New physics searches at NA62

The NA62 experiment at CERN has collected a large sample of $K^+$ and $\pi^+$ decays in flight during Run 1 in 2016--2018 and the ongoing Run 2 which started in 2021. Searches for the decays $K^+\rightarrow\pi^+X$ and $\pi^+\rightarrow e^+N$ are presented using NA62 data collected in 2016--2022 and 2017--2024, respectively. Results are interpreted to constrain a range of new physics scenarios covering all four portal model scenarios. Upper limits on the $K^+\rightarrow\pi^+X$ branching ratio are established at the $10^{-11}$ level, providing constraints on dark photon, scalar and ALP couplings. From the search for heavy neutral lepton production in $\pi^+\rightarrow e^+N$ decays of beam pions, upper limits of the extended neutrino mixing matrix element $|U_{e4}|^2$ are established at the $10^{-8}$ level over the heavy neutral lepton mass range 95--126~MeV/$c^2$.