Measurement of theB0→D*−Ds*+andDs+→ϕπ+branching fractions

We present measurements of the branching fractions $\mathcal{B}(B^0\to D^{*-}{D}_s^{*+})$ and $\mathcal{B}(D_s^{+}\to \varphi {\pi }^{+})$, based on $123\times {10}^6{\rm Y}(4S)\to B\overline{B}$ decays collected by the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}B$ factory. A partial reconstruction technique is used to measure $\mathcal{B}(B^0\to D^{*-}{D}_s^{*+})$ and the decay chain is fully reconstructed to measure the branching fraction product $\mathcal{B}(B^0\to D^{*-}{D}_s^{*+})\times \mathcal{B}(D_s^{+}\to \varphi {\pi }^{+})$. Comparing these two measurements provides a model-independent determination of the $D_s^{+}\to \varphi {\pi }^{+}$ branching fraction. We obtain $\mathcal{B}(B^0\to D^{*-}{D}_s^{*+})=(1.88\pm 0.09\pm 0.17)\%$ and $\mathcal{B}(D_s^{+}\to \varphi {\pi }^{+})=(4.81\pm 0.52\pm 0.38)\%$, where the first uncertainties are statistical and the second systematic.