Rare decay of the top quark t→cl(l)over-bar and single top quark production at the ILC

We perform a complete and detailed analysis of the flavor changing neutral current rare top quark decays t -> cl(+)l(-) and t -> c nu(i)(nu) over bar (i) at one-loop level in the standard model, two Higgs doublet models (I and II), and in minimal supersymmetric standard model (MSSM). The branching ratios are very small in all models, O(10(-14)), except for the case of the unconstrained MSSM, where they can reach O(10(-6)) for e(+)e(-), mu(+)mu(-), and nu i (nu) over bari, and O(10(-5)) for tau(+)tau(-). This branching ratio is comparable to the ones for t -> cV, cH. We also study the production rates of single top and the forward-backward asymmetry in e(+)e(-)-> t (c) over bar and comment on the observability of such a signal at the International Linear Collider.