Exclusive $D_s$ semileptonic branching fraction measurements

We measure absolute branching fractions for six exclusive $D_s$ semileptonic decays. We use data collected in the CLEO-c detector from $e^+e^-$ annihilations delivered by the Cornell Electron Storage Ring with a center-of-mass energy near 4170 MeV. We find $\mathcal{B}(D_s \to \phi e \nu)~= (2.14 \pm 0.17 \pm 0.09)$%, $\mathcal{B}(D_s \to \eta e \nu)~= (2.28 \pm 0.14 \pm 0.20)$%, and $\mathcal{B}(D_s \to \eta' e \nu)~= (0.68 \pm 0.15 \pm 0.06)$% for the largest modes, where the first uncertainties are statistical and the second are systematic. We also obtain $\mathcal{B}(D_s \to K^0 e \nu)~= (0.39 \pm 0.08 \pm 0.03)$%, $\mathcal{B}(D_s \to K^* e \nu)~= (0.18 \pm 0.04 \pm 0.01)$%, and $\mathcal{B}(D_s \to f_0 e \nu, f_0 \to \pi\pi)~= (0.13 \pm 0.02 \pm 0.01)$% for $f_0$ masses within 60 MeV of 980 MeV. We use our results to determine the $\eta-\eta'$ and $f_0$ mixing angles with $s\bar{s}$, and we combine our results with lattice calculations to estimate $|V_{cs}|$. This measurement improves upon the $D_s$ semileptonic branching ratio precision and provides a new approach for future work that eliminates the $D_s^*$ daughter photon reconstruction.