Study of the light scalar $a_{0}(980)$ through the decay $D^{0} \to a_{0}(980)^-e^{+} ν_{e}$ with $a_{0}(980)^- \to ηπ^-$

Using 7.93 ${\rm fb^{-1}}$ of $e^+e^-$ collision data collected at a center-of-mass energy of 3.773 ${\rm GeV}$ with the BESIII detector, we present an analysis of the decay $D^{0} \to ηπ^- e^+ ν_{e}$. The branching fraction of the decay $D^{0} \to a_{0}(980)^{-} e^+ ν_{e}$ with $a_{0}(980)^{-} \to ηπ^{-}$ is measured to be $(0.86\pm0.17_{\text{stat}}\pm0.05_{\text{syst}})\times 10^{-4}$. 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 $|V_{cd}|$ is determined for the first time with the result $f^{ a_0}_+(0)|V_{cd}|=0.126\pm0.013_{\rm stat}\pm0.003_{\rm syst}$.