Figure 1: (Top) $K\to \pi \nu \overline{\nu }$ decays are mediated by the flavor-changing neutral-current transition $s\to d\nu \overline{\nu }$ (here $s$ and $d$ stand for strange and down quarks). (Bottom) Representative one-loop diagrams contributing to the $s\to d\nu \overline{\nu }$ amplitude within the standard model (left) and within an extension of the standard model (right).