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Using 6.32~fb$^{-1}$ of $e^+e^-$ collision data recorded by the BESIIIdetector at center-of-mass energies between $4.178$ to $4.226$~GeV, we presentthe first measurement of the decay $D_s^+\to f_0(980)e^+\nu_e,\,f_0(980)\to\pi^0\pi^0$. The product branching fraction of $D_s^+\tof_0(980)e^+\nu_e,\,f_0(980)\to \pi^0\pi^0$ is measured to be $(7.9\pm1.4_{\rmstat} \pm0.3_{\rm syst})\times 10^{-4}$, with a statistical significance of$7.8\sigma$. Furthermore, the upper limits on the product branching fractionsof $D_s^+\to f_0(500)e^+\nu_e$ with $f_0(500)\to \pi^0\pi^0$ and the branchingfraction of $D_s^+\to K_{S}^{0}K_{S}^{0}e^+\nu_e$ are set to be $6.4\times10^{-4}$ and $3.9\times 10^{-4}$ at 90\% confidence level, respectively. Ourresults provide valuable inputs to the understanding of the structures of lightscalar mesons.

Study of light scalar mesons through $D_s^+ \to \pi^0 \pi^0 e^+ \nu_e$ and $K_S^0 K_S^0 e^+ \nu_e$ decays