Analysis of the dynamics of the decay $D^{+}\to K_S^0{\pi }^0{e}^{+}{\nu }_e$

The branching fraction of $D^{+}\to K_S^0{\pi }^0{e}^{+}{\nu }_e$ is measured for the first time using $7.93{\mathrm{f}\mathrm{b}}^{-1}$ 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 $\mathcal{B}$($D^{+}\to K_S^0{\pi }^0{e}^{+}{\nu }_e$) = $(0.881\pm {0.017}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}}\pm {0.016}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}})$%. Based on an analysis of the $D^{+}\to K_S^0{\pi }^0{e}^{+}{\nu }_e$ decay dynamics, we observe the $S\text{-}\mathrm{w}\mathrm{a}\mathrm{v}\mathrm{e}$ and $P$-wave components with fractions of $f_{S\text{-}\mathrm{w}\mathrm{a}\mathrm{v}\mathrm{e}}$ = $(6.13\pm {0.27}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}}\pm {0.30}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}})\mathrm{\%}$ and $f_{{\bar{K}}^{\ast }(892{)}^0}$ = $(93.88\pm {0.27}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}}\pm {0.29}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}})$%, respectively. From these results, we obtain the branching fractions $\mathcal{B}$($D^{+}\to (K_S^0{\pi }^0{)}_{S\text{-}\mathrm{w}\mathrm{a}\mathrm{v}\mathrm{e}}{e}^{+}{\nu }_e$) = $(5.41\pm {0.35}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}}\pm {0.37}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}})\times {10}^{-4}$ and $\mathcal{B}$($D^{+}\to {\bar{K}}^{\ast }(892{)}^0{e}^{+}{\nu }_e$) = $(4.97\pm {0.11}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}}\pm {0.12}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}})$%. In addition, the hadronic form-factor ratios of $D^{+}\to {\bar{K}}^{\ast }(892{)}^0{e}^{+}{\nu }_e$ at $q^2=0$, assuming a single-pole dominance parameterization, are determined to be $r_V=\frac{V(0)}{A_1(0)}=1.43\pm {0.07}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}}\pm {0.03}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}}$ and $r_2=\frac{A_2(0)}{A_1(0)}=0.72\pm {0.06}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}}\pm {0.02}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}}$.