBF H→ττ, H→WW*, H→γγ, inclusive H→ZZ*, and a new WH, H→bb analysis) to constrain the CP-violating SMEFT Wilson coefficients c_HW, c_HB, and c_HWB in the Warsaw basis. The combination uses shape-based optimal observables and STXS-based parametrizations, with linear-only and linear-plus-quadratic scenarios. Single-parameter fits yield 95% CL intervals for c_HW of [-0.14, 0.49] (linear-only) and [-0.13, 0.60] (linear+quadratic); simultaneous fits provide, for the first time, three-coefficient constraints. No evidence for CP violation is observed.

Significance. If the SMEFT truncation is valid over the quoted ranges, these are the most stringent constraints on these operators and the first simultaneous three-operator combination. The paper is careful about correlations, reports expected and observed limits, and honestly discloses the undefined WH confidence interval in the quadratic scenario. The no-CP-violation conclusion is robust to the EFT-validity concern, since all best-fit values are within about one standard deviation of zero. However, the headline 'most stringent constraints' claim rests on the physical interpretation of the 95% CL intervals, which is asserted but not fully demonstrated.

major comments (2)
  1. [Combination results and Eqs. (1)-(2)] The central claim that the quoted 95% CL intervals are SMEFT constraints is not supported by a quantitative EFT-validity check. The text states that negative-cross-section regions are 'outside the observed 95% CL contours and outside of EFT validity regions,' but no criterion for EFT validity or proof of positivity inside the contours is given. For the linear-only parameterization, μ_p = 1 + Σ A_pj c_j is not positive definite; the simultaneous-fit profile intervals for c_HB (~1.4) and c_HWB (~3.0) (Fig. 4) extend into regions where |A c| can be O(1) and dimension-8 contributions scale as (c v^2/Λ^2)^2 ~ O(0.1–0.5) at Λ=1 TeV, comparable to the dimension-6 linear term. The compatibility of c_HW intervals between linear-only and linear+quadratic fits does not cover c_HB and c_HWB, whose intervals differ substantially. Please provide a concrete EFT-validity assessment (e.g., positivity of
  2. [End Matter, Fig. 6(b)] The WH,H→bb linear+quadratic single-parameter fit has an undefined 95% CL interval, as honestly noted. Since this channel contributes to the combined linear+quadratic c_HW interval ([-0.13,0.60]), the paper should clarify how the combined interval is derived when an input channel's profile-likelihood scan does not reach the 95% CL threshold within the scanned range. Does the non-monotonic NLL behavior in Eq. (4) affect the asymptotic approximation used for the combined interval? A short remark or coverage check would substantiate that the reported combined interval remains statistically meaningful.
minor comments (4)
  1. [Abstract vs. text] The abstract says results from H→γγ are combined, but the simultaneous fits exclude H→γγ 'due to limited sensitivity.' Please clarify in the abstract or introduction that H→γγ is included only in the single-parameter c_HW fit.
  2. [Throughout] Typos: 'constrains' should be 'constraints', 'This limits' should be 'These limits', 'varify' should be 'verify'. Some figure labels in Fig. 6(b) ('Undefined CL') would benefit from a pointer to the explanation in the End Matter.
  3. [Eqs. (1) and (2)] The notational relation between c_i in Eq. (1) (which includes 1/Λ^2) and c_j in Eq. (2) (without explicit Λ factors) is confusing. Since Λ=1 TeV is used, please state explicitly that the quoted coefficients correspond to c_i with Λ fixed, or introduce a rescaled coefficient.
  4. [Conclusions] The claim that these are 'the most stringent constraints to date' would be more convincing with a quantitative comparison to previous results for c_HB and c_HWB, not only the 40% improvement for c_HW quoted relative to [6].

Circularity Check

0 steps flagged

No significant circularity: the quoted limits are direct profile-likelihood fits to measured distributions, not outputs derived from the inputs by construction.

full rationale

The paper's central results are observed and expected 95% CL intervals on the SMEFT Wilson coefficients c_HW, c_HB, c_HWB obtained from profile-likelihood fits to five measured channels. The parameterization in Eq. (1) and the STXS signal-strength form in Eq. (2) are modeling conventions that define the fit template; they do not assert that the data equal the fit or that the fitted interval is already known. The input channels are previously published ATLAS measurements (Refs. [6,7,8,11,43]) plus a newly described WH,H->bb measurement; these serve as data inputs and external benchmarks, not as self-citations that carry the argument. The claim of improvement over the previous H->tau tau result is a comparison against an independent published result, and the simultaneous three-coefficient fit is a direct multidimensional likelihood fit to CP-sensitive observables. The one passage that could superficially resemble a loaded assumption is the statement that negative-cross-section regions are 'outside the observed 95% CL contours and outside of EFT validity regions'; this is an EFT-truncation and positivity-validity concern, not a circularity, because the quoted intervals are not defined in terms of the EFT-valid region nor are the Wilson coefficients fitted from the intervals themselves. No equation reduces a predicted quantity to a fitted input by construction, and no load-bearing argument depends on citing the authors' own uniqueness or prior ansatz. The combination is therefore self-contained as a statistical statement about the data it uses; the unquantified EFT-validity caveat belongs in a correctness-risk discussion rather than circularity.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 0 invented entities

The central fit parameters are the three Wilson coefficients and per-process signal normalizations. No new particles, forces, or conserved quantities are introduced. The interpretation rests on SMEFT truncation, shape-only modeling, and MC-faithfulness assumptions.

free parameters (5)
  • c_HW (linear-only single-parameter fit) = 0.10 (95% CL [-0.28, 0.49])
    Fitted CP-odd Wilson coefficient; central result of the combination.
  • c_HW (linear+quadratic single-parameter fit) = 0.08 (95% CL [-0.30, 0.62])
    Fitted Wilson coefficient including quadratic SMEFT terms.
  • c_HB (simultaneous fit) = 0.11 linear-only ([-1.2, 1.4]); 0.43 linear+quadratic ([-1.0, 1.1])
    Fitted coefficient profiling the other coefficients; shown in Figure 4.
  • c_HWB (simultaneous fit) = 0.54 linear-only ([-1.9, 3.0]); 1.0 linear+quadratic ([-1.6, 2.4])
    Fitted coefficient profiling the other coefficients; strongly correlated with c_HB.
  • Signal normalization factors
    Free-floating per production mode and per pT-bin normalizations in the shape-only fits; some minor contributions fixed to SM predictions.
axioms (6)
  • domain assumption SMEFT Warsaw-basis dimension-6 operators only, restricted to three CP-odd lepton- and baryon-number-conserving operators, with Lambda = 1 TeV.
    Sets the interpretation of the fitted coefficients; introduced in the introduction and used throughout.
  • domain assumption SMEFT truncation at dimension six; linear and quadratic terms in the coefficients are sufficient.
    The cross-section decomposition in Eq. (1) and the linear/quadratic scenarios assume no higher-dimensional operators matter at the quoted limits.
  • domain assumption Shape-only approach: floating signal normalizations remove sensitivity to CP-even contributions and to higher-order BSM corrections.
    Invoked in the paragraph beginning 'All analysis use a shape-only approach'; if false, the extracted CP-odd constraints could be biased.
  • domain assumption Asymptotic approximation for the profile-likelihood ratio defines the 68% and 95% CL intervals.
    Figure 2 caption states intervals assume the asymptotic approximation; with limited WH statistics this may be imperfect.
  • domain assumption MC generators (Powheg+Pythia, MadGraph with SMEFTsim) accurately model SM and BSM signal and background shapes.
    All input channels rely on these simulations; accuracy of the CP-sensitive observables is load-bearing.
  • ad hoc to paper Normalizations for ZH and ggF in WH,H->bb, ggF in H->tautau, and VBF/ggF ratio in H->ZZ* are fixed to SM predictions.
    Introduced specifically for this combination to reduce nuisance parameters; if these predictions are wrong, the constraints shift.

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A combination of measurements of the CP properties of Higgs boson interactions with electroweak gauge bosons is presented, using 140 fb$^{-1}$ of proton-proton collisions at $\sqrt{s} = 13$ TeV recorded by the ATLAS detector. Results from VBF $H\to\tau\tau/WW^{*}/\gamma\gamma$, inclusive $H\to ZZ^{*}$, and $WH,H\to b\bar{b}$ channels are combined. No evidence of CP violation is observed, and constrains on the CP-violating operators in the Standard Model Effective Field Theory framework are set in the Warsaw basis. The results from the combination improve by over 40$\% $ on previous individual limits on $c_{H\tilde{W}}$ and, for the first time, simultaneous constraints on three coefficients $c_{H\tilde{W}}$, $c_{H\tilde{B}}$, and $c_{H\tilde{W}B}$ are set. These limits are the most stringent constraints to date on the relevant Wilson coefficients in the SMEFT framework with minimum model dependence.

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    ATLAS Collaboration,ATLAS Computing Acknowledgements, ATL-SOFT-PUB-2026-001, 2026, url:https://cds.cern.ch/record/2952666. 15 The ATLAS Collaboration G. Aad 102, E. Aakvaag 17, B. Abbott 121, S. Abdelhameed 83b, K. Abeling 54, N.J. Abicht 48, S.H. Abidi 30, M. Aboelela 44, A. Aboulhorma 36e, H. Abramowicz 154, B.S. Acharya 68a,68b,m, A. Ackermann 62a, C. ...

    arXiv 2026