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Measurement of the matrix elements for the decays <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:mi>η</mml:mi><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow></…
Based on a sample of $1.31\ifmmode\times\else\texttimes\fi{}{10}^{9}\text{ }\text{ }J/\ensuremath{\psi}$ events collected with the BESIII detector, the matrix elements for the decays ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ are determined using 351,016 ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}(\ensuremath{\eta}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}){\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and 56,249 ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}(\ensuremath{\eta}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}){\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ events with background levels less than 1%. Two commonly used representations are used to describe the Dalitz plot density. …