Electromagnetic effects and scattering lengths extraction from experimental data on $K \to 3\pi$ decays

Abstract

The final state interactions in $K^\pm\to\pi^\pm\pi^0\pi^0$ decays are considered using the methods of non-relativistic quantum mechanics. We show how to take into account the largest electromagnetic effects in the analysis of experimental data, using the amplitudes calculated earlier. We propose the relevant expressions for amplitude corrections valid both above and below the two charged pion production threshold $M_{\pi^0\pi^0}=2m_{\pi^\pm}$, including the average effect for the threshold bin. These formulae can be used in the procedure of pion scattering lengths measurement from $M_{\pi^0\pi^0}$ spectrum.