The decays $K\to \pi \pi \nu \overline{\nu }$ within the standard model

Abstract

We study the reactions $K\to \pi \pi \nu \overline{\nu }$ 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 $\rho$ and $\eta$. Depending on the value of the CKM angles we find branching ratios in the following ranges: $B(K_L\to {\pi }^{+}{\pi }^{-}\nu \overline{\nu })=[2-5]\times 10^{-13}$; $B(K_L\to {\pi }^0{\pi }^0\nu \overline{\nu })=[1-3]\times 10^{-13}$; $B(K^{+}\to {\pi }^{+}{\pi }^0\nu \overline{\nu })=[1-2]\times 10^{-14}$. We also discuss a possible $CP$-odd observable.

Comments: 10 pages, LaTeX, 2 Postscript figures. Title and abstract have been revised to better reflect the content of the paper. This is the final version as published