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

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 the vector form factors involved the pole dominance hypothesis is valid to good accuracy with pole masses in the expected range. Pole dominance, however, does not apply to the axial form factors which results in specific predictions for the predominant polarization of the $\rho$ meson and the shape of the lepton spectrum. For the total decay rates we find $\Gamma ({\overline{B}}^0\to {\pi }^{+}{e}^{-}\overline{\nu })=(5.1\mathrm{}\pm 1.1){\left|V_{\mathrm{ub}}\right|}^2\times {10}^{12}$ ${\mathrm{s}}^{-1\mathrm{}}$, $\Gamma (D^0\to {\pi }^{-}{e}^{+}\nu )=(8.0\mathrm{}\pm 1.7){\left|V_{\mathrm{cd}}\right|}^2\times {10}^{10}$ ${\mathrm{s}}^{-1\mathrm{}}$, $\Gamma ({\overline{B}}^0\to {\rho }^{+}{e}^{-}\overline{\nu })=(1.2\mathrm{}\pm 0.4){\left|V_{\mathrm{ub}}\right|}^2\times {10}^{13}$ ${\mathrm{s}}^{-1\mathrm{}}$ and $\Gamma (D^0\to {\rho }^{-}{e}^{+}\nu )=(2.4\mathrm{}\pm 0.7){\left|V_{\mathrm{cd}}\right|}^2\times {10}^9$ ${\mathrm{s}}^{-1\mathrm{}}$.