Measurement of the Slope Parameter $\alpha$ for the $\eta\to 3\pi^0$ decay with the Crystal Ball at MAMI-C

The dynamics of the $\eta\to 3\ pi^0$ decay have been studied with the Crystal Ballmultiphoton spectrometer and the TAPS calorimeter. Bremsstrahlungphotons produced by the 1.5 GeV electron beam of the Mainz microtronMAMI-C and tagged by the Glasgow photon spectrometer were used for $\ eta$- mesonproduction. The analysis of $3 \times 10^6$ $\gamma p \to \eta p \to 3\ pi^0 p \to 6\gamma p$ events yields the value $\alpha=-0.032\pm0.003$ for the $\eta\to 3\ pi^0$ slope parameter, which agrees with the majority of recent experimental results and has the smallest uncertainty. The $\ pi^0\ pi^0$ invariant- mass spectrumwas investigated for the occurrence of a cusp-like structure in the vicinity of the $\ pi^+\ pi^-$ threshold. The observed effectis small and does not affect our measured value for the slope parameter.