Study of the light scalar $a_0(980)$ through the decay $D^0\to a_0(980{)}^{-}{e}^{+}{\nu }_e$ with $a_0(980{)}^{-}\to \eta {\pi }^{-}$

Using 7.93 $\mathrm{f}{\mathrm{b}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected at a center-of-mass energy of 3.773 $\mathrm{G}\mathrm{e}\mathrm{V}$ with the BESIII detector, we present an analysis of the decay $D^0\to \eta {\pi }^{-}{e}^{+}{\nu }_e$. The branching fraction of the decay $D^0\to a_0(980{)}^{-}{e}^{+}{\nu }_e$ with $a_0(980{)}^{-}\to \eta {\pi }^{-}$ is measured to be $(0.86\pm {0.17}_{\text{stat}}\pm {0.05}_{\text{syst}})\times {10}^{-4}$. The decay dynamics of this process is studied with a single-pole parameterization of the hadronic form factor and the Flatté formula describing the $a_0(980)$ line shape in the differential decay rate. The product of the form factor $f_{+}^{a_0}(0)$ and the Cabibbo-Kobayashi-Maskawa matrix element $\mathrm{\mid }{V}_{cd}\mathrm{\mid }$ is determined for the first time with the result $f_{+}^{a_0}(0)\mathrm{\mid }{V}_{cd}\mathrm{\mid }=0.126\pm {0.013}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.003}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}$.