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

Abstract.

The ${K_\mathrm{L} \rightarrow \pi^+\pi^-e^+e^-}$ and ${K_\mathrm{S} \rightarrow \pi^+\pi^-e^+e^-}$ decay modes have been studied in detail using the NA48 detector at the CERN SPS. Based on the data collected during the 1998 and 1999 run periods, a sample of 1162 ${K_\mathrm{L} \rightarrow \pi^+\pi^-e^+e^-}$ candidates has been observed with an expected background level of 36.9 events, yielding the branching ratio measurement ${\mathrm{BR}({K_\mathrm{L} \rightarrow \pi^+\pi^-e^+e^-})} =(3.08 \pm 0.20) \times 10^{-7}$. The distribution of events in the $\mathrm{sin\phi cos\phi}$ 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 ${{\cal A}_{\phi}} =(14.2 \pm 3.6)\%$. For the ${K_\mathrm{S} \rightarrow \pi^+\pi^-e^+e^-}$ 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 ${\mathrm{BR}({K_\mathrm{S} \rightarrow \pi^+\pi^-e^+e^-} )} =(4.71 \pm 0.32) \times 10^{-5}$. The combined value of this measurement with the published 1998 result is ${\mathrm{BR}({K_\mathrm{S} \rightarrow \pi^+\pi^-e^+e^-} )} =(4.69 \pm 0.30) \times 10^{-5}$. 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 $\mathrm{a_1/a_2}$ and $\mathrm{\tilde{g}_{M1}}$ in the ${K_\mathrm{L} \rightarrow \pi^+\pi^-e^+e^-}$ direct emission process as well as the value of the K⁰ charge radius have been extracted from the data.