Top quark FCNC in Randall-Sundrum models: post-LHC allowed rates and searches at $e^+e^-$ and $\mu^+ \mu^-$ colliders

Abstract

We present the sensitivity to Flavor Changing Neutral Currents (FCNC) in interactions involving the top quark at future $e^+e^-$ and $\mu^+\mu^-$ machines. We consider the $Ztc$ vertex as well as four-fermion contact interactions involving top and charm quarks. To incorporate limits from (HL-)LHC we consider FCNC from Randall-Sundrum models and we recast LHC searches for the resonances that at the microscopic level give rise to the FCNC effects. We determine the maximal strength of the effective FCNC couplings $Ztc$ coupling allowed by LHC. We find that the LHC currently improves on the limit set by previous machines, e.g. LEP indirect sensitivity to heavy vectors. Future improvements of direct searches at HL-LHC may reach a level equivalent to $BR(t\to c Z)\simeq 10^{-6}$. We explore the possibility to probe even smaller FCNC coupling strength using an $e^+e^-$ machine at center-of-mass energy suitable for a Higgs factory $E_{cm}\in$ [200,240] GeV or to probe contact interactions involving top and charm flavors at a high-energy muon collider at $E_{cm}=10$ TeV.