Decays of $B$, $B_s$ and $B_c$ to $D$-wave heavy-light mesons

Abstract

We study the weak decays of ${\bar{B}}_{(s)}$ and $B_c$ into $D$-wave heavy-light mesons, including $J^P=2^{-}$ ($D_{(s)2},D_{(s)2}^{\prime },B_{(s)2},B_{(s)2}^{\prime }$) and $3^{-}$~($D_{(s)3}^{\ast },B_{(s)3}^{\ast }$) states. The weak decay hadronic matrix elements are achieved based on the instantaneous Bethe-Salpeter method. The branching ratios for $\bar{B}$ decays are $\mathcal{B}[\bar{B}\to D_{2}e{\bar{\nu }}_e]=1.1_{+0.3}^{-0.3}\times 10^{-3}$, $\mathcal{B}[\bar{B}\to D_2^{\prime }e{\bar{\nu }}_e]=4.1_{+0.9}^{-0.8}\times 10^{-4}$, and $\mathcal{B}[\bar{B}\to D_3^{\ast }e{\bar{\nu }}_e]=1.0_{+0.2}^{-0.2}\times 10^{-3}$, respectively. For semi-electronic decays of ${\bar{B}}_s$ to $D_{s2}$, $D_{s2}^{\prime }$, and $D_{s3}^{\ast }$, the corresponding branching ratios are $1.7_{+0.5}^{-0.5}\times 10^{-3}$, $5.2_{+1.6}^{-1.5}\times 10^{-4}$, 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 $D_2^{\prime }$ varying along with mixing angle are presented.

20 pages, 20 figures, 7 tables