Probing flavor constrained SMEFT operators through $tc$ production at the Muon collider

We investigate flavour violating four Fermi Standard Model Effective Field Theory (SMEFT) operators of dimension-six that can be probed via $tc ~(\bar{t}c+t\bar{c})$ production at the multi-TeV muon collider. We study different FCNC and FCCC processes related to $B$, $B_s$, $K$ and $D$ decays and mixings, sensitive to these operators and constrain the corresponding couplings. The tensor operator turns out to be most tightly bound. We perform event simulation of the final state signal from $tc$ production together with the SM background to show that operators after flavour constraint can reach the discovery limit at 10 TeV muon collider. We further adopt the optimal observable technique (OOT) to determine the optimal statistical sensitivity of the Wilson coefficients and compare them with the flavour constraints. We use the limits to predict the observational sensitivities of the rare processes like $K_L \to \pi_0 \ell \ell$, $D_0 \to \mu\mu$, $t \to c\ell\ell$.