K_{L,S} \to \pi \pi \nu \bar{\nu} Decays Within and Beyond the Standard Model

The decays K_{L,S} -> \pi^o \pi^o \nu \bar{\nu} and K_{L,S} -> \pi^+ \pi^- \nu \bar{\nu} involve the weak transition from a strange to a non-strange quark. Although they have considerably smaller branching ratios than those for the corresponding rare processes involving single pions, some may be more distinguishable experimentally from background processes and thus could provide another probe of the s -> d \nu \bar{\nu} transition. Using recent knowledge of the CKM matrix elements and measurements of related processes, we give improved predictions for their branching ratios both within and beyond the Standard Model.