Measurement of the Slope Parameter $alpha$ for the $etato 3pi^0$ decay with the Crystal Ball detector at the Mainz Microtron (MAMI-C)

The dynamics of the $etato 3pi^0$ decay have been studied with the Crystal Ball multiphoton spectrometer and the TAPS calorimeter. Bremsstrahlung photons produced by the 1.5-GeV electron beam of the Mainz microtron MAMI-C and tagged by the Glasgow photon spectrometer were used for $eta$-meson production. The analysis of $3 times 10^6$ $gamma p to eta p to 3pi^0 p to 6gamma p$ events yields the value $alpha=-0.032pm0.003$ for the $etato 3pi^0$ slope parameter, which agrees with the majority of recent experimental results and has the smallest uncertainty. The $pi^0pi^0$ invariant-mass spectrum was investigated for the occurrence of a cusplike structure in the vicinity of the $pi^+pi^-$ threshold. The observed effect is small and does not affect our measured value for the slope parameter.