Rare top quark decays at a 100 TeV proton-proton collider: t → bW Z and t → hc

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 Z boson, t -> bW Z, and flavour-changing neutral decay with a Higgs boson, t -> hc, the former being kinematically suppressed with a branching ratio of O(10(-6)) (Altarelli et al., Phys Lett B 502: 125-132, 2001), and the latter highly loop-suppressed, with a branching ratio of O(10(-15)) (Aguilar-Saavedra, Acta Phys Polon B 35: 2695-2710, 2004). We find that t -> bW Z will be very challenging to observe in top quark pair production, even within well-motivated beyond-the-standard model scenarios. For the mode t -> hc we find a stronger sensitivity than that obtained by any future LHC measurement by at least one order of magnitude.