KS,LKL,S→3π,πlν interferences at φ factories

We study the ${\mathit{K}}_{\mathit{S},}$ ${\mathit{LK}}_{\mathit{L},}$S→3π,πlν time-dependent interferences at a φ factory. We find that, with ${10}^{10}$–${10}^{11}$ φ’s as obtainable with a luminosity scrL=${10}^{33}$ ${\mathrm{cm}}^{\mathrm{-}2}$ ${\mathrm{s}}^{\mathrm{-}1}$, it should be possible to measure the CP-conserving amplitude of the decay ${\mathit{K}}_{\mathit{S}}$→${\mathrm{\pi }}^{+}$ ${\mathrm{\pi }}^{\mathrm{-}}$ ${\mathrm{\pi }}^0$ from the observation of such interferences. Furthermore, we point out that also the final-state-interaction phases of K→3π could be reached experimentally in this way.