Study of decay dynamics and $CP$ asymmetry in $D^{+}\to K_L^0{e}^{+}\hat{I}{½}_e$ decay

Abstract

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 $\mathcal{B}(D^{+}\to K_L^0{e}^{+}\hat{I}{½}_e)=(4.481\pm 0.027(stat.)\pm 0.103(sys.))\%$ and the $CP$ asymmetry $A_{CP}^{D^{+}\to K_L^0{e}^{+}\hat{I}{½}_e}=(-0.59\pm 0.60(stat.)\pm 1.48(sys.))\%$. From the $D^{+}\to K_L^0{e}^{+}\hat{I}{½}_e$ differential decay rate distribution, the product of the hadronic form factor and the magnitude of the CKM matrix element, $f_{+}^K(0)|V_{cs}|$, is determined to be $0.728\pm 0.006(stat.)\pm 0.011(sys.)$. Using $|V_{cs}|$ from the SM constrained fit with the measured $f_{+}^K(0)|V_{cs}|$, $f_{+}^K(0)=0.748\pm 0.007(stat.)\pm 0.012(sys.)$ is obtained, and utilizing the unquenched LQCD calculation for $f_{+}^K(0)$, $|V_{cs}|=0.975\pm 0.008(stat.)\pm 0.015(sys.)\pm 0.025(\mathrm{LQCD})$.

13 pages, 8 figures