Long Distance Contribution to $K_L \to \ell^+ \ell^-$

Abstract

We revisit the calculation of the long distance contribution to $K_L \to \mu^+ \mu^-$. We discuss this process within the framework of chiral perturbation theory, and also using simple models for the $K_L \gamma^* \gamma^*$ vertex. We argue that it is unlikely that this mode can be used to extract information on short distance parameters. The process $K_L \to e^+ e^-$ is also long-distance dominated and we find that $B(K_L \to e^+ e^-) \approx 9 \times 10^{-12}$.