The decays K→πl+l− beyond leading order in the chiral expansion

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 correctionsand a general decomposition of the dispersive amplitude. From the existing dataon $K^+\to\pi^+ e^+ e^-$ we predict the ratio $R=B(K^+\to\pi^+\mu^+\mu^-)/B(K^+\to\pi^+ e^+ e^-)$ to be larger than 0.23, inslight 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.Comment: 18 pages, late