Rare top quark decays at a 100 TeV proton–proton collider: [Formula: see text] and [Formula: see text]

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