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

Abstract

We give a simple expression in linear and quadratic Dalitz--plot slopes which does not depend on the charge combination of the $3\pi$ state $(K^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-}$ or ${\pi }^{\pm }{\pi }^0{\pi }^0$ and $K_L^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$ or ${\pi }^0{\pi }^0{\pi }^0)$, 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 ${\pi }^{\pm }{\pi }^0{\pi }^0$ channel, could help to test theoretical predictions more stringently. A FORTRAN code for the radiatiative corrections is available on request.

Comments: (DESY Int. Rep. 93-05, 16 p., 5 fig.)