Observation of $D^{+}\to f_0(500)e^{+}\hat{I}{½}_e$ and Improved Measurements of $D\to \ddot{I}e^{+}\hat{I}{½}_e$

Abstract

Using a data sample corresponding to an integrated luminosity of 2.93~fb${}^{-1}$ recorded by the BESIII detector at a center-of-mass energy of $3.773$ GeV, we present an analysis of the decays ${\bar{D}}^0\to \ddot{I}{€}^{+}\ddot{I}{€}^0{e}^{-}\bar{\hat{I}}{½}_e$ and $D^{+}\to \ddot{I}{€}^{-}\ddot{I}{€}^{+}{e}^{+}\hat{I}{½}_e$. By performing a partial wave analysis, the $\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ $S$-wave contribution to $D^{+}\to \ddot{I}{€}^{-}\ddot{I}{€}^{+}{e}^{+}\hat{I}{½}_e$ is observed to be $(25.7\pm 1.6\pm 1.1)$% with a statistical significance greater than 10$\ddot{I}ƒ$, besides the dominant $P$-wave contribution. This is the first observation of the $S$-wave contribution. We measure the branching fractions $\mathcal{B}(D^0\to \ddot{I}{}^{-}{e}^{+}\hat{I}{½}_e)=(1.445\pm 0.058\pm 0.039)\times 10^{-3}$, $\mathcal{B}(D^{+}\to \ddot{I}{}^0{e}^{+}\hat{I}{½}_e)=(1.860\pm 0.070\pm 0.061)\times 10^{-3}$, and $\mathcal{B}(D^{+}\to f_0(500)e^{+}\hat{I}{½}_e,f_0(500)\to \ddot{I}{€}^{+}\ddot{I}{€}^{-})=(6.30\pm 0.43\pm 0.32)\times 10^{-4}$. An upper limit of $\mathcal{B}(D^{+}\to f_0(980)e^{+}\hat{I}{½}_e,f_0(980)\to \ddot{I}{€}^{+}\ddot{I}{€}^{-})<2.8\times 10^{-5}$ is set at the 90% confidence level. We also obtain the hadronic form factor ratios of $D\to \ddot{I}e^{+}\hat{I}{½}_e$ at $q^2=0$ assuming the single-pole dominance parameterization: $r_V=\frac{V(0)}{A_1(0)}=1.695\pm 0.083\pm 0.051$, $r_2=\frac{A_2(0)}{A_1(0)}=0.845\pm 0.056\pm 0.039$.