Analysis of $D^{+}\to {\bar{K}}^0{e}^{+}\hat{I}{½}_e$ and $D^{+}\to \ddot{I}{€}^0{e}^{+}\hat{I}{½}_e$ Semileptonic Decays

Abstract

Using 2.93~fb${}^{-1}$ of data taken at 3.773 GeV with the BESIII detector operated at the BEPCII collider, we study the semileptonic decays $D^{+}\to {\bar{K}}^0{e}^{+}\hat{I}{½}_e$ and $D^{+}\to \ddot{I}{€}^0{e}^{+}\hat{I}{½}_e$. We measure the absolute decay branching fractions $\mathcal{B}(D^{+}\to {\bar{K}}^0{e}^{+}\hat{I}{½}_e)=(8.60\pm 0.06\pm 0.15)\times 10^{-2}$ and $\mathcal{B}(D^{+}\to \ddot{I}{€}^0{e}^{+}\hat{I}{½}_e)=(3.63\pm 0.08\pm 0.05)\times 10^{-3}$, where the first uncertainties are statistical and the second systematic. We also measure the differential decay rates and study the form factors of these two decays. With the values of $|V_{cs}|$ and $|V_{cd}|$ from Particle Data Group fits assuming CKM unitarity, we obtain the values of the form factors at $q^2=0$, $f_{+}^K(0)=0.725\pm 0.004\pm 0.012$ and $f^{\ddot{I}}{€}_{+}(0)=0.622\pm 0.012\pm 0.003$. Taking input from recent lattice QCD calculations of these form factors, we determine values of the CKM matrix elements $|V_{cs}|=0.944\pm 0.005\pm 0.015\pm 0.024$ and $|V_{cd}|=0.210\pm 0.004\pm 0.001\pm 0.009$, where the third uncertainties are theoretical.