Form factors for the processes Bc+→D0ℓ+νℓ and Bc+→Ds+ℓ+ℓ-(νν¯) from lattice QCD

Abstract

We present results of the first lattice QCD calculations of the weak matrix elements for the decays Bc+→D0ℓ+νℓ, Bc+→Ds+ℓ+ℓ- 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 flavors 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+→D0ℓ+νℓ is similar in size to that from the present value for Vub. We obtain the ratio Γ(Bc+→D0μ+νμ)/|ηEWVub|2=4.43(63)×1012 s-1. Combining our form factors with those found previously by HPQCD for Bc+→J/ψμ+νμ, we find |Vcb/Vub|2Γ(Bc+→D0μ+νμ)/Γ(Bc+→J/ψμ+νμ)=0.257(36)Bc→D(18)Bc→J/ψ. We calculate the differential decay widths of Bc+→Ds+ℓ+ℓ- 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/ψμ+νμ is 6.31(90)Bc→Ds(65)Bc→J/ψ×10-6. We also give results for the branching fraction of Bc+→Ds+νν¯. Prospects for reducing our errors in the future are discussed.