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 ( toverline{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 toverline{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 toverline{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 that contains all operators relevant for hadronic toverline{t} production up to mass dimension six.