Study of the Decay $D_s^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}\cdot$ and Observation of the W-annihilation Decay $D_s^{+}\to a_0(980{)}^{+}\ddot{I}{}^0$

Abstract

The decay $D_s^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}\cdot$ is observed for the first time, using $e^{+}{e}^{-}$ collision data corresponding to an integrated luminosity of 6.32 fb${}^{-1}$, collected by the BESIII detector at center-of-mass energies between 4.178 and 4.226 GeV. The absolute branching fraction for this decay is measured to be $\mathcal{B}(D_s^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}\cdot )=(3.12\pm 0.13_{stat.}\pm 0.09_{syst.})$%. The first amplitude analysis of this decay reveals the sub-structures in $D_s^{+}\to \ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}\cdot$ and determines the relative fractions and the phases among these sub-structures. The dominant intermediate process is $D_s^{+}\to a_1(1260{)}^{+}\hat{I}\cdot ,a_1(1260{)}^{+}\to \ddot{I}(770{)}^0\ddot{I}{€}^{+}$ with a branching fraction of $(1.73\pm 0.14_{stat.}\pm 0.08_{syst.})$%. We also observe the W-annihilation process $D_s^{+}\to a_0(980{)}^{+}\ddot{I}(770{)}^0$, $a_0(980{)}^{+}\to \ddot{I}{€}^{+}\hat{I}\cdot$ with a branching fraction of $(0.21\pm 0.08_{stat.}\pm 0.05_{syst.})$%, which is larger than the branching fractions of other measured pure W-annihilation decays by one order of magnitude.

8 pages, 3 figures