Top quark FCNC anomalous couplings at the future collider FCC-ee

In this study, we explore the potential of the future circular electron-positron collider (FCC-ee) in searching for Flavor-Changing Neutral Current (FCNC) interactions involving top quarks. Specifically, we investigate the production of single top quarks associated with a light quark ($q=u, c$) in FCNC processes. The analysis relies on Monte Carlo (MC) simulations conducted using the official FCC framework. The simulations are performed for two suggested center-of-mass energies at the FCC-ee: 240 GeV and 365 GeV, corresponding to planned integrated luminosities of 5 ab$^{-1}$ and 1.5 ab$^{-1}$, respectively. The event selections is made considering both the leptonic decay (electron and muon) and the fully hadronic decay of the top quark in the final state. By employing the CLs method, upper limits at a 95\% confidence level (CL) are determined for the sets of branching ratios associated with the decay of the top quark. The statistical combination of results obtained from the leptonic channel, considering both the center-of-mass energy and electron (muon) channel, reveals that at the FCC-ee, upper limits for the branching fractions of $Br(t \to c \gamma) < 1.99 \times 10^{-5}$ and $Br(t \to c Z) < 8.19 \times 10^{-6}$ could be achieved at a 95\% CL. In the case of the fully hadronic analysis, the branching ratio after the statistical combination of center-of-mass energies for the processes under investigation are found to be at the order of $Br(t \to c \gamma) < 7.65 \times 10^{-5}$ and $Br(t \to c Z) < 3.28 \times 10^{-5}$.