Observation of an Altered $a_0(980)$ Line-shape in $D^{+}\to \ddot{I}{€}^{+}\hat{I}\cdot \hat{I}\cdot$ due to the Triangle Loop Rescattering Effect

Abstract

Using 20.3~${\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collision data taken with the BESIII detector at the center-of-mass energy 3.773~GeV, we report the first amplitude analysis of the hadronic decay $D^{+}\to \ddot{I}{€}^{+}\hat{I}\cdot \hat{I}\cdot$. The intermediate process $D^{+}\to a_0(980{)}^{+}\hat{I}\cdot ,a_0(980{)}^{+}\to \ddot{I}{€}^{+}\hat{I}\cdot$ is observed and is found to be the only component and its branching fraction is measured to be $(3.67\pm 0.12_{stat.}\pm 0.06_{syst.})\times 10^{-3}$. Unlike the $a_0(980)$ line-shape observed in the decays of charmed mesons to $a_0(980)\ddot{I}€$ and in the decay $D^0\to a_0(980{)}^{-}{e}^{+}\hat{I}{½}_e$, where the low-mass side of the $a_0(980)$ is wider than the high-mass side, the $a_0(980)$ line-shape in $D^{+}\to a_0(980{)}^{+}\hat{I}\cdot$ is found to be significantly altered, with the high-mass side being wider than the low-mass side. We establish that the $a_0(980)$ line-shape arises from the triangle loop rescattering of $D^{+}\to {\bar{K}}_0^{\ast }(1430{)}^0{K}^{+}\to a_0(980{)}^{+}\hat{I}\cdot$ and $D^{+}\to K_0^{\ast }(1430{)}^{+}{\bar{K}}^0\to a_0(980{)}^{+}\hat{I}\cdot$ with a significance of 5.8$\ddot{I}ƒ$. This is the first experimental confirmation of the triangle loop rescattering effect.