Measurement of the matrix elements for the decays eta' -> eta pi(+) pi(-) and eta' -> eta pi(0)pi(0)

Based on a sample of 1.31 x 10(9) J/psi events collected with the BESIII detector, the matrix elements for the decays eta' -> eta pi(+) pi(-) and eta' -> eta pi(0)pi(0) are determined using 351,016 eta' -> (eta -> gamma gamma)pi' pi(-) and 56,249 eta' -> (eta -> 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' -> eta pi(+) pi(-) and eta' -> 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' -> eta pi(0)pi(0) is observed.