Observation of $D^{+}\to f_0(500)e^{+}{\nu }_e$ and Improved Measurements of $D\to \rho e^{+}{\nu }_e$

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 ${\bar{D}}^0\to {\pi }^{+}{\pi }^0{e}^{-}{\bar{\nu }}_e$ and $D^{+}\to {\pi }^{-}{\pi }^{+}{e}^{+}{\nu }_e$. By performing a partial wave analysis, the ${\pi }^{+}{\pi }^{-}$ $S$-wave contribution to $D^{+}\to {\pi }^{-}{\pi }^{+}{e}^{+}{\nu }_e$ is observed to be $(25.7\pm 1.6\pm 1.1)$% with a statistical significance greater than 10$\sigma$, besides the dominant $P$-wave contribution. This is the first observation of the $S$-wave contribution. We measure the branching fractions $\mathcal{B}(D^0\to {\rho }^{-}{e}^{+}{\nu }_e)=(1.445\pm 0.058\pm 0.039)\times 10^{-3}$, $\mathcal{B}(D^{+}\to {\rho }^0{e}^{+}{\nu }_e)=(1.860\pm 0.070\pm 0.061)\times 10^{-3}$, and $\mathcal{B}(D^{+}\to f_0(500)e^{+}{\nu }_e,f_0(500)\to {\pi }^{+}{\pi }^{-})=(6.30\pm 0.43\pm 0.32)\times 10^{-4}$. An upper limit of $\mathcal{B}(D^{+}\to f_0(980)e^{+}{\nu }_e,f_0(980)\to {\pi }^{+}{\pi }^{-})<2.8\times 10^{-5}$ is set at the 90% confidence level. We also obtain the hadronic form factor ratios of $D\to \rho e^{+}{\nu }_e$ at $q^2=0$ assuming the single-pole dominance parameterization: $r_V=\frac{V(0)}{A_1(0)}=1.695\pm 0.083\pm 0.051$, $r_2=\frac{A_2(0)}{A_1(0)}=0.845\pm 0.056\pm 0.039$.