Measurement of the Ratio Gamma(KL -> pi+ pi-)/Gamma(KL -> pi e nu) and Extraction of the CP Violation Parameter |eta+-|

We present a measurement of the ratio of the decay rates Gamma(KL -> pi+ pi-)/Gamma(KL -> pi e nu), denoted as Gamma(K2pi)/Gamma(Ke3). The analysis is based on data taken during a dedicated run in 1999 by the NA48 experiment at the CERN SPS. Using a sample of 47000 K2pi and five million Ke3 decays, we find Gamma(K2pi)/Gamma(Ke3) = (4.835 +- 0.022(stat) +- 0.016(syst)) x 10^-3. From this we derive the branching ratio of the CP violating decay KL -> pi+ pi- and the CP violation parameter |eta+-|. Excluding the CP conserving direct photon emission component KL -> pi+ pi- gamma, we obtain the results BR(KL -> pi+ pi-) = (1.941 +- 0.019) x 10^-3 and |eta+-| = (2.223 +- 0.012) x 10^-3.