  We have studied the sensitivity to flavor changing neutral current
interaction of top and Higgs boson at the future circular collider in the
hadron-hadron collision mode (FCC-hh). Our main concerns are the processes of
$pp\rightarrow th$ (FCNC production) and $pp\rightarrow t\bar{t}$ (one top FCNC
decay) which contributes to the single lepton, at least three jets and the
missing energy transverse in the final state. On the one hand FCC-hh offers
very high luminosity and large cross section for these signal processes, on the
other hand signal can be distinguished from background which needs application
of ingenious methods. Here, we have inspired and followed the searches at the
LHC using our analysis path and enhanced attainable limits obtained on the
possible top-Higgs FCNC couplings phenomenologically. We obtain new limits
which are beyond the current experimental limits obtained from different
channels and processes at the LHC. The potential discovery or exclusion limits
on branching ratios for $tqH$ FCNC interactions can be set
$BR(\eta_{uc})_{\mathrm{disc}}=9.08\times10^{-6}$ or
$BR(\eta_{uc})_{\mathrm{exc}}=2.78\times10^{-6}$ at an integrated luminosity of
30 ab$^{-1}$ , respectively. Our results are compatible with the other channels
already studied at FCC-hh.

High Energy Physics - Phenomenology