Accessing Quantum Entanglement in off-shell $H^{∗} \to ZZ$ with Separation of Polarisation States

The Higgs boson is the only spin-0 elementary particle within the Standard Model. Its electroweak decays yield a pair of entangled vector bosons. The parity-violating properties of the electro-weak coupling of the $Z^{0}$ bosons allow for testing of their polarisation state. The CMS and ATLAS Collaborations recently provided evidence for off-shell Higgs production in the four lepton final state. The decay of the off-shell Higgs to vector bosons offers a great stage to probe entanglement at the most fundamental level. The decay to leptons is particularly suited for such an analysis because the kinematic variables of the decaying particles can be reconstructed with high precision from the final state particles. A test of quantum entanglement is reformulated as a search for transverse polarisations of the $Z^{0}$ bosons in $H^{*}\to ZZ$ using a deep neural network to discriminate between the different polarisation states.