标题： 矩阵元的测量用于衰变 $η\rightarrow π^{+}π^{-}π^0$ 和 $η/η^{\prime}\rightarrowπ^0π^0π^0$ 显示英文标题

标题： Measurement of the Matrix Elements for the Decays $η\rightarrow π^{+}π^{-}π^0$ and $η/η^{\prime}\rightarrowπ^0π^0π^0$

摘要： 基于在BEPCII对撞机上使用BESIII探测器收集的$1.31 \times 10^9$ $J/\psi$ 个事例，对选定的79,625个$\eta\rightarrow\pi^{+}\pi^{-}\pi^0$事例、33,908个$\eta\rightarrow\pi^0\pi^0\pi^0$事例和1,888个$\eta^{\prime}\rightarrow\pi^0\pi^0\pi^0$事例进行了Dalitz图分析。测量的$\eta\rightarrow\pi^+\pi^-\pi^0$的矩阵元与先前的测量结果有合理的吻合。 Dalitz图斜率参数$\eta\rightarrow\pi^0\pi^0\pi^0$和$\eta^{\prime}\rightarrow\pi^0\pi^0\pi^0$分别被确定为$-0.055 \pm 0.014 \pm 0.004$和$-0.640 \pm 0.046 \pm 0.047$，其中第一个不确定性为统计学的，第二个为系统学的。 这两个值与之前的测量结果一致，而后者精度提高了三倍。 发现末态相互作用在这些衰变中起着重要作用。 显示英文摘要

摘要： Based on a sample of $1.31 \times 10^9$ $J/\psi$ events collected with the BESIII detector at the BEPCII collider, Dalitz plot analyses of selected 79,625 $\eta\rightarrow\pi^{+}\pi^{-}\pi^0$ events, 33,908 $\eta\rightarrow\pi^0\pi^0\pi^0$ events and 1,888 $\eta^{\prime}\rightarrow\pi^0\pi^0\pi^0$ events are performed. The measured matrix elements of $\eta\rightarrow\pi^+\pi^-\pi^0$ are in reasonable agreement with previous measurements. The Dalitz plot slope parameters of $\eta\rightarrow\pi^0\pi^0\pi^0$ and $\eta^{\prime}\rightarrow\pi^0\pi^0\pi^0$ 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.