Based on a sample of $1.31\times {10}^{9}J/\psi$ 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 ${\eta }^{\prime }\to (\eta \to \gamma \gamma ){\pi }^{+}{\pi }^{-}$ and 56,249 ${\eta }^{\prime }\to (\eta \to \gamma \gamma ){\pi }^0{\pi }^0$ 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.

• Received 14 September 2017

DOI:https://doi.org/10.1103/PhysRevD.97.012003

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Published by the American Physical Society