Investigation of $K_{L,S} \rightarrow \pi^{+}\pi^{-}e^{+}e^{-}$ decays

The $K_{L} \to \pi^{+}\pi^{-}e^{+}e^{-}$ and $K_{S} \to \pi^{+}\pi^{-}e^{+}e^{-}$ decay modes have been studied in detail using the NA48 detector at CERN SPS. Based on the data collected during the 1998 and 1999 run periods, a sample of 1162 $K_{L} \to \pi^{+}\pi^{-}e^{+}e^{-}$ candidates has been observed with an expected background level of 36.9 events, yielding the branching ratio measurement $BR(K_{L} \to \pi^{+}\pi^{-}e^{+}e^{-})=(3.08 \pm 0.20) \times 10^{-7}$. The distribution of events in the sin$\phi$cos$\phi$ variable, where $\phi$ is the angle between the $\pi^{+}\pi^{-}$ and the $e^{+}e^{-}$ decay planes in the kaon centre of mass, is found to exhibit a large CP-violating asymmetry with the value $A_{\phi}(14.2 \pm3.6)$%. For the $K_{S} \to \pi^{+}\pi^{-}e^{+}e^{-}$ decay channel, 621 candidates have been identified in the 1999 data sample with an estimated background contribution of 0.7 event. The corresponding branching ratio has been determined to be $BR(K_{S} \to \pi^{+}\pi^{-}e^{+}e^{-})=(4.71 \pm 0.32) \times 10^{-5}$. The combined value of this measurement with the published 1998 result is $BR(K_{S} \to \pi^{+}\pi^{-}e^{+}e^{-})=(4.69 \pm 0.30) \times 10^{-5}$. No asymmetry is observed in this decay mode. Our results are in good agreement with theoretical predictions based on a phenomenological description of radiative kaon decays. The form factor parameters a$_{1}$/a$_{2}$ and $\tilde{g}_{M1}$ in the $K_{L} \to \pi^{+}\pi^{-}e^{+}e^{-}$ direct emission process as well as the value of the $K^{0}$ charge radius have been extracted from the data.