Semileptonic $B_c$ decays from full lattice QCD

We present first lattice QCD results for semileptonic form factors for the decays $B_c \to \eta_c l \nu$ and $B_c \to J/\psi l \nu$ over the full $q^2$ range, using both improved non-relativistic QCD (NRQCD) and fully relativistic (HISQ) formalisms. These can be viewed as prototype calculations for pseudoscalar to pseudoscalar and pseudoscalar to vector decays involving a $b \to c$ transition. In particular we can use information from the relativistic computations to fix the NRQCD current normalisations, which can then be used in improved computations of decays such as $B \to D l \nu$ and $B \to D^* l \nu$.