Simulated $H \to WW^{\ast} \to \ell\nu\ell\nu$ events and backgrounds for collider Bell tests at $\sqrt{s}=13$ TeV

Common simulation chain All samples are $pp$ collisions at $\sqrt{s} = 13$ TeV. Hard-scatter matrix elements are generated with MadGraph5_aMC@NLO 3.4.2, parton-showered and hadronised with Pythia8, and passed through a detector simulation using Delphes 3.5.0 with the default ATLAS card (lepton reconstruction efficiencies, momentum resolution, and missing-transverse-energy response taken from the card defaults). Each row of every CSV contains the reconstructed (detector-level) electron, muon, and missing transverse momentum, together with the truth-level electron, muon, electron-neutrino and muon-neutrino four-vectors. All energies and momenta are in GeV; angles in radians. Columns: e_pt, e_eta, e_phi reconstructed electron mu_pt, mu_eta, mu_phi reconstructed muon met, met_eta, met_phi missing transverse momentum (eta = 0 by construction) truth_e_pt … truth_mu_phi truth-level charged leptons truth_ve_* , truth_vmu_* truth-level neutrinos case analytical neutrino-reconstruction branch flag (1 = real solution to the W on-shell system found) Per-file description hww_1M_MG_no_cuts.csv — Signal sample, $pp \to H \to WW^{\ast} \to e\nu_e,\mu\nu_\mu$. The Higgs is produced via gluon fusion, which dominates the cross section at the LHC. 1×10$^6$ events, no analysis selection applied; the dilepton fiducial and ATLAS signal-region cuts ($p_T^{\ell_1} > 22$ GeV, $p_T^{\ell_2} > 15$ GeV, $|\eta_\ell| < 2.5$, $E_T^{\text{miss}} > 20$ GeV, $m_{\ell\ell} < 55$ GeV, $\Delta\phi_{\ell\ell} < 1.8$, $60 < m_T < 130$ GeV) can be re-applied from the columns above. mangled_hww_1M_MG_no_cuts.csv — Separable-hypothesis template, constructed from the signal sample above by classifying each event by which lepton–neutrino pair is closer to the $W$ on-shell mass ($M_W = 80$ GeV), then randomly re-assigning the electron-side columns (reconstructed and truth-level electron and electron-neutrino) within each subset across events. This destroys the per-event $W^+$–$W^-$ angular correlations that define the entangled quantum state while preserving the single-particle marginal distributions. The missing transverse momentum is regenerated by a small transformer-based regressor trained on the un-shuffled events so that detector-level kinematics remain self-consistent after the swap. The resulting Gell-Mann correlation matrix is consistent with zero, as expected for a fully separable density matrix. hww_500k_Sherpa.csv — Independent generator cross-check for the signal, $5\times 10^5$ events of $H \to WW^\ast \to \ell\nu\ell\nu$ generated with Sherpa 2.2 and the same Delphes ATLAS simulation. Used in the paper to validate that the production MadGraph sample is generator-independent at the sub-percent level for the CGLMP $\mathfrak{I}_3$ observable. ww_1M_MG5_no_cuts.csv — Non-resonant $pp \to W^+W^- \to \ell\nu\ell\nu$ background. 1×10$^6$ events. This is the irreducible background to the analysis: it shares the same $\ell\nu\ell\nu$ final state as the signal, and the kinematic differences between the Higgs-mediated and non-resonant $WW$ production channels are subtle. In the paper this background is normalised to the NNLO theoretical cross section. ttbar_1M_MG5.csv — Top-quark pair production, $pp \to t\bar t \to W^+W^- b\bar b$, with both $W$ bosons decaying leptonically. 1×10$^6$ events. Single-top $Wt$ production is not separately simulated here. In the paper this background is normalised to NNLO+NNLL and is reducible through $b$-jet activity and dilepton mass. ztautau_1M_MG_no_cuts.csv — $Z/\gamma^* \to \tau^+\tau^-$ with both $\tau$ leptons decaying leptonically. 1×10$^6$ events, no selection. Normalised at NLO in the paper. Provides a centrally-peaked $\mathfrak{I}_3$ shape distinct from the signal and the $WW$ background.