Search for the decay $D_s^+rightarrow gamma e^+ u_e$

A search for the rare radiative leptonic decay $D_s^+togamma e^+ u_e$ is performed for the first time using electron-positron collision data corresponding to an integrated luminosity of 3.19 fb$^{-1}$, collected with the BESIII detector at a center-of-mass energy of 4.178 GeV. No evidence for the $D_s^+togamma e^+ u_e$ decay is seen and an upper limit of $mathcal B(D_s^+togamma e^+ u_e)<1.3times 10^{-4}$ is set on the partial branching fraction at a 90% confidence level for radiative photon energies $E_{gamma}^*>0.01$~GeV.