Decays of

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 obtained based on the instantaneous Bethe–Salpeter method. The branching ratios for the $$\bar{B}$$ decays are $$\mathcal {B}[\bar{B}\rightarrow D_{2}e{\bar{\nu }}_e] = 1.1^{-0.3}_{+0.3} \times 10^{-3}$$, $$\mathcal {B}[\bar{B}\rightarrow D'_2e{\bar{\nu }}_e]=4.1^{-0.8}_{+0.9} \times 10^{-4}$$, and $$\mathcal {B}[\bar{B}\rightarrow D^*_3e{\bar{\nu }}_e]=1.0^{-0.2}_{+0.2} \times 10^{-3}$$, respectively. For the 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 the semi-electronic decays of $$B_c$$ to D-wave D mesons are in the order of $$10^{-5}$$. We also obtained the forward–backward asymmetry, angular spectra, and lepton momentum spectra. In particular the distribution of decay widths for the $$2^-$$ states $$D_2$$ and $$D'_2$$ varying along with mixing angle are presented