Lepton flavor violating top quark FCNC processes at the $\mu$TRISTAN

We investigate charged lepton flavor violating top quark flavor-changing neutral current interactions at the proposed asymmetric muon-electron collision stage of the $\mu$TRISTAN collider, operating at a center-of-mass energy of 346 GeV. Specifically, we study the process $\mu^{+} e^{-} \rightarrow t q$ ($t \overline{q} + \overline{t}q$) with $q = u, c$, within the framework of three classes of four-fermion contact interactions: scalar, vector, and tensor operators. A cut-based analysis is performed using boost-invariant kinematic observables, followed by a likelihood-based statistical treatment to derive projected sensitivities for each operator. For an integrated luminosity of $100~\text{fb}^{-1}$, the projected constraints improve upon current LHC bounds on the corresponding effective couplings by approximately an order of magnitude. Projections for $1~\text{ab}^{-1}$ indicate even stronger sensitivity, indicating improved reach at higher luminosity. Additionally, we explore the impact of initial-state beam polarization on these projections, showing how it can further enhance sensitivity to specific operator structures.