We report a study of the semileptonic decays $D^+\to K_S^0\pi^0\ell^+\nu_\ell$ ($\ell = e, \mu$) 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 $D^+\to K_S^0\pi^0\mu^+\nu_\mu$ decay is observed for the first time, with a branching fraction of $(0.896\pm0.017_{ \rm stat}\pm0.008_{ \rm syst})\%$, and the branching fraction of $D^+\to K_S^0\pi^0e^+\nu_e$ is determined with the improved precision as $(0.943\pm0.012_{ \rm stat}\pm0.010_{ \rm syst})\%$. 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 $(7.10 \pm 0.68_{ \rm stat} \pm 0.41_{ \rm syst})\%$ of the total decay rate of the $\mu^+$ channel and $(6.39 \pm 0.17_{ \rm stat} \pm 0.14_{ \rm syst})\%$ of the $e^+$ channel. Assuming a single-pole dominance parameterization, the hadronic form factor ratios are extracted to be $r_V=V(0)/A_1(0)=1.42 \pm\, 0.03_{ \rm stat} \pm\, 0.02_{ \rm syst}$ and $r_2=A_2(0)/A_1(0)=0.75 \pm\, 0.03_{ \rm stat} \pm\, 0.01_{ \rm syst}$. 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 $\mu-e$ lepton-flavor universality is observed in either the full range or the five chosen bins of momentum-transfer squared.
Categories: hep-ex