Measurement of the $D_s^{+}\to \eta {\ell }^{+}\nu$ and $D_s^{+}\to {\eta }^{\prime }{\ell }^{+}\nu$ Branching Ratios

Using the CLEO II detector we measure $\frac{\mathcal{B}(D_s^{+}\to \eta e^{+}\nu )}{\mathcal{B}(D_s^{+}\to \phi e^{+}\nu )}=1.24\mathrm{}\pm 0.12\pm 0.15$, $\frac{\mathcal{B}(D_s^{+}\to {\eta }^{\prime }{e}^{+}\nu )}{\mathcal{B}(D_s^{+}\to \phi e^{+}\nu )}=0.43\mathrm{}\pm 0.11\pm 0.07$, and $\frac{\mathcal{B}(D_s^{+}\to {\eta }^{\prime }{e}^{+}\nu )}{\mathcal{B}(D_s^{+}\to \eta e^{+}\nu )}=0.35\mathrm{}\pm 0.09\pm 0.07$. We find the ratio of vector to pseudoscalar final states, $\frac{\mathcal{B}(D_s^{+}\to \phi e^{+}\nu )}{\mathcal{B}(D_s^{+}\to (\eta +{\eta }^{\prime }\left)e^{+}\nu \right)}=0.60\mathrm{}\pm 0.06\pm 0.06$, which is similar to the ratio found in nonstrange $D$ decays.