Measurements of polarization and spin correlation and observation of entanglement in top quark pairs using (Formula presented) events from proton-proton collisions at (Formula presented)

Measurements of the polarization and spin correlation in top quark pairs ((Formula presented)) are presented using events with a single electron or muon and jets in the final state. The measurements are based on proton-proton collision data from the LHC at (Formula presented) collected by the CMS experiment, corresponding to an integrated luminosity of (Formula presented). All coefficients of the polarization vectors and the spin correlation matrix are extracted simultaneously by performing a binned likelihood fit to the data. The measurement is performed inclusively and in bins of additional observables, such as the mass of the (Formula presented) system and the top quark scattering angle in the (Formula presented) rest frame. The measured polarization and spin correlation are in agreement with the standard model. From the measured spin correlation, conclusions on the (Formula presented) spin entanglement are drawn by applying the Peres-Horodecki criterion. The standard model predicts entangled spins for (Formula presented) states at the production threshold and at high masses of the (Formula presented) system. Entanglement is observed for the first time in events at high (Formula presented) mass, where a large fraction of the (Formula presented) decays are spacelike separated, with an expected and observed significance of above 5 standard deviations.