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Searches for anomalous $Zt$ and $\gamma t$ production provide an excellentprobe of flavour-changing top interactions when the energies considered arevery large. In this note we estimate the sensitivity to these interactions atthe high luminosity phase of the LHC and a future 100 TeV $pp$ collider(FCC-hh). For the LHC, the expected limits on $t \to uZ / u\gamma $ branchingratios from $Zt$ and $\gamma t$ production will reach the $10^{-5}$ level, oneorder of magnitude better than the existing projections for $t \to uZ$ from $t\bar t$ production. For the FCC-hh, the limits on $t \to uZ / u\gamma$ couldreach an impressive sensitivity at the $10^{-6}$ level, with limits on $t \tocZ / c\gamma$ at the $10^{-5}$ level.

Ultraboosted $Zt$ and $\gamma t$ production at the HL-LHC and FCC-hh