Measurement of the branching fractions of the rare decays B0→Ds(*)+π− , B0→Ds(*)+ρ− , and B0→Ds(*)−K(*)+

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We report the measurement of the branching fractions of the rare decays ${B}^{0}\ensuremath{\rightarrow}{D}_{s}^{(*)+}{\ensuremath{\pi}}^{\ensuremath{-}}$, ${B}^{0}\ensuremath{\rightarrow}{D}_{s}^{(*)+}{\ensuremath{\rho}}^{\ensuremath{-}}$, and ${B}^{0}\ensuremath{\rightarrow}{D}_{s}^{(*)\ensuremath{-}}{K}^{(*)+}$ in a sample of $381\ifmmode\times\else\texttimes\fi{}{10}^{6}\mathit{\ensuremath{\Upsilon}}(4S)$ decays into $B\overline{B}$ pairs collected with the BABAR detector at the PEP-II asymmetric-energy ${e}^{+}{e}^{\ensuremath{-}}$ storage ring. We present evidence for the decay ${B}^{0}\ensuremath{\rightarrow}{D}_{s}^{\ensuremath{-}}{K}^{*+}$ and the vector-vector decays ${B}^{0}\ensuremath{\rightarrow}{D}_{s}^{*+}{\ensuremath{\rho}}^{\ensuremath{-}}$ and ${B}^{0}\ensuremath{\rightarrow}{D}_{s}^{*\ensuremath{-}}{K}^{*+}$, as well as the first measurement of the vector meson polarization in these decays. We also determine the ratios of the CKM-suppressed to CKM-favored amplitudes $r({D}^{(*)}\ensuremath{\pi})$ and $r({D}^{(*)}\ensuremath{\rho})$ in decays ${B}^{0}\ensuremath{\rightarrow}{D}^{(*)\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\pi}}^{\ensuremath{\mp}}$ and ${B}^{0}\ensuremath{\rightarrow}{D}^{(*)\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\rho}}^{\ensuremath{\mp}}$, and comment on the prospects for measuring the $CP$ observable $\mathrm{sin}(2\ensuremath{\beta}+\ensuremath{\gamma})$.

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