What can we learn from new measurements of Dalitz plot parameters for K $\rightarrow 3 π$ decays ?

Abstract

We give a simple expression in linear and quadratic Dalitz--plot slopes which does not depend on the charge combination of the $3π$ state $(K^\pm \to π^{\pm}π^{+}π^{-}$ or $π^{\pm}π^{0}π^{0}$ and $K_L^{0} \to π^{+}π^{-}π^{0}$ or $π^{0}π^{0}π^{0})$, if all phases between final states are negligible. After investigating the influence of radiative corrections, it is shown how new measurements, especially of quadratic slopes in the $π^{\pm} π^{0} π^{0}$ channel, could help to test theoretical predictions more stringently. A FORTRAN code for the radiatiative corrections is available on request.