Long distance contribution to $K^+ \to \pi^+ \nu {\bar \nu}$ decay and $O(p^4)$ terms in CHPT

The long distance contribution to $K^+ \to \pi^+ \nu {\bar \nu} $ is calculated using chiral perturbation theory. The leading contribution comes from $O(p^4)$ tree terms. The branching ratio of the $O(p^4)$ long distance contribution is found to be of order $10_{-3}$ smaller than the short distance contributions.