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

TL;DR

This paper investigates the weak decays of B, Bs, and Bc mesons into D-wave heavy-light mesons using the Bethe-Salpeter method, providing decay rates, asymmetries, and spectra relevant for experimental detection.

Contribution

It introduces a comprehensive calculation of decay properties of D-wave heavy-light mesons from B, Bs, and Bc decays, including mixing effects and detailed spectra, using the instantaneous Bethe-Salpeter approach.

Findings

Branching ratios for B decays to D-wave mesons are on the order of 10^{-3} to 10^{-4}.

Branching ratios for Bs decays are around 10^{-3}.

B_c decays to D-wave mesons have branching ratios near 10^{-5}.

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.