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.
Categories: hep-ex