Observation of $D^{+}\to K_S^0{a}_0(980{)}^{+}$ in the amplitude analysis of $D^{+}\to K_S^0\ddot{I}{€}^{+}\hat{I}\cdot$

Abstract

We perform for the first time an amplitude analysis of the decay $D^{+}\to K_S^0\ddot{I}{€}^{+}\hat{I}\cdot$ and report the observation of the decay $D^{+}\to K_S^0{a}_0(980{)}^{+}$ using 2.93 fb${}^{-1}$ of $e^{+}{e}^{-}$ collision data taken at a center-of-mass energy of 3.773 GeV with the BESIII detector. As the only W-annihilation free decay among $D$ to $a_0(980)$-pseudoscalar, $D^{+}\to K_S^0{a}_0(980{)}^{+}$ is the ideal decay to extract the contributions of the external and internal $W$-emission amplitudes involving $a_0(980)$ and study the final-state interactions. The absolute branching fraction of $D^{+}\to K_S^0\ddot{I}{€}^{+}\hat{I}\cdot$ is measured to be $(1.27\pm 0.04_{stat.}\pm 0.03_{syst.})\%$. The product branching fractions of $D^{+}\to K_S^0{a}_0(980{)}^{+}$ with $a_0(980{)}^{+}\to \ddot{I}{€}^{+}\hat{I}\cdot$ and $D^{+}\to \ddot{I}{€}^{+}{K}_0^{\ast }(1430{)}^0$ with $K_0^{\ast }(1430{)}^0\to K_S^0\hat{I}\cdot$ are measured to be $(1.33\pm 0.05_{stat.}\pm 0.04_{syst.})\%$ and $(0.14\pm 0.03_{stat.}\pm 0.01_{syst.})\%$, respectively.