Measurement of the matrix elements for the decaysη→π+π−π0andη/η′→π0π0π0

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Abstract

Based on a sample of $1.31\ifmmode\times\else\texttimes\fi{}1{0}^{9}$ $J/\ensuremath{\psi}$ events collected with the BESIII detector at the BEPCII collider, Dalitz plot analyses of selected 79,625 $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$ events, 33,908 $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ events, and 1,888 ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ events are performed. The measured matrix elements of $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$ are in reasonable agreement with previous measurements. The Dalitz plot slope parameters of $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ are determined to be $\ensuremath{-}0.055\ifmmode\pm\else\textpm\fi{}0.014\ifmmode\pm\else\textpm\fi{}0.004$ and $\ensuremath{-}0.640\ifmmode\pm\else\textpm\fi{}0.046\ifmmode\pm\else\textpm\fi{}0.047$, respectively, where the first uncertainties are statistical and the second systematic. Both values are consistent with previous measurements, while the precision of the latter one is improved by a factor of 3. Final state interactions are found to have an important role in those decays.

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