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 $K_L{\gamma }^{\ast }{\gamma }^{\ast }$ 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 $B(K_L\to e^{+}{e}^{-})\approx 9\times 10^{-12}$.

References added, one typo corrected. Version to appear in Nuclear Physics B