Measurements of the absolute branching fractions for   $D_{s}^{+}\rightarrow\eta e^{+}\nu_{e}$ and   $D_{s}^{+}\rightarrow\eta^{\prime} e^{+}\nu_{e}$
  By analyzing 482 pb$^{-1}$ of $e^+e^-$ collision data collected at $\sqrt s=4.009$ GeV with the BESIII detector at the BEPCII collider, we measure the absolute branching fractions for the semileptonic decays $D_{s}^{+}\to\eta e^{+}\nu_{e}$ and $D_{s}^{+}\to \eta'e^{+}\nu_{e}$ to be ${B}(D_{s}^{+}\rightarrow\eta e^{+}\nu_{e})=(2.30\pm0.31\pm0.08)$\% and ${B}(D_{s}^{+}\rightarrow\eta'e^{+} \nu_{e}) = (0.93\pm0.30\pm0.05)$\%, respectively, and their ratio $\frac{{B}(D_{s}^{+}\rightarrow\eta'e^{+}\nu_{e})} {{B}(D_{s}^{+}\rightarrow\eta e^{+}\nu_{e})}=0.40\pm0.14\pm0.02$, where the first uncertainties are statistical and the second ones are systematic. The results are in good agreement with previous measurements within uncertainties; they can be used to determine the $\eta-\eta'$ mixing angle and improve upon the $D_s^+$ semileptonic branching ratio precision. 
M. Ablikim, M. N. Achasov, X. C. Ai, O. Albayrak, M. Albrecht, D. J.   Ambrose, A. Amoroso, F. F. An, Q. An, J. Z. Bai, R. B...
hep-ex