Using $2.92{\mathrm{fb}}^{-1}$ of electron-positron annihilation data collected at $\sqrt{s}=3.773\mathrm{GeV}$ with the BESIII detector, we obtain the first measurements of the absolute branching fraction $\mathcal{B}(D^{+}\to K_L^0{e}^{+}{\nu }_e)=(4.481\pm 0.027(\text{stat})\pm 0.103(\text{sys}))\%$ and the $CP$ asymmetry $A_{CP}^{D^{+}\to K_L^0{e}^{+}{\nu }_e}=(-0.59\pm 0.60(\text{stat})\pm 1.48(\text{sys}))\%$. From the $D^{+}\to K_L^0{e}^{+}{\nu }_e$ differential decay rate distribution, the product of the hadronic form factor and the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element, $f_{+}^K(0)|V_{cs}|$, is determined to be $0.728\pm 0.006(\text{stat})\pm 0.011(\text{sys})$. Using $|V_{cs}|$ from the SM constrained fit with the measured $f_{+}^K(0)|V_{cs}|$, $f_{+}^K(0)=0.748\pm 0.007(\text{stat})\pm 0.012(\text{sys})$ is obtained, and utilizing the unquenched Lattice QCD (LQCD) calculation for $f_{+}^K(0)$, $|V_{cs}|=0.975\pm 0.008(\text{stat})\pm 0.015(\text{sys})\pm 0.025(\mathrm{LQCD})$.

• Received 2 October 2015

DOI:https://doi.org/10.1103/PhysRevD.92.112008