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

The decays $t\to \mathrm{cV}$, where $V=\gamma , g, or Z$, and $t\to \mathrm{cH}$ 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 $B(t\to cH)\sim {10}^{-7\mathrm{}}$ and $B(t\to cg)\sim {10}^{-10\mathrm{}}$. Our calculations are then extended to include the possible contributions of charged Higgs bosons to the transitions $t\to \mathrm{cV}$ 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., $B(t\to cg)\sim {10}^{-7\mathrm{}}-{10}^{-6\mathrm{}}$, 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.