Observation of $B_s^0\to D_s^{*-}{\pi }^{+}$ and $B_s^0\to D_s^{(*)-}{\rho }^{+}$ and Measurement of the $B_s^0\to D_s^{*-}{\rho }^{+}$ Longitudinal Polarization Fraction

First observations of the $B_s^0\to D_s^{*-}{\pi }^{+}$, $B_s^0\to D_s^{-}{\rho }^{+}$ and $B_s^0\to D_s^{*-}{\rho }^{+}$ decays are reported together with measurements of their branching fractions: $\mathcal{B}(B_s^0\to D_s^{*-}{\pi }^{+})=[{2.4}_{-0.4}^{+0.5}(\mathrm{stat})\pm 0.3(\mathrm{syst})\pm 0.4(f_s)]\times {10}^{-3}$, $\mathcal{B}(B_s^0\to D_s^{-}{\rho }^{+})=[{8.5}_{-1.2}^{+1.3}(\mathrm{stat})\pm 1.1(\mathrm{syst})\pm 1.3(f_s)]\times {10}^{-3}$ and $\mathcal{B}(B_s^0\to D_s^{*-}{\rho }^{+})=[{11.9}_{-2.0}^{+2.2}(\mathrm{stat})\pm 1.7(\mathrm{syst})\pm 1.8(f_s)]\times {10}^{-3}$ ($f_s=N_{B_s^{(*)}{\overline{B}}_s^{(*)}}/N_{b\overline{b}}$). From helicity-angle distributions, we measured the longitudinal polarization fraction in $B_s^0\to D_s^{*-}{\rho }^{+}$ decays to be $f_L(B_s^0\to D_s^{*-}{\rho }^{+})={1.05}_{-0.10}^{+0.08}(\mathrm{stat}{)}_{-0.04}^{+0.03}(\mathrm{syst})$. These results are based on a $23.6{\mathrm{fb}}^{-1}$ data sample collected at the ${\rm Y}(5S)$ resonance with the Belle detector at the KEKB $e^{+}{e}^{-}$ collider.

Figure 1

Left (right): $M_{\mathrm{bc}}$ ($\Delta E$) distributions for the $B_s^0\to D_s^{*-}{\pi }^{+}$ (top) and $B_s^0\to D_s^{-}{\rho }^{+}$ (bottom) candidates with $\Delta E$ ($M_{\mathrm{bc}}$) restricted to the $\pm 2.5\sigma$ $B_s^{*}{\overline{B}}_s^{*}$ signal region. The blue solid curve is the total PDF, while the green (black) dotted curve is the peaking (continuum) background and the red dashed curve is the signal. The errors bars correspond to the Poissonian standard deviation.

Figure 2

Distributions for the $B_s^0\to D_s^{*-}{\rho }^{+}$ candidates. Top: $M_{\mathrm{bc}}$ and $\Delta E$ distributions, as in Fig. 1. Bottom: helicity distributions of the $D_s^{*-}$ (left) and ${\rho }^{+}$ (right) with $M_{\mathrm{bc}}$ and $\Delta E$ restricted to the $B_s^{*}{\overline{B}}_s^{*}$ kinematic region. The components of the total PDF (blue solid line) are shown separately: the black dotted curve is the background and the two red dashed curves are the signal. The large (small) signal shape corresponds to the longitudinal (transverse) component.