Electromagnetic corrections to final state interactions in $K\to 3\pi $ decays

Abstract

The final state interactions of pions in decays $K^\pm\to\pi^\pm\pi^0\pi^0$ are considered using the methods of quantum mechanics. We show how to incorporate the electromagnetic effects in the amplitudes of these decays and to work out the relevant expressions valid above and below the two charged pions production threshold $M_c=2m$. The electromagnetic corrections are given as evaluated in a potential model.