Rare decays of the top quark in the standard and two-Higgs-doublet models

The decays t→cV, where V=γ, g, or Z, and t→cH are calculated, keeping all masses, in the standard model (SM) for all possible values of the top-quark mass that are consistent with present data. We find that the branching fractions for these processes are small, the largest being B(t→cH)~10^-7 and B(t→cg)~10^-10. Our calculations are then extended to include the possible contributions of charged Higgs bosons to the transitions t→cV in the context of general two-Higgs-doublet models. These new contributions can enhance the SM branching fractions by as much as 3-4 orders of magnitude, e.g., B(t→cg)~10^-7-10^-6, for various values of the parameters. General expressions for flavor-changing neutral-current decays of heavy quarks including all masses and momenta, in the SM and in the two-Higgs-doublet models, are also given.