Investigation of K_L,S → π⁺π ^-e⁺e^- decays

The K_L → π⁺π^-e ⁺e^- and K_S → π⁺π ^-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_L → π ⁺π^-e⁺e^- candidates has been observed with an expected background level of 36.9 events, yielding the branching ratio measurement BR(K_L → π⁺π ^-e⁺e^-) = (3.08 ± 0.20) × 10 ^-7. The distribution of events in the sinφ cosφ variable, where φ is the angle between the π⁺π^- 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_φ = (14.2 ± 3.6)%. For the K_S → π⁺π ^-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 → π⁺π^-e⁺e^-) = (4.71 ± 0.32) × 10^-5. The combined value of this measurement with the published 1998 result is BR(K_S → π ⁺π^-e⁺e^-) = (4.69 ± 0.30) × 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 a₁/a₂ and g̃_M1 in the K _L → π⁺π^-e⁺e^- direct emission process as well as the value of the K⁰ charge radius have been extracted from the data.