Observation of $D^{+}\to K_S^0\ddot{I}{€}^0\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$, Test of Lepton Flavor Universality and First Angular Analysis of $D^{+}\to {\bar{K}}^{\ast }(892{)}^0{\ell }^{+}\hat{I}{½}_{\ell }$

Abstract

We report a study of the semileptonic decays $D^{+}\to K_S^0\ddot{I}{€}^0{\ell }^{+}\hat{I}{½}_{\ell }$ ($\ell =e,\hat{I}¼$) based on $20.3{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected at the center-of-mass energy of 3.773 GeV with the BESIII detector. The $D^{+}\to K_S^0\ddot{I}{€}^0\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ decay is observed for the first time, with a branching fraction of $(0.896\pm 0.017_{\mathrm{stat}}\pm 0.008_{\mathrm{syst}})\%$, and the branching fraction of $D^{+}\to K_S^0\ddot{I}{€}^0{e}^{+}\hat{I}{½}_e$ is determined with the improved precision as $(0.943\pm 0.012_{\mathrm{stat}}\pm 0.010_{\mathrm{syst}})\%$. From the analysis of the dynamics, we observe that the dominant ${\bar{K}}^{\ast }(892{)}^0$ component is accompanied by an $S$-wave contribution, which accounts for $(7.10\pm 0.68_{\mathrm{stat}}\pm 0.41_{\mathrm{syst}})\%$ of the total decay rate of the $\hat{I}{¼}^{+}$ channel and $(6.39\pm 0.17_{\mathrm{stat}}\pm 0.14_{\mathrm{syst}})\%$ of the $e^{+}$ channel. Assuming a single-pole dominance parameterization, the hadronic form factor ratios are extracted to be $r_V=V(0)/A_1(0)=1.42\pm 0.03_{\mathrm{stat}}\pm 0.02_{\mathrm{syst}}$ and $r_2=A_2(0)/A_1(0)=0.75\pm 0.03_{\mathrm{stat}}\pm 0.01_{\mathrm{syst}}$. Based on the first comprehensive angular and the decay-rate $CP$ asymmetry analysis, the full set of averaged angular and $CP$ asymmetry observables are measured as a function of the momentum-transfer squared; they are consistent with expectations from the Standard Model. No evidence for violation of $\hat{I}¼-e$ lepton-flavor universality is observed in either the full range or the five chosen bins of momentum-transfer squared.