The decays K → ππνν within the standard model

We study the reactions K → ππνν within the minimal standard model. We use isospin symmetry to relate the matrix elements to the form factors measured in Kℓ4. We argue that these modes are short distance dominated and can be used for precise determinations of the CKM parameters ϱ and η. Depending on the value of the CKM angles we find branching ratios in the following ranges: B(KL → π+π−νν) = [2–5] × 10−13; B(KL → π0π0νν) = [1–3] × 10−13; B(K+ → π+π0νν) = [1–2] × 10−14. We also discuss a possible CP-odd observable.