Study of the decay $D^0\to {\bar{K}}^0{\pi }^{-}{e}^{+}{\nu }_e$

We report a study of the decay $D^0\to {\bar{K}}^0{\pi }^{-}{e}^{+}{\nu }_e$ based on a sample of $2.93{\mathrm{f}\mathrm{b}}^{-1}$ $e^{+}{e}^{-}$ 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 $$\mathcal{B}$(D^0\rightarrow \bar{K}^0\pi^-e^+\nu_{e})=(1.434\pm0.029({\rm stat.})\pm0.032({\rm syst.}))%$, which is the most precise to date. According to a detailed analysis of the involved dynamics, we find this decay is dominated with the $K^{\ast }(892{)}^{-}$ contribution and present an improved measurement of its branching fraction to be $$\mathcal{B}$(D^0\rightarrow K^{*}(892)^-e^+\nu_e)=(2.033\pm0.046({\rm stat.})\pm0.047({\rm syst.}))%$. We further access their hadronic form-factor ratios for the first time as $r_V=V(0)\mathrm{/}{A}_1(0)=1.46\pm 0.07(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.})\pm 0.02(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.})$ and $r_2=A_2(0)\mathrm{/}{A}_1(0)=0.67\pm 0.06(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.})\pm 0.01(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.})$. In addition, we observe a significant ${\bar{K}}^0{\pi }^{-}$ $S$-wave component accounting for $(5.51\pm 0.97(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.})\pm 0.62(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}))\mathrm{\%}$ of the total decay rate.