Sensitivity to top-quark FCNC interactions at future muon colliders

We investigate flavor-changing neutral current (FCNC) interactions of the top quark at a future muon collider with a center-of-mass energy of $\sqrt{s} = 10~\mathrm{TeV}$. The process $\mu^{+}\mu^{-} \to \nu_{\mu}\,\mu^+\,b\,j$ and its corresponding charge conjugate are considered as a probe of anomalous $tqZ$ and $tq\gamma$ couplings, parametrized within an effective field theory framework in terms of $\kappa_{tqZ}$ and $\lambda_{tq\gamma}$. Signal and background events are simulated using Monte Carlo techniques, including parton showering and hadronization with \texttt{Pythia} and a fast detector simulation based on \texttt{Delphes} with a dedicated 10~TeV muon collider setup. A multivariate analysis based on boosted decision trees is employed to enhance the signal discrimination. Assuming an integrated luminosity of $10~\mathrm{ab}^{-1}$, we obtain projected sensitivities to the anomalous couplings at the $\mathcal{O}(10^{-3})$ level, corresponding to branching ratio limits of $\mathcal{O}(10^{-6})$ for the rare $t \to qZ$ and $t \to q\gamma$ decays. These results significantly improve upon the current bounds from the CMS and ATLAS collaborations, extending the sensitivity by more than one order of magnitude. Our findings demonstrate that a multi-TeV muon collider provides a powerful and complementary platform for probing rare top-quark interactions, offering a unique opportunity to explore physics beyond the Standard Model through FCNC processes.