Observation of $B_s^0\to D_s^{\ast -}{\pi }^{+}$, $B_s^0\to D_s^{(\ast )-}{\rho }^{+}$ and $B_s^0\to D_s^{(\ast )+}{D}_s^{(\ast )-}$ and Estimate of $\mathrm{\Delta }{\mathrm{\Gamma }}_{CP}$ at Belle

The large data sample being recorded with the Belle detector at the $\mathrm{{\rm Y}}$(5S) energy provides a unique opportunity to study the less-well-known $B_s^0$ meson decays. Following our recent measurement of $B_s^0\to D_s^{-}{\pi }^{+}$ in a sample of 23.6 fb${}^{-1}$, we extend the analysis to include decays with photons in the final state. Using the same sample, we report the first observation of three other dominant exclusive $B_s^0$ decays, in the modes $B_s^0\to D_s^{\ast -}{\pi }^{+}$, $B_s^{0}\to D_s^{-}\rho^+$and$B_s^{0}\to D_s^{*-}\rho^+$. We measure their respective branching fractions and, using helicity-angle distributions, the longitudinal polarization fraction of the $B_s^0\to D_s^{\ast -}{\rho }^{+}$ decay. We also present a measurement of the branching fractions for the decays $B_s^0\to D_s^{(\ast )+}{D}_s^{(\ast )-}$. In the heavy quark limit, this branching fraction is directly related to the width difference between the $B_s$ CP-even and CP-odd eigenstates.