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Investigating Top-Higgs FCNC Couplings at the FCC-hh

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 $BR(η_{uc})_{\mathrm{disc}}=9.08\times10^{-6}$ or $BR(η_{uc})_{\mathrm{exc}}=2.78\times10^{-6}$ at an integrated luminosity of 30 ab$^{-1}$ , respectively. Our results are compatible with the other channels already studied at FCC-hh.