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A set of top quark spin correlation and polarization observables for the LHC: Standard Model predictions and new physics contributions

We consider top-antitop quark ($t{\bar t}$) production at the Large Hadron Collider (LHC) with subsequent decay into dileptonic and lepton plus jets final states. We present a set of leptonic angular correlations and distributions with which experiments can probe all the independent coefficient functions of the top-spin dependent parts of the $t{\bar t}$ production spin density matrices. We compute these angular correlations and distributions for LHC center-of-mass energies 8, 13, and 14 TeV within the Standard Model at next-to-leading order in the QCD coupling including the mixed QCD-weak corrections and for the transverse top-quark polarization and the $t{\bar t}$ charge asymmetry also the mixed QCD-QED corrections. In addition we analyze and compute the effects of new interactions on these observables in terms of a gauge-invariant effective Lagrangian which contains all operators relevant for hadronic $t{\bar t}$ production up to mass dimension six.