Long Distance Contribution to $K^+ \rightarrow π^+ ν\barν$

Abstract

We estimate the long distance contribution to the $K^+ \rightarrow π^+ ν\barν$ decay amplitude using chiral perturbation theory. We find that it is likely to be less than a few percent of the part of the short distance contribution proportional to the square of the charm quark mass. In the large $N_c$ limit the leading (in chiral perturbation theory) long distance contribution to $K^+ \rightarrow π^+ ν\barν$ from Feynman diagrams with a $W$ and $Z^0$ vanishes.