The semileptonic B→π l^+ ν_l decay is studied starting from a simple quark model which includes the influence of the B^* pole. To extend the predictions of a nonrelativistic constituent quark model from its region of applicability near q^2_ max=(m_B-m_π)^2 to all q^2 values accessible in the physical decay, we use a novel multiply-subtracted Omnès dispersion relation, which considerably diminishes the form factor dependence on the elastic π B →π B scattering amplitudes at high energies. By

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... rison to the experimental branching fraction we extract |V_ub| = 0.0034 ± 0.0003 ( exp) ± 0.0007 ( theory). To further test our framework, we also study D→π and D→ K decays and find excellent results f^+_π(0)/f^+_K(0) = 0.80 ± 0.03, B(D^0→π^- e^+ ν_e)/ B(D^0→ K^- e^+ ν_e)= 0.079 ± 0.008. In particular for the D→π case, we reproduce, with high accuracy, the three-flavor lattice QCD results recently obtained by the Fermilab-MILC-HPQCD Collaboration. While for the D→ K case, we successfully describe the data for f^+(q^2)/f^+(0) recently measured by the FOCUS Collaboration.