Rare top quark decays at a 100 TeV proton-proton collider: t rightarrow bWZ and trightarrow 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, $t \rightarrow b WZ$, and flavour-changing neutral decay with a Higgs boson, $t \rightarrow h c$, the former being kinematically suppressed with a branching ratio of $\mathcal{O}(10^{-6})$, and the latter highly loop-suppresed, with a branching ratio of $\mathcal{O}(10^{-15})$. We find that $t \rightarrow b WZ$ will be very challenging to observe in top quark pair production, even within well-motivated beyond-the-Standard Model scenarios. For the mode $t\rightarrow h c$ we find a stronger sensitivity than that obtained by any future LHC measurement by at least one order of magnitude.