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 operating at a center-of-mass energy of $\sqrt{s}=10~\mathrm{TeV}$. The process $\mu^{+}\mu^{-}\rightarrow\nu_{\mu}\,\mu^{+}\,b\,j$ together with its charge-conjugate channel is considered as a probe of anomalous $tqZ$ and $tq\gamma$ interactions within a model-independent effective field theory framework. Starting from the most general FCNC Lagrangian, we examine the contributions of vector and tensor operators as well as the chiral structure of the anomalous interactions. Owing to the strong chiral suppression of the right-handed contributions at multi-TeV energies, the detector-level sensitivity analysis is performed for the left-handed tensor couplings. Signal and Standard Model background events are generated using a complete Monte Carlo simulation chain, including matrix-element generation, parton showering and hadronization with \texttt{Pythia}, and fast detector simulation with \texttt{Delphes} using a dedicated $10$~TeV muon collider detector card. Signal discrimination is optimized through a boosted decision tree (BDT) analysis employing an extended set of kinematic observables. Assuming an integrated luminosity of $10~\mathrm{ab}^{-1}$, we derive projected exclusion and discovery sensitivities from a simultaneous two-dimensional scan of the real and imaginary components of the anomalous left-handed couplings $\kappa_{qt}^{L}$ and $\lambda_{qt}^{L}$. The obtained limits reach the $\mathcal{O}(10^{-3})$ level for the effective couplings, corresponding to branching-ratio sensitivities of $\mathcal{O}(10^{-6})$ for the rare decays $t\rightarrow qZ$ and $t\rightarrow q\gamma$. These projections improve the current experimental limits from the ATLAS and CMS collaborations by approximately one order of magnitude.