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\text{}\text{}{\mathrm{fb}}^{-1}$ of $ {e}^{+}{e}^{-}$ collision data collected at a center-of-mass energy of 3.773 GeV 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 0.1{7}_{\mathrm{stat}}\pm 0.0{5}_{\mathrm{syst}})\times {10}^{-4}$. The decay dynamics of this process is studied with a single-pole parametrization 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 $ |{V}_{cd}|$ is determined for the first time with the result $ {f}_{+}^{{a}_{0}}(0)|{V}_{cd}|=0.126\pm 0.01{3}_{\mathrm{stat}}\pm 0.00{3}_{\mathrm{syst}}$.