Search for flavor-changing neutral currents in top quark decays $t\to Hc$ and $t \to Hu$ in multilepton final states in proton-proton collisions at $\sqrt{s}= 13$ TeV with the ATLAS detector

Flavor-changing neutral currents are not present in the Standard Model at tree level and are suppressed in loop processes by the unitarity of the Cabibbo-Kobayashi-Maskawa matrix; the corresponding rates for top quark decay processes are experimentally unobservable. Extensions of the Standard Model can generate new flavor-changing neutral current processes, leading to signals which, if observed, would be unambiguous evidence of new interactions. A dataset corresponding to an integrated luminosity of 36.1 fb$^{-1}$ of $pp$ collisions at a center-of-mass energy of $\sqrt{s}=$ 13 TeV recorded with the ATLAS detector at the Large Hadron Collider is used to search for top quarks decaying to up or charm quarks with the emission of a Higgs boson, with subsequent Higgs boson decay to final states with at least one electron or muon. No signal is observed and limits on the branching fractions $\mathcal{B}(t \to Hc)