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

Using $6.32\text{}\text{}{\mathrm{fb}}^{-1}$ of ${e}^{+}{e}^{-}$ collision data recorded by the BESIII detector at center-of-mass energies between 4.178 to 4.226 GeV, we present the first measurement of the decay ${D}_{s}^{+}\to {f}_{0}\left(980\right){e}^{+}{\nu }_{e},\phantom{\rule{0ex}{0ex}}{f}_{0}\left(980\right)\to {\pi }^{0}{\pi }^{0}$. The product branching fraction of ${D}_{s}^{+}\to {f}_{0}\left(980\right){e}^{+}{\nu }_{e},{f}_{0}\left(980\right)\to {\pi }^{0}{\pi }^{0}$ is measured to be $\left(7.9±1.{4}_{\mathrm{stat}}±0.{4}_{\mathrm{syst}}\right)×{10}^{-4}$, with a statistical significance of $7.8\sigma $. Furthermore, the upper limits on the product branching fractions of ${D}_{s}^{+}\to {f}_{0}\left(500\right){e}^{+}{\nu }_{e}$ with ${f}_{0}\left(500\right)\to {\pi }^{0}{\pi }^{0}$ and the branching fraction of ${D}_{s}^{+}\to {K}_{S}^{0}{K}_{S}^{0}{e}^{+}{\nu }_{e}$ are set to be $7.3×{10}^{-4}$ and $3.8×{10}^{-4}$ at 90% confidence level, respectively. Our results provide valuable inputs to the understanding of the structures of light scalar mesons.