Determination of the structure of the $K\to \pi \pi \pi$ amplitudes from recent data

This Letter provides a new determination of the ten real coefficients that describe the structure of the $K\to \pi \pi \pi$ amplitudes in the limit where isospin is conserved and complex phases, due to either CP violation or final-state rescattering, are neglected. This determination is obtained through a fit to the data on the Dalitz-plot structures and partial-decay rates collected during the last twenty years by several high-precision experiments. The fitting procedure and the way the experimental data have been handled in the fit are discussed in detail. Our fit leads to a more precise determination of the coefficients describing the linear and quadratic slopes of the $K\to \pi \pi \pi$ amplitudes.