  The discovery of the top quark, the most massive elementary particle yet
known, has given us a distinct window into investigating the physics of the
Standard Model and Beyond. With a plethora of top quarks to be produced in the
High Luminosity era of the LHC, the exploration of its rare decays holds great
promise in revealing potential new physics phenomena. We consider
higher-dimensional operators contributing to top decays in the SMEFT and its
extension by a light singlet species of spin 0, 1/2, or 1, and exhibit that the
HL-LHC may observe many exotic top decays in a variety of channels. Light
singlets which primarily talk to the SM through such a top interaction may also
lead to distinctive long-lived particle signals. Searching for such long-lived
particles in top-quark decays has the additional advantage that the SM decay of
the other top quark in the same event provides a natural trigger.
