Determination of the absolute branching fractions of $D^0\to K^{-}{e}^{+}{\nu }_e$ and $D^{+}\to {\bar{K}}^0{e}^{+}{\nu }_e$

Using 2.93 fb${}^{-1}$ of $e^{+}{e}^{-}$ collision data collected with the BESIII detector at a center-of-mass energy of 3.773 GeV, we measure the absolute branching fractions of the decays $D^0\to K^{-}{e}^{+}{\nu }_e$ and $D^+\to \bar K^0 e^+\nu_e$tobe$(3.567\pm0.031_{\rm stat}\pm 0.025_{\rm syst})%$and$(8.68\pm0.14_{\rm stat}\pm 0.16_{\rm syst})%$, respectively. Starting with the process $e^{+}{e}^{-}\to D\bar{D}$, a new reconstruction method is employed to select events that contain candidates for both $D\to \bar{K}{e}^{+}{\nu }_e$ and $\bar D\to Ke^-\bar \nu_e$ decays. The branching fractions reported in this work are consistent within uncertainties with previous BESIII measurements that selected events containing $D\to \bar{K}{e}^{+}{\nu }_e$ and hadronic $\bar{D}$ decays. Combining our results with the lifetimes of the $D^0$ and $D^{+}$ mesons and the previous BESIII measurements leads to a ratio of the two decay partial widths of $\frac{\bar \Gamma_{D^0\to K^{-}e^+\nu_{e}}}{\bar \Gamma_{D^{+}\to \bar K^{0}e^+\nu_{e}}}=1.039\pm0.021$\mathrm{.}Thisratiosupportsisospinsymmetryinthe$D^0\to K^-e^+\nu_e$and$D^+\to \bar K^0 e^+\nu_e$decayswithin$1.9\sigma$.