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We investigate the semileptonic decays of B and D mesons into $\pi$ and$\rho$ mesons, respectively, by means of QCD sum rules. We find that for thevector formfactors involved the pole dominance hypothesis is valid to goodaccuracy with pole masses in the expected range. Pole dominance, however, doesnot apply to the axial formfactors which results in specific predictions forthe predominant polarization of the $\rho$ meson and the shape of the leptonspectrum. For the total decay rates we find $\Gamma (\bar B^0 \to \pi^+ e^-\bar\nu) = (5.1\pm 1.1)\,|V_{ub}|^2\, 10^{12}\,{\rm s^{-1}}$, $\Gamma ( D^0 \to\pi^- e^+ \nu) = (8.0\pm 1.7)\,|V_{cd}|^2\, 10^{10}\,{\rm s^{-1}}$, $\Gamma(\bar B^0 \to \rho^+ e^- \bar\nu) = (1.2\pm 0.4\,)\,|V_{ub}|^2\, 10^{13}\,{\rms^{-1}}$ and $\Gamma (D^0 \to \rho^- e^+\nu) = (2.4\pm 0.7)\,|V_{cd}|^2\,10^{9}\,{\rm s^{-1}}$.Comment: 23 pages, 12 figures included as uu-encoded file, needs REVTEX,  TUM--T31--39/9

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:mi>D</mml:mi><mml:mo>→</mml:mo><mml:mi>π</mml:mi><mml:mo>(</mml:mo><mml:mi>ρ</mml:mi><mml:mo>)</mml:mo><mml:mi>e</mml:mi><mml:mi>ν</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo>→</mml:mo><mml:mi>π</mml:mi><mml:mo>(</mml:mo><mml:mi>ρ</mml:mi><mml:mo>)</mml:mo><mml:mi>e</mml:mi><mml:mi>ν</mml:mi></mml:math>from QCD sum rules

Semileptonic decaysD→π(ρ)eνandB→π(ρ)eνfrom QCD sum rules