Observation of $D\to a_0(980)\ddot{I}€$ in the decays $D^0\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}\cdot$ and $D^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^0\hat{I}\cdot$

Abstract

We report the first amplitude analysis of the decays $D^0\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}\cdot$ and $D^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^0\hat{I}\cdot$ 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 ${\mathrm{fb}}^{-1}$. The contribution from the process $D^{0(+)}\to a_0(980{)}^{+}\ddot{I}{€}^{-(0)}$ is significantly larger than the $D^{0(+)}\to a_0(980{)}^{-(0)}\ddot{I}{€}^{+}$ contribution. The ratios $\mathcal{B}(D^0\to a_0(980{)}^{+}\ddot{I}{€}^{-})/\mathcal{B}(D^0\to a_0(980{)}^{-}\ddot{I}{€}^{+})$ and $\mathcal{B}(D^{+}\to a_0(980{)}^{+}\ddot{I}{€}^0)/\mathcal{B}(D^{+}\to a_0(980{)}^0\ddot{I}{€}^{+})$ are measured to be $7.5_{-0.8stat.}^{+2.5}\pm 1.7_{syst.}$ and $2.6\pm 0.6_{stat.}\pm 0.3_{syst.}$, respectively. The measured $D^0$ ratio disagrees with the theoretical predictions by orders of magnitudes, thus implying a substantial contribution from final-state interactions.