Semileptonic B→π decays from an Omnes improved nonrelativistic constituent quark model

The semileptonic B→πl+νl 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 qmax2=(mB-mπ)2 to all q2 values accessible in the physical decay, we use a novel multiply subtracted Omnes dispersion relation, which considerably diminishes the form-factor dependence on the elastic πB→πB scattering amplitudes at high energies. By comparison to the experimental branching fraction we extract |Vub|=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 fπ+(0)/fK+(0)=0.80±0.03, B(D0→π-e+νe)/B(D0→K-e+νe)=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+(q2)/f+(0) recently measured by the FOCUS Collaboration