The observed baryon asymmetry of the universe is a significant open question in physics. The Sakharov criteria require sufficient violation of combined charge conjugation and parity (CP) invariance to explain this asymmetry. The Standard Model (SM) only offers a complex phase in the Cabibbo-Kobayashi-Maskawa (CKM) matrix for quark mixing as a source of CP violation, which is insufficient to account for the observed asymmetry. This motivates the search for new sources of CP violation, including investigations into the production and decay of the Higgs boson. The SM predicts the Higgs boson to have a spin-parity (JP) of 0+ with even C-parity. Any observation of CP violation in Higgs boson production or decay would be a clear indication of physics beyond the Standard Model (BSM). Previous analyses using lower luminosity data from the LHC at 7 and 8 TeV ruled out pure spin-parity states (0⁻, 1⁻, 1⁺, 2⁺, and 2⁻) at high confidence levels, and provided initial constraints on CP-odd contributions to Higgs boson to vector-boson couplings (HVV) in Higgs boson decays. With significantly increased luminosity (139 fb⁻¹ at 13 TeV), this analysis aims to improve constraints on CP invariance, particularly focusing on the H → ZZ* → 4l decay channel (l = e, μ), where the decay features a large number of Higgs candidates. Previous cross-section measurements in this channel, comparing observations with SM expectations, set constraints on both CP-even and CP-odd BSM couplings, but couldn’t distinguish between them. This analysis addresses this limitation by employing optimal observables, which are CP-odd by construction and thus can directly reveal CP-violating effects in VBF production and the H → ZZ* → 4l decay. The analysis utilizes approximately 200 expected Higgs bosons decaying into four leptons, including about 10 events in a VBF production phase space.

Numerous studies have explored CP violation in Higgs boson interactions. Early experiments at lower LHC energies focused on excluding various spin-parity assignments for the Higgs boson using its decays into γγ, ZZ, and WW. These analyses provided the first limits on possible CP-odd contributions to HVV couplings. Subsequent searches, leveraging increased luminosity at 13 TeV, tightened constraints on HVV couplings and extended them to Higgs Yukawa couplings with fermions, examining decays like H → ττ and associated production like ttH. These investigations utilized various decay channels (γγ, ZZ, WW, ττ, bb) and production mechanisms. While many studies explored cross-section measurements to constrain CP properties, a direct search for visible CP-odd effects in production and decay using CP-odd observables was needed for clearer distinction between CP-even and CP-odd contributions. This analysis directly builds on this body of work, refining the sensitivity by using optimal observables designed to enhance the detection of CP violation.

This analysis uses data from proton-proton collisions at √s = 13 TeV, collected by the ATLAS detector from 2015 to 2018. The Standard Model Effective Field Theory (SMEFT) framework is employed to interpret results, focusing on three CP-odd dimension-six operators that affect both VBF production and H → ZZ* → 4l decay. These operators are considered in both the Warsaw basis and the Higgs basis, allowing for results to be presented in both frameworks. The key methodological innovation is the use of matrix element-based optimal observables. These observables are constructed from the interference term between the SM and BSM matrix elements, normalized by the SM matrix element squared. This approach ensures that the observables are CP-odd by construction; a symmetric distribution indicates no CP violation, while an asymmetric distribution points towards CP-violating effects. The optimal observables are calculated at both the production and decay levels. Production-level observables consider VBF production, while decay-level observables are agnostic to the production mechanism, focusing solely on the decay process. A morphing method is employed to predict the optimal observable distributions for various combinations of BSM couplings. This method relies on the fact that the cross-section in each phase space bin is a polynomial function of the EFT couplings, allowing the prediction for any arbitrary combination of couplings to be built as a linear combination of a limited number of simulated predictions. This is crucial because it avoids the need to generate an enormous number of Monte Carlo samples, saving considerable computational resources. To separate CP-odd from CP-even effects, the analysis focuses on the shape of the optimal observable distributions, leaving the predicted event rates to float in the fit. This decoupling allows for a precise measurement of the CP-odd couplings, relatively insensitive to potential CP-even BSM effects that might affect event rates. The analysis involves three different types of fits: decay-only, production-only, and combined, each employing specific categories of events (inclusive, VBF-enriched, and control regions) to maximize sensitivity. Systematic uncertainties arising from experimental and theoretical sources are also carefully considered and included in the analysis.

The analysis reveals good agreement between the observed and expected event yields in all categories, indicating no significant deviations from the SM prediction. The observed distributions of both production-level and decay-level optimal observables show no measurable asymmetry, meaning the mean values are compatible with zero. This lack of asymmetry suggests no evidence of CP violation in the Higgs boson's couplings. The analysis employs profile likelihood ratio fits to constrain the CP-odd couplings. The resulting 68% and 95% confidence intervals on the Wilson coefficients for several BSM couplings (in both the Warsaw and Higgs bases) are determined. These intervals are presented both for the individual production-only, decay-only, and combined fits and in two-dimensional plots showing the correlations between pairs of couplings. Most of the results show good agreement with the expected limits from simulation. A few decay-only results show less constrained limits than expected, and this is associated with minor fluctuations in the observed optimal observable distributions. In most cases, the effect of systematic uncertainties on the limits is small. The impact of including quadratic terms in the BSM couplings in the morphing method is assessed and found to be negligible. Similarly, the impact of also considering the predicted cross-section changes resulting from the BSM couplings is small for decay-only, but more significant for production-only results. The analysis also assesses potential effects from unmodeled CP-even BSM couplings and finds these to be minimal. Additionally, the analysis presents measurements of fiducial differential cross-sections for the optimal observables and measures fiducial cross-sections for VBF production in a VBF-enriched fiducial region, both with and without explicit subtraction of the ggF background. These cross-section measurements are all in agreement with the SM predictions.

The absence of any significant CP-odd signal in this comprehensive analysis strongly supports the SM prediction of a CP-even Higgs boson. The consistency of all measurements with the SM expectation reinforces our current understanding of the Higgs boson's interactions. While minor fluctuations exist in some observed distributions, they are not statistically significant enough to claim evidence of new physics. The high precision of the measurements, particularly the utilization of optimal observables sensitive to CP-odd effects, provide robust constraints on BSM scenarios involving CP-violating couplings. The detailed study of systematic uncertainties further bolsters the reliability of these results. These findings contribute significantly to our knowledge of Higgs boson properties, narrowing the parameter space for potential BSM models. Future studies with even higher luminosities from the LHC will allow further refinement of these constraints and could potentially reveal subtle CP-violating effects not yet observable.

This ATLAS analysis provides a comprehensive search for CP violation in Higgs boson production and decay in the H → ZZ* → 4l channel, employing innovative matrix element-based optimal observables. The high-precision measurements, encompassing both differential cross-sections and direct coupling constraints, are consistent with the SM prediction of a CP-even Higgs boson. No significant CP-odd component is observed, strengthening our understanding of Higgs boson interactions. Future high-luminosity runs of the LHC will offer enhanced sensitivity to explore this area further.

The analysis relies on the SMEFT framework, which is an effective field theory valid up to a certain energy scale. The results are interpreted within this framework and might not be directly transferable to other BSM models. The statistical power of the analysis is limited by the available data; particularly for the VBF enriched analysis, where the number of events is relatively small. This limitation is particularly relevant in the interpretation of production-level observables, where sensitivity is lower. While systematic uncertainties are carefully considered, residual uncertainties remain.