Chiral phenomenological relations between rates of rare radiative decays of kaon to pion and leptons and the meson form factors

Abstract

In framework of the chiral perturbation theory we obtain the phenomenological relations between decay branches of rare radiative kaon to pion and leptons $K^+ \to \pi^+ l^+ l^-$ and $K^0_S \to \pi^0 l^+ l^-$ and meson form factors. The comparison of these results with the present day experimental data shows us that the ChPT relations for a charge kaon can determine meson form factors from already measured decay rates at high precision level. However, in the case of the neutral kaon decays $K^0 \to \pi^0 e^+ e^- (\mu^+ \mu^-)$ the formfactor data are known to a high precision than data on the differential rates of radiative kaon decay $K^0 \to \pi^0 e^+ e^- (\mu^+ \mu^-)$.