  We investigate the sensitivity to new physics of the process e+e- -> t bar{t}
when the top polarization is analyzed using leptonic final states e+e- -> t
\bar{t} -> l+l- b \bar{b} nu_l \bar{nu}_l. We first show that the kinematical
reconstruction of the complete kinematics is experimentally tractable for this
process. Then we apply the matrix element method to study the sensitivity to
the Vt\bar{t} coupling (V being a vector gauge boson), at the tree level and in
the narrow width approximation. Assuming the ILC baseline configuration,
sqrt{S}=500 GeV, and a luminosity of 500 fb^{-1}, we conclude that this optimal
analysis allows to determine simultaneously the ten form factors that
parameterize the Vt\bar{t} coupling, below the percent level. We also discuss
the effects of the next leading order (NLO) electroweak corrections using the
GRACE program with polarized beams. It is found that the NLO corrections to
different beam polarization lead to significantly different patterns of
contributions.
