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

Based on a sample of $1.31times10^9$ $J/psi$ events collected with the BESIII detector, the matrix elements for the decays $eta^{prime}toetapi^{+}pi^{-}$ and $eta^{prime}toeta pi^{0}pi^{0}$ are determined using 351,016 $eta^{prime}to(etatogammagamma)pi^+pi^-$ and 56,249 $eta^{prime}to(etatogammagamma)pi^0pi^0$ 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 $eta^{prime}toetapi^{+}pi^{-}$ and $eta^{prime}toeta pi^{0}pi^{0}$ is probably caused by the mass difference between charged and neutral pions or radiative corrections. No cusp structure in $eta^{prime}toeta pi^{0}pi^{0}$ is observed.