Displaced vertices as probes of sterile neutrino mixing at the LHC

We investigate the reach at the LHC to probe light sterile neutrinos with displaced vertices. We focus on sterile neutrinos $N$ with masses $m_{N} \sim $ (5-30) GeV, that are produced in rare decays of the Standard Model gauge bosons and decay inside the inner trackers of the LHC detectors. With a strategy that triggers on the prompt lepton accompanying the $N$ displaced vertex and considers charged tracks associated to it, we show that the 13 TeV LHC with $3000$/fb is able to probe active-sterile neutrino mixings down to $|V_{lN}|^2\approx 10^{-9}$, with $l=e,\mu$, which is an improvement of up to four orders of magnitude when comparing with current experimental limits from trileptons and proposed lepton-jets searches. In the case when $\tau$ mixing is present, mixing angles as low as $|V_{\tau N}|^2 \approx 10^{-8}$ can be accessed.