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

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