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We present a lattice QCD calculation of the form factors and differentialdecay rates for semileptonic decays of the heavy-light mesons $B$ and $D$ tothe final state $\pi l\nu$. The results are obtained with three methodologicalimprovements over previous lattice calculations: a matching procedure thatreduces heavy-quark lattice artifacts, the first study of lattice-spacingdependence, and the introduction of kinematic cuts to reduce model dependence.We show that the main systematics are controllable (within the quenchedapproximation) and outline how the calculations could be improved to aidcurrent experiments in the determination of~$|V_{ub}|$ and~$|V_{cd}|$.Comment: 35 pp, 12 fig

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Semileptonic decays<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mo>→</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mi>π</mml:mi><mml:mi>l</mml:mi><mml:mi>ν</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mo>→</mml:mo></mml:mrow></mml:mover…

Semileptonic decaysB→πlνandD→