Measurements of $Z$-boson pair entanglement in decays of Higgs bosons at the ATLAS experiment

Abstract

Entanglement is a key property of quantum systems. In this Letter the first measurements of quantum entanglement between spins in pairs of $Z$ bosons are reported, using proton-proton collision data from the Large Hadron Collider (LHC) at center-of-mass energies of 13 TeV and 13.6 TeV, recorded with the ATLAS detector. Measurements of angular observables sensitive to $ZZ^*$ spin-density-matrix elements in the $H\rightarrow ZZ^* \rightarrow \ell^+\ell^-\ell^+\ell^-$ process yield coefficients $C_{2,1,2,-1} = -0.71 \pm 0.45$ and $C_{2,2,2,-2}=0.08 \pm 0.44$, consistent with their Standard Model predictions. A complementary hypothesis test using the full angular distribution, and relying on several Standard Model assumptions in the decays, provides substantially higher sensitivity to quantum correlations and disfavors the separable-state hypothesis at a significance of 4.7 standard deviations (expected $4.9σ$) relative to the entangled Standard Model hypothesis. These results provide strong evidence of quantum entanglement between massive bosons (spin qutrits) at the electroweak scale.

Figures (6)

• Figure 1: Example of a leading-order Feynman diagram of the dominant Higgs-boson production process via gluon–gluon fusion through a fermion loop and its decay process into two leptonically decaying $Z$ bosons, $pp\rightarrow H \rightarrow ZZ^* \rightarrow \ell^+\ell^-\ell^+\ell^-$. The superscript (*) refers to a particle that is off its mass shell.
• Figure 2: The observed (full circles) and the expected (histograms) four-lepton invariant mass distribution around the observed Higgs boson resonance. The expectation shows the contributions from $H\rightarrow ZZ^* \rightarrow 4\ell$ and from various background processes as described in the text. The uncertainty bar on data points are Poisson errors, and the uncertainty band includes statistical and systematic contributions added in quadrature.
• Figure 3: An illustration of the decay angle definitions in the $pp\rightarrow H\rightarrow ZZ^* \rightarrow 4\ell$ process. The azimuthal angles $\phi_1$ and $\phi_2$ are not shown in the figure and are defined in the conventional manner for right-handed coordinate systems. The unprimed frame is the laboratory frame with the $z$-axis along the beam direction. The primed frame is that in which the polarization of $Z$ bosons is defined.
• Figure 4: The observed distributions of events (full circles) overlaid on the expected (shaded) distributions of the estimator \ref{['fig:c212-1,qe-nonqe']}$c_{2,1,2,-1}$ and \ref{['fig:c222-2,qe-nonqe']}$c_{2,2,2,-2}$ for the entangled hypothesis (blue solid line) and the separable non-QE hypothesis (orange dashed line) and background.
• Figure 5: Observed values of \ref{['fig:C_combination:c212-1']}$C_{2,1,2,-1}$ and \ref{['fig:C_combination:c222-2']}$C_{2,2,2,-2}$ in the Run 2 and Run 3 datasets and their combination, together with the corresponding individual measurements. The $p$-values are calculated using the $\chi^2$ statistic for the six channels.