Dark-sector physics in the search for the rare decays $K^+\rightarrow \pi^+ \bar \nu \nu$ and $K_L\rightarrow \pi^0 \bar \nu \nu$

Understand

We compute the contribution of the decays $K_L \rightarrow \pi^0 Q \bar Q$ and $K^+ \rightarrow \pi^+ Q \bar Q$, where $Q$ is a dark fermion of the dark sector, to the measured widths for the rare decays $K^+\rightarrow \pi^+ \nu \bar \nu$ and $K_L\rightarrow \pi^0 \nu \bar \nu$.

• The recent experimental limit for $\Gamma (K^+ \rightarrow \pi^+ \nu \bar \nu)$ from NA62 sets a new and very strict bound on the dark-sector parameters.
• A branching ratio for $K_L \rightarrow \pi^0 Q \bar Q$ 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.