Bc → J / ψ form factors for the full q2 range from lattice QCD

We present the first lattice QCD determination of the Bc → J/ψ vector and axial-vector form factors. These will enable experimental information on the rate for Bc semileptonic decays to J/ψ to be converted into a value for Vcb. Our calculation covers the full physical q2 range of the decay and uses nonperturbatively renormalized lattice currents. We use the highly improved staggered quark (HISQ) action for all valence quarks on the second generation MILC ensembles of gluon field configurations including u, d, s and c HISQ sea quarks. Our HISQ heavy quarks have masses ranging upwards from that of c; we are able to reach that of the b on our finest lattices. This enables us to map out the dependence on heavy quark mass and determine results in the continuum limit at the b . We use our form factors to construct the differential rates for Bc → J/ψμ− νμ and obtain a total rate with 7% uncertainty: Γ ( Bc → J/ψμ− νμ ) / |ηEW Vcb |2 = 1.73 ( 12 ) × 1013 s−1. Including values for V c b , η EW and τ B c yields a branching fraction for this decay mode of 0.0150(11)(10)(3) with uncertainties from lattice QCD, ηEWVcb and τBc respectively.