Search for K S,L oscillations and invisible decays into the dark sector at NA64

The decays KS,L → invisible have never been experimentally tested. In the Standard Model (SM), their branching ratios for the decay into two neutrinos are predicted to be extremely small, Br (KS,L → νν̄) ≲ 10−16. We consider several natural extensions of the SM, such as two-Higgs-doublet (2HDM), 2HDM and light scalar, and dark mirror sector models, that allow one to enhance the Br (KS,L → invisible) up to a measurable level. We briefly discuss the possible search for KS,L → invisible decays and KS,L oscillations into the dark sector at the NA64 experiment at CERN with the sensitivity to Br (KS,L → invisible) ≲ 10−7−10−5.