Measurement of the matrix elements for the decays ${\eta }^{\prime }\to \eta {\pi }^{+}{\pi }^{-}$ and ${\eta }^{\prime }\to \eta {\pi }^{0}{\pi }^{0}$

Based on a sample of $1.31×{10}^{9}\text{}\text{}J/\psi $ events collected with the BESIII detector, the matrix elements for the decays ${\eta }^{\prime }\to \eta {\pi }^{+}{\pi }^{-}$ and ${\eta }^{\prime }\to \eta {\pi }^{0}{\pi }^{0}$ are determined using 351,016 ${\eta }^{\prime }\to \left(\eta \to \gamma \gamma \right){\pi }^{+}{\pi }^{-}$ and 56,249 ${\eta }^{\prime }\to \left(\eta \to \gamma \gamma \right){\pi }^{0}{\pi }^{0}$ events with background levels less than 1%. Two commonly used representations are used to describe the Dalitz plot density. We find that an assumption of a linear amplitude does not describe the data well. A small deviation of the obtained matrix elements between ${\eta }^{\prime }\to \eta {\pi }^{+}{\pi }^{-}$ and ${\eta }^{\prime }\to \eta {\pi }^{0}{\pi }^{0}$ is probably caused by the mass difference between charged and neutral pions or radiative corrections. No cusp structure in ${\eta }^{\prime }\to \eta {\pi }^{0}{\pi }^{0}$ is observed.