Test of CP-invariance of the Higgs boson in vector-boson fusion production and in its decay into four leptons

The baryon asymmetry of the universe requires sources of CP violation beyond the known complex phase in the CKM matrix, which is insufficient to account for the observed asymmetry. The Higgs sector provides a compelling place to search for new CP-violating effects. While the Standard Model (SM) predicts a CP-even scalar Higgs boson (J^P = 0^+), any observable CP-odd effect in its production or decay would indicate beyond-the-SM (BSM) physics. Previous ATLAS and CMS measurements at √s = 7–13 TeV have excluded various non-SM spin-parity states and set constraints on CP-odd contributions in HVV and Yukawa couplings across several channels. In the H → ZZ* → 4ℓ channel, prior work constrained CP-even and CP-odd effects via cross-section measurements but could not disentangle CP-even from CP-odd contributions when only rates were used. This study targets direct signatures of CP violation through CP-odd, interference-based optimal observables sensitive to CP-odd SMEFT operators affecting VBF production and H → ZZ* → 4ℓ decay, using the full Run 2 ATLAS dataset (139 fb⁻¹ at 13 TeV).

Early LHC analyses with 7–8 TeV data established the Higgs boson’s scalar nature and excluded pure J^P = 0⁻, 1⁻, 1⁺, 2⁺, 2⁻ states at >99% CL, providing first limits on CP-odd HVV couplings in bosonic decays. Subsequent 13 TeV datasets (~139 fb⁻¹) tightened CP constraints in HVV and extended them to Yukawa couplings (e.g., H → ττ, ttH in γγ and bb channels). In H → ZZ* → 4ℓ at 13 TeV, cross-section-based interpretations set bounds on BSM couplings but lacked discrimination between CP-even and CP-odd sources. Prior VBF CP tests used H → ττ (ATLAS) and VH, H → bb (CMS), and alternative CP-odd parameterizations such as ṡd. The present analysis advances by employing CP-odd optimal observables—linear in SMEFT interference terms—enabling direct sensitivity to CP violation and complementing prior rate-based measurements.

Dataset and detector: The analysis uses the full Run 2 ATLAS dataset of pp collisions at √s = 13 TeV collected in 2015–2018, corresponding to 139 fb⁻¹. Events were recorded with single-, di-, and tri-lepton triggers with ~97–99% efficiency for selected H → ZZ* → 4ℓ candidates. The ATLAS detector provides near-4π coverage with precision tracking, calorimetry, and muon spectrometry. Signal and background simulation: SM Higgs production (ggF, VBF, VH, ttH, tH, bbH) was simulated with high-order generators (e.g., POWHEG NNLOPS for ggF) and normalized to LHC Higgs WG predictions. The dominant non-resonant ZZ* background was modeled with SHERPA 2.2.2 (NLO QCD up to one extra parton) with NLO EW corrections, and gluon-initiated ZZ at LO normalized to an NLO calculation. Reducible backgrounds (Z+jets, tt, WZ) used data-driven estimates; smaller backgrounds (VVV, ttV, tXX) were simulated. BSM samples with CP-odd SMEFT couplings were generated at LO with MADGRAPH5_AMC@NLO using SMEFTsim (U(3)^5, m_W scheme), with Λ = 1 TeV. Theory framework and observables: The SMEFT Lagrangian includes dimension-6 CP-odd operators affecting HVV vertices. The analysis interprets results in both the Warsaw basis (C_{HẆ}, C_{HḂ}, C_{HẆB}) and the Higgs basis (c̃_ZZ, c̃_Zγ, c̃_γγ), with linear transformations provided. A traditional single-parameter CP-odd direction ṡd is also considered for comparison. Optimal observables (OOs) are constructed as OO = 2 Re(M_SM M_BSM*) / |M_SM|² from leading-order matrix elements, yielding CP-odd distributions that are symmetric with zero mean for a CP-even Higgs and asymmetric for CP-odd admixtures. Two OO types are used: (i) production-level OOs sensitive to VBF production (built from the reconstructed Higgs and two leading jets, via PDF-weighted partonic sums), and (ii) decay-level OOs sensitive to H → ZZ* → 4ℓ decay (built from the four-lepton kinematics, with separate treatment for 4ℓ same- and mixed-flavour states). Dedicated OOs are constructed for each coupling in both bases and ṡd. Signal morphing: Predicted OO distributions for arbitrary coupling points are obtained via a morphing technique, exploiting the polynomial dependence of cross sections on the couplings (including up to quartic terms when both production and decay vertices can be modified). Simulated samples spanning coupling grids are combined with polynomial weights to predict shapes for any parameter point while decoupling overall rate effects in the direct-coupling fits. Event reconstruction and selection: Events require at least four isolated leptons (e or μ) forming two same-flavour, opposite-charge pairs from a common vertex. Electrons (|η| < 2.47, E_T > 7 GeV) and muons (|η| < 2.7, p_T > 5 GeV; calorimeter-tagged μ > 15 GeV) must satisfy identification and isolation criteria. The three highest-p_T leptons exceed 20, 15, 10 GeV. Lepton pairs must satisfy ΔR > 0.1 and m(ℓℓ) > 5 GeV. The four-lepton mass window is 115–130 GeV for signal regions; 105–115 and 130–160 GeV define ZZ* control regions. Final-state radiation recovery is applied. Jets are anti-k_t R=0.4 with p_T > 30 GeV, |η| < 4.5, and pile-up suppression. Analysis strategy and categories: Three fits are performed: (1) decay-only fit using decay-level OOs in the inclusive signal region (115 < m_4ℓ < 130 GeV) with sideband ZZ* control regions; (2) production-only fit using production-level OOs in VBF-enriched regions defined by ≥2 jets and m_jj ≥ 120 GeV, further split into four VBF SRs by a neural-network VBF score, plus a VBF-depleted resonant control region and ZZ* sidebands; and (3) a combined fit using decay-level OOs in the VBF-depleted signal region and production-level OOs in VBF SR1–4. To isolate CP-odd shape effects, overall normalizations for SM signal and backgrounds float freely in the likelihood, decoupling rate information. Binning and statistics: Decay-level OOs use 48 bins (or 6×6 in 2D for pairs) and production-level OOs use 12 bins, with binning optimized for roughly flat expected populations across SM and near-limit BSM mixtures. Profile-likelihood scans provide 68% and 95% confidence intervals (CIs), validated with toys for asymptotic behavior. Differential fiducial measurements: OO differential fiducial cross-sections are unfolded from data within a fiducial phase space aligned with detector-level selections. The response matrix and non-fiducial fractions are derived from SM MC; the m_4ℓ spectrum is simultaneously fit across bins to extract signal yields. Additional measurements are performed in a VBF-enriched fiducial region defined by m_jj ≥ 400 GeV and |Δη_jj| ≥ 3.0, both with and without subtracting ggF (treated as background in the latter). Systematic uncertainties: Statistical uncertainties dominate. Experimental systematics include lepton and jet energy scales/resolutions and efficiencies, luminosity (1.7%), pile-up modeling, and background estimation systematics. Theoretical systematics cover PDF, QCD scale, shower/UE modeling, and acceptance/composition uncertainties, with ggF modeling a key source in production-level categories. Unfolding-specific uncertainties from production-mode composition and potential response biases are included. MC statistical uncertainties are propagated, notably for the ZZ* background shapes. Sensitivity studies show small impact from quadratic (CP-even) terms in the morphing and from omitting rate constraints in shape-only fits, and limited bias from plausible CP-even BSM admixtures within current bounds.

- No evidence for CP violation: All optimal-observable distributions are consistent with SM expectations; observed mean values of CP-odd OOs are compatible with zero. - Direct coupling limits (95% CL), one parameter at a time, Λ = 1 TeV: • Warsaw basis (decay-only unless noted): - c_HB ∈ [−0.61, 0.54]; best fit −0.078; p = 0.86. - c_HWB ∈ [−0.97, 0.98]; best fit −0.017; p = 0.99. - c_HW (combined production+decay) ∈ [−0.81, 1.54]; best fit 0.60; p = 0.37. - ṡd ∈ [−0.026, 0.025]; best fit −0.003; p = 0.86. • Higgs basis: - c̃_ZZ (production-only) ∈ [−1.20, 1.75]; best fit 0.78; p = 0.11. - c̃_Zγ (decay-only) ∈ [−0.84, 0.83]; best fit 0.083; p = 0.93. - c̃_γγ (decay-only) ∈ [−0.99, 0.93]; best fit −0.01; p = 0.99. Two-dimensional contours in the Warsaw basis (pairs of c_HB, c_HWB, c_HW) contain the SM within the 68% CL. - Likelihood scan features: A small excess of VBF-like candidates produces a shallow minimum at positive c̃_ZZ in production-only scans; overall compatibility with SM remains better than ~2σ. Systematics (notably ggF parton-shower modeling) modestly broaden limits near zero in production scans; systematics are negligible in decay-only scans. - Differential fiducial cross-sections of OOs: Measured OO spectra (production and decay) agree with SM predictions (NNLOPS and MG5 FxFx, normalized appropriately). Reported p-values indicate good compatibility; a single decay observable bin shows a low p-value (~5%) but overall agreement is maintained. - VBF-enriched fiducial cross-sections (m_jj ≥ 400 GeV, |Δη_jj| ≥ 3.0): • With all production modes considered as signal: measured σ_fid ≈ 0.215 fb vs expected ≈ 0.134 fb; p-values 82% (NNLOPS) and 80% (MG5 FxFx). • Treating ggF as background (higher VBF purity): measured σ_fid ≈ 0.172 fb vs expected ≈ 0.088 fb; p-value ≈ 19% for SM VBF+VH+ttH. In both scenarios, measured cross-sections are higher than expectations (signal strengths ~1.6–2) but statistically compatible with the SM. - Robustness checks: Excluding quadratic (rate-only) terms in morphing changes limits by ≤3% (95% CL). Including rate constraints would only mildly tighten decay-only limits (<10%) but could improve production-only sensitivities (up to ~50%), consistent with quadratic contributions affecting rates but not OO asymmetries.

The analysis directly targets CP-violating effects by exploiting CP-odd optimal observables constructed from SM–BSM interference terms, which produce asymmetries in the presence of CP-odd couplings. Observed OO distributions are symmetric with zero means within uncertainties, demonstrating no detectable CP-odd admixture in either VBF production or H → ZZ* → 4ℓ decay at current sensitivity. The results translate into stringent one-parameter limits on CP-odd SMEFT operators in both Warsaw and Higgs bases, complementing and in several cases improving upon rate-based and prior channel-specific constraints by isolating the interference-dominated (O(Λ⁻²)) contributions. Sensitivity is stronger in the decay-only fits due to higher event counts in inclusive H → 4ℓ, while production-only fits are limited by the small VBF yield; the combined fit improves constraints for couplings with comparable sensitivity in production and decay (e.g., c_HW). Differential OO cross-sections provide a model-independent benchmark for reinterpretations and show overall agreement with SM predictions. The VBF-enriched fiducial cross-sections are somewhat higher than expectations but remain compatible with SM within uncertainties and are consistent with other ATLAS STXS measurements of VBF in H → ZZ* → 4ℓ. Overall, the findings support the SM’s CP-even Higgs scenario and significantly constrain potential CP-odd HVV interactions.

Using 139 fb⁻¹ of ATLAS pp collision data at 13 TeV, this study performs the first comprehensive H → ZZ* → 4ℓ optimal-observable analysis targeting CP-odd effects in both VBF production and Higgs decay, interpreted in SMEFT Warsaw and Higgs bases and in terms of ṡd. The direct coupling fits, dominated by interference-sensitive shape information, show no evidence of CP violation and yield competitive limits on CP-odd Wilson coefficients. Differential fiducial OO cross-sections and VBF-enriched fiducial cross-sections are also provided and are compatible with the SM. Future work can enhance sensitivity by: increasing statistics (Run 3 and HL-LHC), extracting VBF-optimized OO differentials in VBF-enriched fiducial regions, improving theoretical modeling (especially ggF in multi-jet topologies), and extending to multi-parameter fits and combined channels to probe correlated CP-odd effects across production and decay vertices.

- Statistical limitation: Sensitivity in production-level (VBF) fits is constrained by the small VBF dataset (~O(10) events in signal regions). - Theoretical modeling: Production-only categories are sensitive to ggF modeling uncertainties (scale, resummation, and parton-shower/UE), which impact migrations between control and signal regions and modestly broaden limits near zero. - LO BSM modeling: BSM SMEFT samples are generated at LO; however, uncertainties are taken from higher-order SM samples. Residual dependence of uncertainties on BSM couplings is assumed negligible. - Shape-only fit: Direct coupling fits intentionally discard rate information to isolate CP-odd asymmetries; while tested to have small impact on decay-only limits, including rate information could strengthen production-only constraints. - Unfolding assumptions: Differential measurements use SM-derived response matrices and production-mode compositions; potential biases from BSM effects and composition variations were assessed and found small (typically ≤ a few percent), but remain an approximation. - Assumed absence of CP-even BSM: Limits are obtained under the assumption that CP-even BSM couplings are zero; injecting CP-even admixtures at current limits slightly weakens decay limits and can shift fitted CP-odd values by a few percent. - EFT validity: Results are interpreted at Λ = 1 TeV; neglected dimension-8 terms enter at O(Λ⁻⁴) and are expected to be subdominant given the interference-dominated sensitivity, but EFT truncation remains an intrinsic limitation.