The decays $K \to ππν\overlineν$ within the standard model

Abstract

We study the reactions $K \rightarrow ππν\overlineν$ within the minimal standard model. We use isospin symmetry to relate the matrix elements to the form factors measured in $K_{\ell 4}$. 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: $B(K_L \rightarrow π^+ π^- ν\overlineν) = [2-5] \times 10^{-13}$; $B(K_L \rightarrow π^0 π^0 ν\overlineν) = [1-3] \times 10^{-13}$; $B(K^+ \rightarrow π^+ π^0 ν\overlineν) = [1-2] \times 10^{-14}$. We also discuss a possible $CP$-odd observable.