Chiral Phenomenological Relations between Rates of Rare Radiative Decay of Kaon to Pion and leptons and the meson Formfactors

TL;DR

This paper derives phenomenological relations between rare radiative kaon decay rates and meson form factors using chiral perturbation theory, showing how experimental data can determine form factors with high precision.

Contribution

It establishes chiral perturbation theory-based relations linking decay rates and meson form factors, enabling precise extraction of form factors from experimental decay data.

Findings

ChPT relations can determine meson form factors from decay rates of charged kaons.

Form factor data for neutral kaons are more precise than differential decay rate measurements.

The approach allows high-precision extraction of meson form factors from existing experimental data.

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 $K^0 \to \pi^0 e^+ e^- (\mu^+ \mu^-)$.