Abstract
We study the semi-leptonic and non-leptonic decays of $B_c$ meson to $D$-wave charmonia, namely, $\eta_{c2}(1^1\!D_2)$, $\psi_2(1^3\!D_2)$, and $\psi_3(1^3\!D_3)$. In our calculations, the instantaneous Bethe-Salpeter method is applied to achieve the hadronic matrix elements. This method includes relativistic corrections which are important especially for the higher orbital excited states. For the semi-leptonic decay channels with electron as the final lepton, we get the branching ratios $\mathcal{B}[B_c \rightarrow \eta_{c2}e\bar{\nu}_e] = 5.9^{-0.8}_{+1.0}\times 10^{-4}$, $\mathcal{B}[B_c \rightarrow \psi_2e\bar{\nu}_e]=1.5^{-0.2}_{+0.3}\times 10^{-4}$, and $\mathcal{B}[B_c \rightarrow \psi_3e\bar{\nu}_e]=3.5^{-0.6}_{+0.8}\times 10^{-4}$. The transition form factors, forward-backward asymmetries, and lepton spectra in these processes are also presented. For the non-leptonic decay channels, those with $\rho$ as the lighter meson have the largest branching ratios, $\mathcal{B}[B_c \rightarrow \eta_{c2}\rho] = 8.1^{-1.0}_{+1.0}\times 10^{-4}$, $\mathcal{B}[B_c \rightarrow \psi_2\rho]=9.6^{-1.0}_{+1.0}\times 10^{-5}$, and $\mathcal{B}[B_c \rightarrow \psi_3\rho]=4.1^{-0.7}_{+0.8}\times 10^{-4}$.
Highlights
IntroductionIn 2013, the Belle Collaboration reported the evidence of a new resonance X (3823) in the B decay channel B± → X (→ χc1γ )K ± with a statistical significance of 3.8σ [1]
We study the semileptonic and nonleptonic decays of Bc meson to D-wave charmonia, namely, ηc2(11D2), ψ2(13D2), and ψ3(13D3)
In 2013, the Belle Collaboration reported the evidence of a new resonance X (3823) in the B decay channel B± → X (→ χc1γ )K ± with a statistical significance of 3.8σ [1]
Summary
In 2013, the Belle Collaboration reported the evidence of a new resonance X (3823) in the B decay channel B± → X (→ χc1γ )K ± with a statistical significance of 3.8σ [1]. The BESIII Collaboration verified its existence with a statistical significance of 6.2σ [2] Both groups got a similar mass and ratio of the partial decay widths for this particle. We will use the Bethe–Salpeter (BS) method to investigate the exclusive semileptonic and nonleptonic decays of the Bc meson to the D-wave charmonium This method has been used to study processes with P-wave charmonium [24,28].
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