Study of the decay $D^0rightarrow bar{K}^0pi^-e^+ u_e$

We report a study of the decay $D^0 rightarrow bar{K}^0pi^-e^+ u_{e}$ based on a sample of $2.93~mathrm{fb}^{-1}$ $e^+e^-$ annihilation data collected at the center-of-mass energy of 3.773~GeV with the BESIII detector at the BEPCII collider. The total branching fraction is determined to be $mathcal{B}(D^0rightarrow bar{K}^0pi^-e^+ u_{e})=(1.434pm0.029({rm stat.})pm0.032({rm syst.}))%$, which is the most precise to date. According to a detailed analysis of the involved dynamics, we find this decay is dominated with the $K^{*}(892)^-$ contribution and present an improved measurement of its branching fraction to be $mathcal{B}(D^0rightarrow K^{*}(892)^-e^+ u_e)=(2.033pm0.046({rm stat.})pm0.047({rm syst.}))%$. We further access their hadronic form-factor ratios for the first time as $r_{V}=V(0)/A_1(0)=1.46pm0.07({rm stat.})pm0.02({rm syst.})$ and $r_{2}=A_2(0)/A_1(0)=0.67pm0.06({rm stat.})pm0.01({rm syst.})$. In addition, we observe a significant $bar{K}^0pi^-$ $S$-wave component accounting for $(5.51pm0.97({rm stat.})pm0.62({rm syst.}))%$ of the total decay rate.