Dark-sector physics in the search for the rare decays K+→ π+νν ̄ and KL→ πνν ̄

We compute the contribution of the decays KL→ πQQ ̄ and K+→ π+QQ ̄ , where Q is a dark fermion of the dark sector, to the measured widths for the rare decays K+→ π+νν ̄ and KL→ πνν ̄. The recent experimental limit for Γ(K+→ π+νν ̄) from NA62 sets a new and very strict bound on the dark-sector parameters. A branching ratio for KL→ πQQ ̄ within the reach of the KOTO sensitivity is possible. The Grossman–Nir bound is weakened by the asymmetric effect of the different kinematic cuts enforced by the NA62 and KOTO experiments. This last feature holds true for all models where the decay into invisible states takes place through a light or massless intermediate state.