Speaker
Description
We present HPQCD’s results of the first lattice QCD calculation of the weak matrix elements for $B_c^+ \to D^0 \ell^+ \nu_{\ell}$ facilitated by a $b \to u$ transition. Together with observation of this process from LHCb, our form factors will lead to a new determination of $V_{ub}$. In tandem, we also calculate the form factors for rare $B_c^+ \to D_s^+ \ell^+ \ell^-$. Results are derived from correlation functions computed on MILC Collaboration gauge configurations with three different lattice spacings including 2+1+1 flavours of dynamical sea quarks in the Highly Improved Staggered Quark (HISQ) formalism. HISQ is also used for all of the valence quarks. We cover the full range of $q^2$. The uncertainty on the branching fractions $\mathcal{B}(B_c^+ \to D^0 \ell^+ \nu_{\ell})$ from the error on our form factors is roughly twice as large as the contribution from the uncertainty on the present PDG value for $V_{ub}$. Prospects for reducing errors on our form factors are discussed which will guide future calculations, setting out the path towards highly precise determinations of the form factors.
