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

We report an improved study of the semileptonic decay $D^0\to {\bar{K}}^0{\pi }^{-}{e}^{+}{\nu }_e$ based on a sample of $7.9{\mathrm{f}\mathrm{b}}^{-1}$ of $e^{+}{e}^{-}$ annihilation data collected at a center-of-mass energy of 3.773~GeV with the BESIII detector at the BEPCII collider. The branching fraction of this decay is measured to be $\mathcal{B}(D^0\to {\bar{K}}^0{\pi }^{-}{e}^{+}{\nu }_e)=(1.444\pm {0.022}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.024}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}})\mathrm{\%}$, which is the most precise to date, where the first uncertainty is statistical and the second is systematic. Based on investigation of the decay dynamics, we find that the decay is dominated by the $K^{\ast }(892{)}^{-}$ component and present an improved measurement of its branching fraction to be $\mathcal{B}(D^0\to K^{\ast }(892{)}^{-}{e}^{+}{\nu }_e)=(2.039\pm {0.032}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.034}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}})\mathrm{\%}$. We also determine the ratios of the hadronic form factors for the $K^{\ast }(892{)}^{-}{e}^{+}{\nu }_e$ decay to be $r_V=V(0)\mathrm{/}{A}_1(0)=1.48\pm {0.05}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.02}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}$ and $r_2=A_2(0)\mathrm{/}{A}_1(0)=0.70\pm {0.04}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.02}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}$, where $V(0)$ is the vector form factor and $A_{1,2}(0)$ are the axial form factors. In addition, the ${\bar{K}}^0{\pi }^{-}$ $\mathcal{S}$-wave component is found to account for $(5.87\pm {0.32}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.16}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}})\mathrm{\%}$ of the total decay rate, corresponding to a branching fraction of $\mathcal{B}[D^0\to ({\bar{K}}^0{\pi }^{-}{)}_{S-\mathrm{w}\mathrm{a}\mathrm{v}\mathrm{e}}{e}^{+}{\nu }_e]=(0.085\pm {0.005}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.003}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}})\mathrm{\%}$.