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Using 6.32 fb$^{-1}$ of electron-positron collision data recorded by theBESIII detector at center-of-mass energies between 4.178 and 4.226~GeV, wepresent the first search for the decay $D_s^+\to a_0(980)^0e^+\nu_e,\,a_0(980)^0\rightarrow \pi^0\eta$, which could proceed via$a_0(980)$-$f_0(980)$ mixing. No significant signal is observed. An upper limitof $1.2 \times 10^{-4}$ at the $90\%$ confidence level is set on the product ofthe branching fractions of $D_{s}^{+}\to a_0(980)^0 e^+\nu_e$ and$a_0(980)^0\rightarrow \pi^0\eta$ decays.

Search for the decay $D_s^+\to a_0(980)^0e^+\nu_e$