Approaches to inclusive semileptonic B$_{(s)}$-meson decays from Lattice QCD

We address the nonperturbative calculation of the inclusive decay rate of semileptonic B$_{(s)}$-meson decays from lattice QCD. Precise Standard-Model predictions are key ingredients in searches for new physics, and this type of computation may eventually provide new insight into the long-standing tension between the inclusive and exclusive determinations of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements |V$_{cb}$| and |V$_{ub}$|. We present results from a pilot lattice computation for B$_{s}$ → X$_{c}$lν$_{l}$, where the initial b quark described by the relativistic-heavy-quark (RHQ) formalism on the lattice and the other valence quarks discretised with domain-wall fermions are simulated approximately at their physical quark masses. We compare two different methods for computing the decay rate from lattice data of Euclidean n-point functions, namely Chebyshev and Backus-Gilbert approaches. We further study how much the ground-state meson dominates the inclusive decay rate and indicate our strategy towards a computation with a more comprehensive systematic error budget.