We develop a method to compute inclusive semi-leptonic decay rate of hadrons fully non-perturbatively using lattice QCD simulations. The sum over all possible final states is achieved by a calculation of the forward-scattering matrix elements on the lattice, and the phase-space integral is evaluated using their dependence on the time separation between two inserted currents. We perform a pilot lattice computation for the B_s -> X_c l nu decay with an unphysical bottom quark mass and compare the results with the corresponding OPE calculation. The method to treat the inclusive processes on the lattice can be applied to other processes, such as the lepton-nucleon inelastic scattering.
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