We calculate, in the continuum limit of quenched lattice QCD, the matrix elements of the heavy-heavy vector current between heavy-light pseudoscalar meson states. We present the form factors for different values of the initial and final meson masses at finite momentum transfer. In particular, we calculate the non-perturbative correction to the differential decay rate of the process B --> D l nu including the case of a non-vanishing lepton mass.
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