Comments on long distance contribution to $K^{+}\to {\pi }^{+}\nu \bar{\nu }$

Abstract

We study the long distance contribution to K^+\to\pi^+\nu\bar{\nu by using chiral perturbation theory. We find that the tree level $O(P^2)$ contribution vanishes identically without assuming the large $N_c$ limit. The leading contribution arises from the one-loop amplitude, which is $O(P^4)$ in the chiral power counting. The branching ratio of the long distance contribution is found to be of order $10^{-7}$ smaller compared with that of short distance one and hence is completely negligible.

Comments: 8 pages, LaTeX file