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 fb −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 $B\left({D}^{+}\to {K}_{S}^{0}{\pi }^{0}{e}^{+}{\nu }_{e}\right)=\left(0.881±{0.017}_{\text{stat}.}±{0.016}_{\text{syst}.}\right)%$ . Based on an analysis of the ${D}^{+}\to {K}_{S}^{0}{\pi }^{0}{e}^{+}{\nu }_{e}$ decay dynamics, we observe the S-wave and P-wave components with fractions of f S-wave = (6.13 ± 0.27stat. ± 0.30syst. )% and ${f}_{{\overline{K}}^{\ast }{\left(892\right)}^{0}}=\left(93.88±{0.27}_{\text{stat}.}±{0.29}_{\text{syst}.}\right)%$ , respectively. From these results, we obtain the branching fractions $B\left({D}^{+}\to {\left({K}_{S}^{0}{\pi }^{0}\right)}_{S-\text{wave}}{e}^{+}{\nu }_{e}\right)=\left(5.41±{0.35}_{\text{stat}.}±{0.37}_{\text{syst}.}\right)×{10}^{-4}$ and $B\left({D}^{+}\to {\overline{K}}^{\ast }{\left(892\right)}^{0}{e}^{+}{\nu }_{e}\right)=\left(4.97±{0.11}_{\text{stat}.}±{0.12}_{\text{syst}.}\right)%$ . In addition, the hadronic form-factor ratios of ${D}^{+}\to {\overline{K}}^{\ast }{\left(892\right)}^{0}{e}^{+}{\nu }_{e}$ at q 2 = 0, assuming a single-pole dominance parameterization, are determined to be ${r}_{V}=\frac{V\left(0\right)}{{A}_{1}\left(0\right)}=1.43±{0.07}_{\text{stat}.}±{0.03}_{\text{syst}.}$ and ${r}_{2}=\frac{{A}_{2}\left(0\right)}{{A}_{1}\left(0\right)}=0.72±{0.06}_{\text{stat}.}±{0.02}_{\text{syst}.}$ .