Long Distance Contribution to $K^{+}\to {\pi }^{+}\nu \bar{\nu }$

Abstract

We estimate the long distance contribution to the $K^{+}\to {\pi }^{+}\nu \bar{\nu }$ 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 $K^{+}\to {\pi }^{+}\nu \bar{\nu }$ from Feynman diagrams with a $W$ and $Z^0$ vanishes.

Comments: 6 pages, uses phyzzx, 1 page of figures included