Measurements of polarization and spin correlation and observation of entanglement in top quark pairs using $\mathrm{lepton}+\text{jets}$ events from proton-proton collisions at $\sqrt{s}=13\text{}\text{}\mathrm{TeV}$

Measurements of the polarization and spin correlation in top quark pairs ($t\overline{t}$) 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 $\sqrt{s}=13\text{}\text{}\mathrm{TeV}$ collected by the CMS experiment, corresponding to an integrated luminosity of $138\text{}\text{}{\mathrm{fb}}^{-1}$. 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 $t\overline{t}$ system and the top quark scattering angle in the $t\overline{t}$ rest frame. The measured polarization and spin correlation are in agreement with the standard model. From the measured spin correlation, conclusions on the $t\overline{t}$ spin entanglement are drawn by applying the Peres-Horodecki criterion. The standard model predicts entangled spins for $t\overline{t}$ states at the production threshold and at high masses of the $t\overline{t}$ system. Entanglement is observed for the first time in events at high $t\overline{t}$ mass, where a large fraction of the $t\overline{t}$ decays are spacelike separated, with an expected and observed significance of above 5 standard deviations.