Study of Long Distance Contributions to $K\to n\pi\nu\bar{\nu}$

Abstract

We calculate long distance contributions to $K\to\pi\nu\bar{\nu}\,,\ \pi\pi\nu\bar{\nu}$, and $\pi\pi\pi\nu\bar{\nu}$ modes within the framework of chiral perturbation theory. We find that these contributions to decay rates of $K\to \pi\nu\bar{\nu}$ and $K\to \pi\pi\nu\bar{\nu}$ in the chiral logarithmic approximation are at least seven orders of magnitude suppressed relative to those from the short distance parts. The long distance effects in this class of decays are therefore negligible.