Measurement of the matrix elements for the decays η′→ηπ+π− and η′→ηπ0π0

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Abstract

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. We find that an assumption of a linear amplitude does not describe the data well. A small deviation of the obtained matrix elements between ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ is probably caused by the mass difference between charged and neutral pions or radiative corrections. No cusp structure in ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ is observed.

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