Form factors for the decay processes $B_c^+ \to D^0 \ell^+ \nu_{\ell}$ and $B_c^+ \to D_s^+ \ell^+ \ell^-$ from lattice QCD

We present results of the first lattice QCD calculations of the weak matrix elements for the decays Bc → D`ν`, Bc → Ds `+`− and Bc → Ds νν . Form factors across the entire physical q2 range are then extracted and extrapolated to the continuum limit with physical quark masses. Results are derived from correlation functions computed on MILC collaboration gauge configurations with three different lattice spacings and including 2+1+1 flavours of sea quarks in the Highly Improved Staggered Quark (HISQ) formalism. HISQ is also used for all of the valence quarks. The uncertainty on the decay widths from our form factors for Bc → D`ν` is similar in size to that from the present value for Vub. We obtain the ratio Γ(Bc → Dμνμ)/ |ηEWVub| = 4.43(63)× 1012 s−1. Combining our form factors with those found previously by HPQCD for Bc → J/ψμνμ , we find |Vcb/Vub| Γ(Bc → Dμνμ)/Γ(Bc → J/ψμνμ) = 0.257(36)Bc→D(18)Bc→J/ψ . We calculate the differential decay widths of Bc →Ds `+`− across the full q2 range, and give integrated results in q2 bins that avoid possible effects from charmonium and uu resonances. For example, we find that the ratio of differential branching fractions integrated over the range q2 = 1 GeV2−6 GeV2 for Bc →Ds μ+μ− and Bc → J/ψμνμ is 6.31(90)Bc→Ds(65)Bc→J/ψ×10. We also give results for the branching fraction of Bc → Ds νν .