Measurement of the Matrix Elements for the Decays $η\rightarrow π^{+}π^{-}π^0$ and $η/η^{\prime}\rightarrowπ^0π^0π^0$
Based on a sample of $1.31 \times 10^9$ $J/ψ$ events collected with the BESIII detector at the BEPCII collider, Dalitz plot analyses of selected 79,625 $η\rightarrowπ^{+}π^{-}π^0$ events, 33,908 $η\rightarrowπ^0π^0π^0$ events and 1,888 $η^{\prime}\rightarrowπ^0π^0π^0$ events are performed. The measured matrix elements of $η\rightarrowπ^+π^-π^0$ are in reasonable agreement with previous measurements. The Dalitz plot slope parameters of $η\rightarrowπ^0π^0π^0$ and $η^{\prime}\rightarrowπ^0π^0π^0$ are determined to be $-0.055 \pm 0.014 \pm 0.004$ and $-0.640 \pm 0.046 \pm 0.047$, respectively, where the first uncertainties are statistical and the second systematic. Both values are consistent with previous measurements, while the precision of the latter one is improved by a factor of three. Final state interactions are found to have an important role in those decays.