Rare three-body decay t -> c h gamma in the standard model and the two-Higgs doublet model

A complete calculation of the rare three-body decay t --> c h gamma is presented in the framework of the standard model. In the unitary gauge, such a calculation involves about 20 Feynman diagrams. We also calculate this decay in the general two-Higgs doublet model (model III), in which it arises at the tree-level. While in the standard model the decay t --> c h gamma is extremely suppressed, with a branching fraction of the order of $10^{-15}$ for a Higgs boson mass of the order of 115 GeV, in the model III it may have a branching ratio up to $10^{-5}$. We also discuss the crossed decay h --> b \bar{s} gamma.