Projected NA62 sensitivity to heavy neutral lepton production in $K^+ \to \pi^0 e^+ N$ decays

Heavy neutral leptons (HNLs) appear in many extensions of the Standard Model of particle physics. In this study, we investigate to which extent the NA62 experiment at CERN could improve the existing bounds on the HNL mixing angle $|U_e|^2$ by performing a missing mass search in $K^+ \to \pi^0 e^+ N$ decays in flight. We show that the limit $|U_e|^2 \simeq 2\times 10^{-6}$ can be reached with the currently available data in the mass range 125 -- 144 MeV, which is currently not well covered by production searches. Future data, together with a dedicated trigger and/or improvements in rejection of out-of-acceptance photons, can improve this limit by another order of magnitude.