K → πℓ+ℓ− decays in the effective chiral lagrangian of the standard model

Abstract

The decay amplitudes of K → πℓ+ℓ− transitions (ℓ = e or μ) are calculated in chiral perturbation theory to lowest non-trivial order. This includes one-loop contributions as well as contributions from all possible tree level counterterms to the corresponding order in momenta and meson masses. After relating the local counterterms in the chiral realization to the lowest dimensional local transition operator at the quark level, only one combination of counterterm coupling constants appearing in the decay amplitudes remains unknown. Two possible solutions for this constant are found from a comparison with the experimentally known K+ → π+e+e− decay rate. Predictions are then obtained for the rates of K+ → π+μ+μ−, Ks0 → π0e+e− and Ks0 → π0μ+μ− decays as well as for the corresponding spectra in the invariant mass of the lepton pair. The CP-violating transition KL0 → π0‘γ’ → π0ℓ+ℓ− is also discussed.