Search for rare top quark decays

The ATLAS searches for the Flavour Changing Neutral Current (FCNC) processes in top-quark pair-production and single top events are presented. In pair-production events, the signal is characterized by one top quark decaying through $t\to Zq$ or $t\to Hq$ FCNC ($Z\to\ell^+\ell^-$, $H\to\gamma\gamma$ and $q=u, c$) channel, and the other through the Standard Model dominant mode $t\to Wb$. In single top production, a light quark interacts with a gluon to produce the top quark, which decays through the Standard Model mode. No evidence for signal was found and limits are derived. The ATLAS sensitivity for the search of FCNC processes in top-quark decays at the high-luminosity phase of the LHC (HL-LHC) is also presented for the $t\to\gamma q$ and $t\to Zq$