The charm semileptonic decays $D^{+}\to \eta e^{+}{\nu }_e$ and $D^{+}\to {\eta }^{\prime }{e}^{+}{\nu }_e$ are studied with a sample of $e^{+}{e}^{-}$ collision data corresponding to an integrated luminosity of $2.93{\mathrm{fb}}^{-1}$ collected at $\sqrt{s}=3.773\mathrm{GeV}$ with the BESIII detector. We measure the branching fractions for $D^{+}\to \eta e^{+}{\nu }_e$ to be $(10.74\pm 0.81\pm 0.51)\times {10}^{-4}$, and for $D^{+}\to {\eta }^{\prime }{e}^{+}{\nu }_e$ to be $(1.91\pm 0.51\pm 0.13)\times {10}^{-4}$, where the uncertainties are statistical and systematic, respectively. In addition, we perform a measurement of the form factor in the decay $D^{+}\to \eta e^{+}{\nu }_e$. All the results are consistent with those obtained by the CLEO-c experiment.

• Received 15 March 2018

DOI:https://doi.org/10.1103/PhysRevD.97.092009