D-wave charmonia ηc2(¹¹D2) , ψ2(¹³D2) , and ψ3(¹³D3) in B_cdecays

We study the semileptonic and nonleptonic decays of B_cmeson to D-wave charmonia, namely, ηc2(11D2), ψ2(13D2), and ψ3(13D3). In our calculations, the instantaneous Bethe–Salpeter method is applied to obtain the hadronic matrix elements. This method includes relativistic corrections which are important especially for the higher orbital excited states. For the semileptonic decay channels with electron as the final lepton, we get the branching ratios B[Bc→ηc2eν¯e]=5.9+1.0-0.8×10-4, B[Bc→ψ2eν¯e]=1.5+0.3-0.2×10-4, and B[Bc→ψ3eν¯e]=3.5+0.8-0.6×10-4. The transition form factors, forward–backward asymmetries, and lepton spectra in these processes are also presented. For the nonleptonic decay channels, those with ρ as the lighter meson have the largest branching ratios, B[Bc→ηc2ρ]=8.1+1.0-1.0×10-4, B[Bc→ψ2ρ]=9.6+1.0-1.0×10-5, and B[Bc→ψ3ρ]=4.1+0.8-0.7×10-4.