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

Abstract

Using 7.93 $\mathrm{f}{\mathrm{b}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected at a center-of-mass energy of 3.773 $\mathrm{GeV}$ 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 $(0.86\pm 0.17_{\text{stat}}\pm 0.05_{\text{syst}})\times 10^{-4}$. 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 $|V_{cd}|$ is determined for the first time with the result $f_{+}^{a_0}(0)|V_{cd}|=0.126\pm 0.013_{\mathrm{stat}}\pm 0.003_{\mathrm{syst}}$.

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