Dark matter as the trigger of flavor changing neutral current decays of the top quark

We suggest a simplified model that simultaneously addresses the dark-matter problem and give rise to top quark flavor changing neutral current (FCNC) interactions at the one-loop order. The model consists of two extra $SU(2)_L$ gauge singlets: a colored mediator of spin zero ($S$) and a right-handed fermion ($\chi$) both are odd under an ad-hoc $Z_2$ symmetry. The right-handed fermion plays the role of the dark-matter candidate. In this model, the presence of the two dark sector particles generates one-loop induced FCNC decays of the top quark into light quarks and bosons such as the gluon, the photon, the $Z$-boson or the Higgs boson. As a case study, we analyze the top quark FCNC decays into light quarks ($u$ or $c$) and a $Z$ or Higgs bosons. We then study the reliable solutions to the dark-matter problem by estimating the regions in the parameter space that are consistent with the \textsc{Planck} measurement of the dark-matter relic density. We also revisit the bounds from the searches of dark matter in events with at least one high-$p_T$ jet and large missing transverse energy at the Large Hadron Collider (LHC). We then define four benchmark points that are consistent with the existing constraints from collider experiments and cosmology. We finally estimate, for these benchmark scenarios, the rates of a broad range of channels that can be used to probe the connection between the top FCNC transitions and dark matter both at the HL-LHC and a future $100$ TeV collider.