The K⁺ → π⁺νν¯ decay and new physics searches at NA62

The NA62 experiment at CERN was designed to measure the branching ratio of the ultra-rare K⁺ → π⁺νν¯ decay with a decay-in-flight technique. The Standard Model prediction for this branching ratio is very precise and this process is an ideal candidate for the indirect search of New Physics at high-mass scale. NA62 took physics data from 2016 to 2018: the results of the K⁺ → π⁺νν¯ analysis in the 2016+2017 data sets are presented. Moreover, the high-intensity setup, the flexibility of its trigger system, and the hermetic coverage of the experiment make NA62 a useful tool for the search of exotic particles in the MeV–GeV range weakly coupled to the Standard Model, such as heavy neutral leptons and dark photons. The status of these analyses will be reviewed, along with other New Physics studies carried out at NA62, such as the search for lepton flavour and lepton number violating K⁺ decays.