The Decays $K\to \pi {\ell }^{+}{\ell }^{-}$ beyond Leading Order in the Chiral Expansion

Abstract

We present a model-independent analysis of $K^{+}\to {\pi }^{+}{\ell }^{+}{\ell }^{-}$ and $K_S\to {\pi }^0{\ell }^{+}{\ell }^{-}$ decays, including $K\to 3\pi$ unitarity corrections and a general decomposition of the dispersive amplitude. From the existing data on $K^{+}\to {\pi }^{+}{e}^{+}{e}^{-}$ we predict the ratio $R=B(K^{+}\to {\pi }^{+}{\mu }^{+}{\mu }^{-})/B(K^{+}\to {\pi }^{+}{e}^{+}{e}^{-})$ to be larger than 0.23, in slight disagreement with the recent measurement $R=0.167\pm 0.036$. Consequences for the $K^{\pm }\to {\pi }^{\pm }{e}^{+}{e}^{-}$ charge asymmetries and for the $K_L\to {\pi }^0{e}^{+}{e}^{-}$ mode are also discussed.

Comments: 18 pages, latex