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

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 $D_s^+to a_0(980)^0 e^+ u_e,,a_0(980)^0rightarrow pi^0eta$, 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 $D_{s}^{+}to a_0(980)^0 e^+ u_e$ and $a_0(980)^0rightarrow pi^0eta$ decays.