Direct and Indirect Searches for Top-Higgs FCNC Couplings

Large top quark flavor changing through neutral currents is expected by many extensions of the standard model. Direct and indirect searches for flavor changing neutral currents (FCNC) in the top quark decays to an up type quark (up,charm) and a Higgs boson are presented. We probe the observability of the top-Higgs FCNC couplings through the process e$^-$e$^+ \rightarrow t (\rightarrow \ell \nu_{\ell} b) \,\, \bar{t} (\rightarrow q H)$, where $\ell$ = e, $\mu$ and $q$ reflects up and charm quarks. It is shown that the branching ratio $Br(t\rightarrow qH)$ can be probed down to $1.12\times 10^{-3}$ at $95\%$ C.L. at the center-of-mass energy of 500 GeV with the integrated luminosity of 3000 fb$^{-1}$. We also update the constraint on the top-Higgs FCNC coupling using the electroweak precision observables related to $Z\rightarrow c\bar{c}$ decay.