Rare top quark decays at a 100 TeV proton-proton collider: and .

We investigate extremely rare top quark decays at a future proton-proton collider with centre-of-mass energy of 100 TeV. We focus on two decay modes: radiative decay with a boson, , and flavour-changing neutral decay with a Higgs boson, , the former being kinematically suppressed with a branching ratio of (Altarelli et al., Phys Lett B 502:125-132, 2001), and the latter highly loop-suppressed, with a branching ratio of (Aguilar-Saavedra, Acta Phys Polon B 35:2695-2710, 2004). We find that will be very challenging to observe in top quark pair production, even within well-motivated beyond-the-standard model scenarios. For the mode we find a stronger sensitivity than that obtained by any future LHC measurement by at least one order of magnitude.