Leveraging on-shell interference to search for FCNCs of the top quark and the Z boson

Flavour-changing-neutral currents (FCNCs) involving the top quark are highly suppressed within the Standard Model (SM). Hence, any signal in current or planned future collider experiments would constitute a clear manifestation of physics beyond the SM. We propose a novel, interference-based strategy to search for top-quark FCNCs involving the $Z$ boson that has the potential to complement traditional search strategies due to a more favourable luminosity scaling. The strategy leverages on-shell interference between the FCNC and SM decay of the top quark into hadronic final states. We estimate the feasibility of the most promising case of anomalous $tZc$ couplings using Monte Carlo simulations and a simplified detector simulation. We consider the main background processes and discriminate the signal from the background with a deep neural network that is parametrised in the value of the anomalous $tZc$ coupling. We present sensitivity projections for the HL-LHC and the FCC-hh. We find an expected $95\%$ CL upper limit of $\mathcal{B}_{\mathrm{excl}}(t\rightarrow Zc) = 6.4 \times 10^{-5}$ for the HL-LHC. In general, we conclude that the interference-based approach has the potential to provide both competitive and complementary constraints to traditional multi-lepton searches and other strategies that have been proposed to search for $tZc$ FCNCs.