Decays of $B$, $B_s$ and $B_c$ to $D$-wave heavy-light mesons (1607.07167v3)

Abstract: We study the weak decays of $\bar{B}{(s)}$ and $B_c$ into $D$-wave heavy-light mesons, including $J^P=2^-$ ($D{(s)2},D'{(s)2},B{(s)2}, B'{(s)2}$) and $3^-$~($D^*{(s)3}, B^*_{(s)3}$) states. The weak decay hadronic matrix elements are achieved based on the instantaneous Bethe-Salpeter method. The branching ratios for $\bar{B}$ decays are $\mathcal{B}[\bar{B}\to D_{2}e\bar{\nu}e] = 1.1^{-0.3}{+0.3} \times 10^{-3}$, $\mathcal{B}[\bar{B}\to D'2e\bar{\nu}_e]=4.1^{-0.8}{+0.9} \times 10^{-4}$, and $\mathcal{B}[\bar{B}\to D^*3e\bar{\nu}_e]=1.0^{-0.2}{+0.2} \times 10^{-3}$, respectively. For semi-electronic decays of $\bar B_s$ to $D_{s2}$, $D'{s2}$, and $D^*{s3}$, the corresponding branching ratios are $1.7^{-0.5}_{+0.5}\times 10^{-3}$, $5.2^{-1.5}_{+1.6}\times 10^{-4}$, and $1.5^{-0.4}_{+0.4}\times 10^{-3}$, respectively. The branching ratios of semi-electronic decays of $B_c$ to $D$-wave $D$ mesons are in the order of $10^{-5}$. We also achieved the forward-backward asymmetry, angular spectra, and lepton momentum spectra. In particular the distribution of decay widths for $2^-$ states $D_2$ and $D'_2$ varying along with mixing angle are presented.