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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 $\mathcal{B}(D_s \to ϕe ν)~= (2.14 \pm 0.17 \pm 0.09)$%, $\mathcal{B}(D_s \to ηe ν)~= (2.28 \pm 0.14 \pm 0.20)$%, and $\mathcal{B}(D_s \to η' e ν)~= (0.68 \pm 0.15 \pm 0.06)$% for the largest modes, where the first uncertainties are statistical and the second are systematic. We also obtain $\mathcal{B}(D_s \to K^0 e ν)~= (0.39 \pm 0.08 \pm 0.03)$%, $\mathcal{B}(D_s \to K^* e ν)~= (0.18 \pm 0.04 \pm 0.01)$%, and $\mathcal{B}(D_s \to f_0 e ν, f_0 \to ππ)~= (0.13 \pm 0.02 \pm 0.01)$% for $f_0$ masses within 60 MeV of 980 MeV. We use our results to determine the $η-η'$ 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.