  In this work we investigate the NLO QCD+EW corrections to the top quark pair
production and their effects on the spin correlation coefficients and
asymmetries at fixed-order top quark pair production and LO decay in the
dilepton channel, within the narrow-width approximation. The spin correlations
are implicitly measured through the lepton kinematics. Moreover we study the EW
effects to the leptonic differential distributions. We find that the EW
corrections to the $t \bar t$ production are within the NLO QCD theoretical
uncertainties for the spin correlation coefficients and the leptonic
asymmetries. On the other hand, for the differential distributions we find that
the EW corrections exceed the NLO QCD scale uncertainty band in the high
rapidity regimes and are of the order of the NLO QCD scale uncertainty in the
case of invariant mass and transverse momentum distributions.
