Messung der Zerfallsasymmetrien der radiativen Hyperonzerfälle $\Xi^0 \to \Delta\gamma$ und $\Xi^0 \to \Sigma^0\gamma$ mit dem NA48/1-Experiment

The radiative decay of a hyperon into a light hyperon and a photon allows to study the structure of the electroweak interaction of hadrons. For this purpose, the decay asymmetry is an appropriate observable. It describes the distribution of the daughter hyperon with respect to the polarization $vec{P}$ of the mother hyperon by $dN / d cos(Theta) propto 1 + alpha |vec{P}| cos(Theta)$, where $Theta$ is the angle between $vec{P}$ and the momentum of the daughter hyperon. The radiative decay $Xi^0 to Lambda gamma$ is of particular interest since all calculations at quark level predict a positive decay asymmetry whereas two existing measurements result in a negative value of $alpha_{Lambda gamma} = -0.73 pm 0.17$. The goal of the analysis presented here was to verify these results and to improve the accuracy of the decay asymmetry measurement. In addition, the decay asymmetry of the similar decay $Xi^0 to Sigma^0 gamma$ was measured, and the well-known decay $Xi^0 to Lambda pi^0$ was used to test the analysis strategy. During the data taking period in 2002, the NA48/1 experiment at CERN was searching for rare $K_S$ and hyperon decays. The collected data represents the world's largest sample of $Xi^0$ decays. From this sample, about 52,000 $Xi^0 to Lambda gamma$ decays, 15,000 $Xi^0 to Sigma^0 gamma$ decays and 4 mill. $Xi^0 to Lambda pi^0$ decays with small background were extracted as well as the corresponding $antiXi$ decays. The available $antiXi$ samples amount about one tenth of the $Xi^0$ samples. The measurement of the decay asymmetries was based on the comparison between data and a detailed Monte Carlo simulation, giving the following results: $alpha_{Lambda gamma} = -0.701 +- 0.019_{stat} +- 0.064_{sys}$, n$alpha_{Sigma^0 gamma} = -0.683 +- 0.032_{stat} +- 0.077_{sys}$, $alpha_{Lambda pi^0} = -0.439 +- 0.002_{stat} +- 0.056_{sys}$, $alpha_{antiLambda gamma} = 0.772 +- 0.064_{stat} +- 0.066_{sys}$, $alpha_{antiSigma^0 gamma} = 0.811 +- 0.103_{stat} +- 0.135_{sys}$, $alpha_{antiLambda pi^0} = 0.451 +- 0.005_{stat} +- 0.057_{sys}$. The uncertainty on the $Xi^0 to Lambda gamma$ decay asymmetry could be reduced by a factor 3, confirming the negative value of this asymmetry and, as a result, the disagreement with the predictions of the calculations at quark level. The $antiXi$ asymmetries have been measured for the first time, allowing to set limits on possible CP violation in $Xi^0$ decays.