Determination of the absolute branching fractions of $D^0to K^-e^+ u_e$ and $D^+to bar K^0 e^+ u_e$

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 $D^0to K^-e^+ u_e$ and $D^+to bar K^0 e^+ u_e$ to be $(3.567pm0.031_{rm stat}pm 0.025_{rm syst})%$ and $(8.68pm0.14_{rm stat}pm 0.16_{rm syst})%$, respectively. Starting with the process $e^+e^-to Dbar{D}$, a new reconstruction method is employed to select events that contain candidates for both $Dto bar Ke^+ u_e$ and $bar Dto Ke^-bar u_e$ decays. The branching fractions reported in this work are consistent within uncertainties with previous BESIII measurements that selected events containing $Dto bar Ke^+ u_e$ 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 $frac{bar Gamma_{D^0to K^{-}e^+ u_{e}}}{bar Gamma_{D^{+}to bar K^{0}e^+ u_{e}}}=1.039pm0.021$. This ratio supports isospin symmetry in the $D^0to K^-e^+ u_e$ and $D^+to bar K^0 e^+ u_e$ decays within $1.9sigma$.