Analysis of the dynamics of the decay $D^{+}\to K_S^0\ddot{I}{€}^0{e}^{+}\hat{I}{½}_e$

Abstract

The branching fraction of $D^{+}\to K_S^0\ddot{I}{€}^0{e}^{+}\hat{I}{½}_e$ is measured for the first time using $7.93{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ annihilation data collected at the center-of-mass energy $\sqrt{s}=3.773$~GeV with the BESIII detector operating at the BEPCII collider, and is determined to be $\mathcal{B}$($D^{+}\to K_S^0\ddot{I}{€}^0{e}^{+}\hat{I}{½}_e$) = $(0.881\pm 0.017_{stat.}\pm 0.016_{syst.})$\%. Based on an analysis of the $D^{+}\to K_S^0\ddot{I}{€}^0{e}^{+}\hat{I}{½}_e$ decay dynamics, we observe the $S\text{-}\mathrm{wave}$ and $P$-wave components with fractions of $f_{S\text{-}\mathrm{wave}}$ = $(6.13\pm 0.27_{stat.}\pm 0.30_{syst.})\%$ and $f_{{\bar{K}}^{\ast }(892{)}^0}$ = $(93.88\pm 0.27_{stat.}\pm 0.29_{syst.})$\%, respectively. From these results, we obtain the branching fractions $\mathcal{B}$($D^{+}\to (K_S^0\ddot{I}{€}^0{)}_{S\text{-}\mathrm{wave}}{e}^{+}\hat{I}{½}_e$) = $(5.41\pm 0.35_{stat.}\pm 0.37_{syst.})\times 10^{-4}$ and $\mathcal{B}$($D^{+}\to {\bar{K}}^{\ast }(892{)}^0{e}^{+}\hat{I}{½}_e$) = $(4.97\pm 0.11_{stat.}\pm 0.12_{syst.})$\%. In addition, the hadronic form-factor ratios of $D^{+}\to {\bar{K}}^{\ast }(892{)}^0{e}^{+}\hat{I}{½}_e$ at $q^2=0$, assuming a single-pole dominance parameterization, are determined to be $r_V=\frac{V(0)}{A_1(0)}=1.43\pm 0.07_{stat.}\pm 0.03_{syst.}$ and $r_2=\frac{A_2(0)}{A_1(0)}=0.72\pm 0.06_{stat.}\pm 0.02_{syst.}$.