Measurement of the matrix elements for the decays $η^{\prime}\rightarrowηπ^+π^-$ and $η^{\prime}\rightarrowηπ^0π^0$

Abstract

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

11 pages, 7 figures