Amplitude analysis of $D_s^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^0\hat{I}\cdot$ and first observation of the pure $W$-annihilation decays $D_s^{+}\to a_0(980{)}^{+}\ddot{I}{€}^0$ and $D_s^{+}\to a_0(980{)}^0\ddot{I}{€}^{+}$

Abstract

We present the first amplitude analysis of the decay $D_s^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^0\hat{I}\cdot$. We use an $e^{+}{e}^{-}$ collision data sample corresponding to an integrated luminosity of 3.19~${\mbox{\,fb}^{-1}}$ collected with the BESIII detector at a center-of-mass energy of $4.178$ GeV. We observe for the first time the pure $W$-annihilation decays $D_s^{+}\to a_0(980{)}^{+}\ddot{I}{€}^0$ and $D_s^{+}\to a_0(980{)}^0\ddot{I}{€}^{+}$. We measure the absolute branching fractions $\mathcal{B}(D_s^{+}\to a_0(980{)}^{+(0)}\ddot{I}{€}^{0^{(}+)},a_0(980{)}^{+(0)}\to \ddot{I}{€}^{+(0)}\hat{I}\cdot )=(1.46\pm 0.15_{stat.}\pm 0.23_{sys.})$\%, which is larger than the branching fractions of other measured pure $W$-annihilation decays by at least one order of magnitude. In addition, we measure the branching fraction of $D_s^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^0\hat{I}\cdot$ with significantly improved precision.

7 pages, 3 figures