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Using $e^+e^-$ collision data corresponding to an integrated luminosity of7.33 ${\rm fb^{-1}}$ recorded by the BESIII detector at center-of-mass energiesbetween 4.128 and 4.226 ${\rm GeV}$, we present an analysis of the decay$D_{s}^{+} \to f_{0}(980)e^{+}\nu_{e}$ with $f_{0}(980) \to \pi^{+}\pi^{-}$,where the $D_s^+$ is produced via the process $e^+e^- \toD_{s}^{*\pm}D_{s}^{\mp}$. We observe the $f_{0}(980)$ in the $\pi^+\pi^-$system and the branching fraction of the decay $D_{s}^{+} \tof_{0}(980)e^{+}\nu_{e}$ with $f_0(980)\to\pi^+\pi^-$ is measured to be $(1.72\pm 0.13_{\rm stat} \pm 0.10_{\rm syst}) \times10^{-3}$, where theuncertainties are statistical and systematic, respectively. The dynamics of the$D_{s}^{+} \to f_{0}(980)e^{+}\nu_{e}$ decay are studied with the simple poleparameterization of the hadronic form factor and the Flatt\'e formuladescribing the $f_0(980)$ in the differential decay rate, and the product ofthe form factor $f^{f_0}_{+}(0)$ and the $c\to s$ Cabibbo-Kobayashi-Maskawamatrix element $|V_{cs}|$ is determined for the first time to be$f^{f_0}_+(0)|V_{cs}|=0.504\pm0.017_{\rm stat}\pm0.035_{\rm syst}$.

Study of the $f_{0}(980)$ through the decay $D_{s}^{+} \to \pi^{+} \pi^{-} e^{+} \nu_{e}$