Study of decay dynamics and $CP$ asymmetry in $D^{+}\to K_L^0{e}^{+}{\nu }_e$ decay

Using 2.92~fb${}^{-1}$ of electron-positron annihilation data collected at $\sqrt{s}=3.773$~GeV with the BESIII detector, we obtain the first measurements of the absolute branching fraction $$\mathcal{B}$(D^+ \to K^0_L e^+ \nu_e) = (4.481 \pm 0.027($\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}$) \pm 0.103($\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{.}$))%$andthe$CP$asymmetry$A_{CP}^{D^+ \to K^0_L e^+ \nu_e} = (-0.59 \pm 0.60($\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}$) \pm 1.48($\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{.}$))%$\mathrm{.}Fromthe$D^+ \to K^0_L e^+ \nu_e$ differential decay rate distribution, the product of the hadronic form factor and the magnitude of the CKM matrix element, $f_{+}^K(0)\mathrm{\mid }{V}_{cs}\mathrm{\mid }$, is determined to be $0.728\pm 0.006(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.})\pm 0.011(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{.})$. Using $\mathrm{\mid }{V}_{cs}\mathrm{\mid }$ from the SM constrained fit with the measured $f_{+}^K(0)\mathrm{\mid }{V}_{cs}\mathrm{\mid }$, $f_{+}^{K}(0) = 0.748 \pm 0.007($\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}$) \pm 0.012($\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{.}$)$ is obtained, and utilizing the unquenched LQCD calculation for $f_{+}^K(0)$, $|V_{cs}| = 0.975 \pm 0.008($\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}$) \pm 0.015($\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{.}$) \pm 0.025($\mathrm{L}\mathrm{Q}\mathrm{C}\mathrm{D}$)$.