  Using $7.33~\mathrm{fb}^{-1}$ of $e^+e^-$ collision data taken with the
BESIII detector at the BEPCII collider, we report the first experimental study
of the purely leptonic decay $D_s^{*+}\to e^+\nu_e$. A signal for the decay
$D_s^{*+}\to e^+\nu_e$ is observed with a statistical significance of
$2.9\sigma$. The branching fraction of ${D_s^{*+}\to e^+\nu_e}$ is measured to
be $(2.1{^{+1.2}_{-0.9}}_{\rm stat.}\pm0.2_{\rm syst.})\times 10^{-5}$,
corresponding to an upper limit of $4.0\times10^{-5}$ at the 90\% confidence
level. Taking the total width of the $D_s^{*+}$~(($0.070\pm0.028$) keV)
predicted by lattice quantum chromodynamics as input, the decay constant of the
$D^{*+}_s$ is determined to be $f_{D_s^{*+}}=(213.6{^{+61.0}_{-45.8}}_{\rm
stat.}\pm43.9_{\rm syst.})$ MeV, corresponding to an upper limit of 353.8 MeV
at the 90\% confidence level.

High Energy Physics - Experiment