Measurements of the absolute branching fractions for $D_{s}^{+}\rightarrow\eta e^{+}\nu_{e}$ and $D_{s}^{+}\rightarrow\eta^{\prime} e^{+}\nu_{e}$

TL;DR

This paper measures the absolute branching fractions of specific semileptonic decays of the $D_s^+$ meson using BESIII data, providing results consistent with previous measurements and aiding in understanding $ ext{eta-eta'}$ mixing.

Contribution

First precise measurement of the absolute branching fractions for $D_s^+ o ext{eta} e^+ u_e$ and $D_s^+ o ext{eta'} e^+ u_e$ decays using BESIII data.

Findings

Branching fraction for $D_s^+ o ext{eta} e^+ u_e$ is (2.30 ± 0.31 ± 0.08)%

Branching fraction for $D_s^+ o ext{eta'} e^+ u_e$ is (0.93 ± 0.30 ± 0.05)%

Ratio of branching fractions is 0.40 ± 0.14 ± 0.02

Abstract

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.