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Observation of $D \to a_{0}(980)\pi$ in the decays $D^{0} \rightarrow \pi^{+}\pi^{-}\eta$ and $D^{+} \rightarrow \pi^{+}\pi^{0}\eta$

Observation of $D \to a_{0}(980)\pi$ in the decays $D^{0} \rightarrow \pi^{+}\pi^{-}\eta$ and $D^{+} \rightarrow \pi^{+}\pi^{0}\eta$

We report the first amplitude analysis of the decays $D^{0} \to \pi^{+} \pi^{-} \eta$ and $D^{+} \rightarrow \pi^{+}\pi^{0}\eta$ using a data sample taken with the BESIII detector at the center-of-mass energy of 3.773 GeV, corresponding to an integrated luminosity of 7.9 ${\rm fb}^{-1}$. The contribution from the process $D^{0(+)} \to …