Top Quark Spin and Polarization Properties in Searches for New Phenomena with the CMS Detector at the LHC

In this work, a search for heavy pseudoscalar and scalar (A/H) Higgs bosons decaying to top-anti-top quark pairs ($t$$\bar{t}$) and a measurement of top quark polarization and $t$$\bar{t}$ spin correlation are presented, performed using 35.9 /fb of data recorded by the CMS experiment in 2016. The dileptonic $t$$\bar{t}$ final state is investigated in both analyses.The A/H Higgs boson search exploits the 2-dimensional spectrum of $t$$\bar{t}$ invariant mass and an angular observable sensitive to both the spin and parity of the $t$$\bar{t}$ system. The search probes mass and relative decay width ranges of 400 - 750 GeV and 0.5% - 50%, respectively. An excess consistent with the A (400 GeV, 5%) signal hypothesis is observed with a local significance of 4$\sigma$ in the dileptonic channel and 3.7$\sigma$ in the combination of dileptonic and semileptonic channels. The global significance of such an excess is found to be 2$\sigma$. Exclusion regions on the coupling modifier of the A/H to top quarks are derived. These results are converted into exclusion regions in the context of a supersymmetric model, the hMSSM, and are given in the parameter space m$_{A}$ -tan $\beta$. In the spin correlation measurement, the distributions of all independent observables that are directly sensitive to the elements of top quark polarization vector and $t$$\bar{t}$ spin density matrix are measured, unfolded to the level of generated partons, and extrapolated to the full phase space. In addition, the distributions of two angles between the charged leptons in the laboratory frame, which are, however, only indirectly sensitive to the $t$$\bar{t}$ spin correlations but can be extracted with excellent experimental resolution, are measured. An overall good agreement with the standard model is observed. However, there is some tension between the data and predictions in the distribution of the azimuthal gap between the charged leptons in the laboratory frame. The measurements are used to constrain anomalous contributions within an Effective Field Theory framework.